From d34f3ca7fa84f42673f3556565b1776d3009e6a6 Mon Sep 17 00:00:00 2001 From: Atsushi Sakai Date: Sun, 21 Nov 2021 22:39:18 +0900 Subject: [PATCH] clean up SLAM docs (#572) * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs --- .../lidar_to_grid_map_tutorial.ipynb | 318 --- SLAM/EKFSLAM/ekf_slam.ipynb | 1784 ----------------- SLAM/FastSLAM1/FastSLAM1.ipynb | 676 ------- SLAM/FastSLAM1/animation.png | Bin 44443 -> 0 bytes SLAM/GraphBasedSLAM/LaTeX/.gitignore | 3 - SLAM/GraphBasedSLAM/LaTeX/graphSLAM.bib | 30 - .../LaTeX/graphSLAM_formulation.tex | 175 -- .../graphSLAM_SE2_example.ipynb | 332 --- SLAM/GraphBasedSLAM/graphSLAM_formulation.pdf | Bin 276368 -> 0 bytes docs/_static/custom.css | 23 + docs/conf.py | 5 +- ...g_started.rst => getting_started_main.rst} | 0 docs/{index.rst => index_main.rst} | 0 ...igation.rst => aerial_navigation_main.rst} | 0 .../{appendix.rst => appendix_main.rst} | 0 ...navigation.rst => arm_navigation_main.rst} | 0 ...introduction.rst => introduction_main.rst} | 0 ...localization.rst => localization_main.rst} | 0 .../mapping/{mapping.rst => mapping_main.rst} | 0 ...th_planning.rst => path_planning_main.rst} | 0 ...th_tracking.rst => path_tracking_main.rst} | 0 docs/modules/slam/FastSLAM1.rst | 17 +- docs/modules/slam/ekf_slam.rst | 593 ++++++ .../slam/ekf_slam_files/ekf_slam_1_0.png | Bin docs/modules/slam/graphSLAM_SE2_example.rst | 209 ++ .../Graph_SLAM_optimization.gif | Bin .../graphSLAM_SE2_example_13_0.png | Bin 0 -> 32748 bytes .../graphSLAM_SE2_example_15_0.png | Bin 0 -> 30123 bytes .../graphSLAM_SE2_example_16_0.png | Bin 0 -> 29350 bytes .../graphSLAM_SE2_example_4_0.png | Bin 0 -> 52368 bytes .../graphSLAM_SE2_example_8_0.png | Bin 0 -> 31076 bytes .../graphSLAM_SE2_example_9_0.png | Bin 0 -> 49650 bytes docs/modules/slam/graphSLAM_doc.rst | 557 +++++ docs/modules/slam/graphSLAM_formulation.rst | 216 ++ docs/modules/slam/{slam.rst => slam_main.rst} | 34 +- 35 files changed, 1617 insertions(+), 3355 deletions(-) delete mode 100644 Mapping/lidar_to_grid_map/lidar_to_grid_map_tutorial.ipynb delete mode 100644 SLAM/EKFSLAM/ekf_slam.ipynb delete mode 100644 SLAM/FastSLAM1/FastSLAM1.ipynb delete mode 100644 SLAM/FastSLAM1/animation.png delete mode 100644 SLAM/GraphBasedSLAM/LaTeX/.gitignore delete mode 100644 SLAM/GraphBasedSLAM/LaTeX/graphSLAM.bib delete mode 100644 SLAM/GraphBasedSLAM/LaTeX/graphSLAM_formulation.tex delete mode 100644 SLAM/GraphBasedSLAM/graphSLAM_SE2_example.ipynb delete mode 100644 SLAM/GraphBasedSLAM/graphSLAM_formulation.pdf create mode 100644 docs/_static/custom.css rename docs/{getting_started.rst => getting_started_main.rst} (100%) rename docs/{index.rst => index_main.rst} (100%) rename docs/modules/aerial_navigation/{aerial_navigation.rst => aerial_navigation_main.rst} (100%) rename docs/modules/appendix/{appendix.rst => appendix_main.rst} (100%) rename docs/modules/arm_navigation/{arm_navigation.rst => arm_navigation_main.rst} (100%) rename docs/modules/{introduction.rst => introduction_main.rst} (100%) rename docs/modules/localization/{localization.rst => localization_main.rst} (100%) rename docs/modules/mapping/{mapping.rst => mapping_main.rst} (100%) rename docs/modules/path_planning/{path_planning.rst => path_planning_main.rst} (100%) rename docs/modules/path_tracking/{path_tracking.rst => path_tracking_main.rst} (100%) create mode 100644 docs/modules/slam/ekf_slam.rst rename SLAM/EKFSLAM/animation.png => docs/modules/slam/ekf_slam_files/ekf_slam_1_0.png (100%) create mode 100644 docs/modules/slam/graphSLAM_SE2_example.rst rename {SLAM/GraphBasedSLAM/images => docs/modules/slam/graphSLAM_SE2_example_files}/Graph_SLAM_optimization.gif (100%) create mode 100644 docs/modules/slam/graphSLAM_SE2_example_files/graphSLAM_SE2_example_13_0.png create mode 100644 docs/modules/slam/graphSLAM_SE2_example_files/graphSLAM_SE2_example_15_0.png create mode 100644 docs/modules/slam/graphSLAM_SE2_example_files/graphSLAM_SE2_example_16_0.png create mode 100644 docs/modules/slam/graphSLAM_SE2_example_files/graphSLAM_SE2_example_4_0.png create mode 100644 docs/modules/slam/graphSLAM_SE2_example_files/graphSLAM_SE2_example_8_0.png create mode 100644 docs/modules/slam/graphSLAM_SE2_example_files/graphSLAM_SE2_example_9_0.png create mode 100644 docs/modules/slam/graphSLAM_doc.rst create mode 100644 docs/modules/slam/graphSLAM_formulation.rst rename docs/modules/slam/{slam.rst => slam_main.rst} (75%) diff --git a/Mapping/lidar_to_grid_map/lidar_to_grid_map_tutorial.ipynb b/Mapping/lidar_to_grid_map/lidar_to_grid_map_tutorial.ipynb deleted file mode 100644 index 9e8a00f009a..00000000000 --- a/Mapping/lidar_to_grid_map/lidar_to_grid_map_tutorial.ipynb +++ /dev/null @@ -1,318 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## LIDAR to 2D grid map example\n", - "\n", - "This simple tutorial shows how to read LIDAR (range) measurements from a file and convert it to occupancy grid.\n", - "\n", - "Occupancy grid maps (_Hans Moravec, A.E. Elfes: High resolution maps from wide angle sonar, Proc. IEEE Int. Conf. Robotics Autom. (1985)_) are a popular, probabilistic approach to represent the environment. The grid is basically discrete representation of the environment, which shows if a grid cell is occupied or not. Here the map is represented as a `numpy array`, and numbers close to 1 means the cell is occupied (_marked with red on the next image_), numbers close to 0 means they are free (_marked with green_). The grid has the ability to represent unknown (unobserved) areas, which are close to 0.5.\n", - "\n", - "![Example](grid_map_example.png)\n", - "\n", - "\n", - "In order to construct the grid map from the measurement we need to discretise the values. But, first let's need to `import` some necessary packages." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import math\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from math import cos, sin, radians, pi" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The measurement file contains the distances and the corresponding angles in a `csv` (comma separated values) format. Let's write the `file_read` method:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "def file_read(f):\n", - " \"\"\"\n", - " Reading LIDAR laser beams (angles and corresponding distance data)\n", - " \"\"\"\n", - " measures = [line.split(\",\") for line in open(f)]\n", - " angles = []\n", - " distances = []\n", - " for measure in measures:\n", - " angles.append(float(measure[0]))\n", - " distances.append(float(measure[1]))\n", - " angles = np.array(angles)\n", - " distances = np.array(distances)\n", - " return angles, distances" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "From the distances and the angles it is easy to determine the `x` and `y` coordinates with `sin` and `cos`. \n", - "In order to display it `matplotlib.pyplot` (`plt`) is used." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "ang, dist = file_read(\"lidar01.csv\")\n", - "ox = np.sin(ang) * dist\n", - "oy = np.cos(ang) * dist\n", - "plt.figure(figsize=(6,10))\n", - "plt.plot([oy, np.zeros(np.size(oy))], [ox, np.zeros(np.size(oy))], \"ro-\") # lines from 0,0 to the \n", - "plt.axis(\"equal\")\n", - "bottom, top = plt.ylim() # return the current ylim\n", - "plt.ylim((top, bottom)) # rescale y axis, to match the grid orientation\n", - "plt.grid(True)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The `lidar_to_grid_map.py` contains handy functions which can used to convert a 2D range measurement to a grid map. For example the `bresenham` gives the a straight line between two points in a grid map. Let's see how this works." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "import lidar_to_grid_map as lg\n", - "map1 = np.ones((50, 50)) * 0.5\n", - "line = lg.bresenham((2, 2), (40, 30))\n", - "for l in line:\n", - " map1[l[0]][l[1]] = 1\n", - "plt.imshow(map1)\n", - "plt.colorbar()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "line = lg.bresenham((2, 30), (40, 30))\n", - "for l in line:\n", - " map1[l[0]][l[1]] = 1\n", - "line = lg.bresenham((2, 30), (2, 2))\n", - "for l in line:\n", - " map1[l[0]][l[1]] = 1\n", - "plt.imshow(map1)\n", - "plt.colorbar()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To fill empty areas, a queue-based algorithm can be used that can be used on an initialized occupancy map. The center point is given: the algorithm checks for neighbour elements in each iteration, and stops expansion on obstacles and free boundaries." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "from collections import deque\n", - "def flood_fill(cpoint, pmap):\n", - " \"\"\"\n", - " cpoint: starting point (x,y) of fill\n", - " pmap: occupancy map generated from Bresenham ray-tracing\n", - " \"\"\"\n", - " # Fill empty areas with queue method\n", - " sx, sy = pmap.shape\n", - " fringe = deque()\n", - " fringe.appendleft(cpoint)\n", - " while fringe:\n", - " n = fringe.pop()\n", - " nx, ny = n\n", - " # West\n", - " if nx > 0:\n", - " if pmap[nx - 1, ny] == 0.5:\n", - " pmap[nx - 1, ny] = 0.0\n", - " fringe.appendleft((nx - 1, ny))\n", - " # East\n", - " if nx < sx - 1:\n", - " if pmap[nx + 1, ny] == 0.5:\n", - " pmap[nx + 1, ny] = 0.0\n", - " fringe.appendleft((nx + 1, ny))\n", - " # North\n", - " if ny > 0:\n", - " if pmap[nx, ny - 1] == 0.5:\n", - " pmap[nx, ny - 1] = 0.0\n", - " fringe.appendleft((nx, ny - 1))\n", - " # South\n", - " if ny < sy - 1:\n", - " if pmap[nx, ny + 1] == 0.5:\n", - " pmap[nx, ny + 1] = 0.0\n", - " fringe.appendleft((nx, ny + 1))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This algotihm will fill the area bounded by the yellow lines starting from a center point (e.g. (10, 20)) with zeros:" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "flood_fill((10, 20), map1)\n", - "map_float = np.array(map1)/10.0\n", - "plt.imshow(map1)\n", - "plt.colorbar()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's use this flood fill on real data:" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The grid map is 150 x 100 .\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "xyreso = 0.02 # x-y grid resolution\n", - "yawreso = math.radians(3.1) # yaw angle resolution [rad]\n", - "ang, dist = file_read(\"lidar01.csv\")\n", - "ox = np.sin(ang) * dist\n", - "oy = np.cos(ang) * dist\n", - "pmap, minx, maxx, miny, maxy, xyreso = lg.generate_ray_casting_grid_map(ox, oy, xyreso, False)\n", - "xyres = np.array(pmap).shape\n", - "plt.figure(figsize=(20,8))\n", - "plt.subplot(122)\n", - "plt.imshow(pmap, cmap = \"PiYG_r\") \n", - "plt.clim(-0.4, 1.4)\n", - "plt.gca().set_xticks(np.arange(-.5, xyres[1], 1), minor = True)\n", - "plt.gca().set_yticks(np.arange(-.5, xyres[0], 1), minor = True)\n", - "plt.grid(True, which=\"minor\", color=\"w\", linewidth = .6, alpha = 0.5)\n", - "plt.colorbar()\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/SLAM/EKFSLAM/ekf_slam.ipynb b/SLAM/EKFSLAM/ekf_slam.ipynb deleted file mode 100644 index 7634bfde9ed..00000000000 --- a/SLAM/EKFSLAM/ekf_slam.ipynb +++ /dev/null @@ -1,1784 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# EKF SLAM" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "execution_count": 1, - "metadata": { - "image/png": { - "width": 600 - } - }, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.display import Image\n", - "Image(filename=\"animation.png\",width=600)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Simulation\n", - "\n", - "This is a simulation of EKF SLAM. \n", - "\n", - "- Black stars: landmarks\n", - "- Green crosses: estimates of landmark positions\n", - "- Black line: dead reckoning \n", - "- Blue line: ground truth\n", - "- Red line: EKF SLAM position estimation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Introduction\n", - "\n", - "EKF SLAM models the SLAM problem in a single EKF where the modeled state is both the pose $(x, y, \\theta)$ and \n", - "an array of landmarks $[(x_1, y_1), (x_2, x_y), ... , (x_n, y_n)]$ for $n$ landmarks. The covariance between each of the positions and landmarks are also tracked. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$\\begin{equation}\n", - "X = \\begin{bmatrix} x \\\\ y \\\\ \\theta \\\\ x_1 \\\\ y_1 \\\\ x_2 \\\\ y_2 \\\\ \\dots \\\\ x_n \\\\ y_n \\end{bmatrix}\n", - "\\end{equation}$\n", - "\n", - "$\\begin{equation}\n", - "P = \\begin{bmatrix} \n", - "\\sigma_{xx} & \\sigma_{xy} & \\sigma_{x\\theta} & \\sigma_{xx_1} & \\sigma_{xy_1} & \\sigma_{xx_2} & \\sigma_{xy_2} & \\dots & \\sigma_{xx_n} & \\sigma_{xy_n} \\\\\n", - "\\sigma_{yx} & \\sigma_{yy} & \\sigma_{y\\theta} & \\sigma_{yx_1} & \\sigma_{yy_1} & \\sigma_{yx_2} & \\sigma_{yy_2} & \\dots & \\sigma_{yx_n} & \\sigma_{yy_n} \\\\\n", - " & & & & \\vdots & & & & & \\\\\n", - "\\sigma_{x_nx} & \\sigma_{x_ny} & \\sigma_{x_n\\theta} & \\sigma_{x_nx_1} & \\sigma_{x_ny_1} & \\sigma_{x_nx_2} & \\sigma_{x_ny_2} & \\dots & \\sigma_{x_nx_n} & \\sigma_{x_ny_n}\n", - "\\end{bmatrix}\n", - "\\end{equation}$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A single estimate of the pose is tracked over time, while the confidence in the pose is tracked by the \n", - "covariance matrix $P$. $P$ is a symmetric square matrix whith each element in the matrix corresponding to the \n", - "covariance between two parts of the system. For example, $\\sigma_{xy}$ represents the covariance between the \n", - "belief of $x$ and $y$ and is equal to $\\sigma_{yx}$. \n", - "\n", - "The state can be represented more concisely as follows. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$\\begin{equation}\n", - "X = \\begin{bmatrix} x \\\\ m \\end{bmatrix}\n", - "\\end{equation}$\n", - "$\\begin{equation}\n", - "P = \\begin{bmatrix} \n", - "\\Sigma_{xx} & \\Sigma_{xm}\\\\\n", - "\\Sigma_{mx} & \\Sigma_{mm}\\\\\n", - "\\end{bmatrix}\n", - "\\end{equation}$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here the state simplifies to a combination of pose ($x$) and map ($m$). The covariance matrix becomes easier to \n", - "understand and simply reads as the uncertainty of the robots pose ($\\Sigma_{xx}$), the uncertainty of the \n", - "map ($\\Sigma_{mm}$), and the uncertainty of the robots pose with respect to the map and vice versa \n", - "($\\Sigma_{xm}$, $\\Sigma_{mx}$).\n", - "\n", - "Take care to note the difference between $X$ (state) and $x$ (pose). " - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "\"\"\"\n", - "Extended Kalman Filter SLAM example\n", - "original author: Atsushi Sakai (@Atsushi_twi)\n", - "notebook author: Andrew Tu (drewtu2)\n", - "\"\"\"\n", - "\n", - "import math\n", - "import numpy as np\n", - "%matplotlib notebook\n", - "import matplotlib.pyplot as plt\n", - "\n", - "\n", - "# EKF state covariance\n", - "Cx = np.diag([0.5, 0.5, np.deg2rad(30.0)])**2 # Change in covariance\n", - "\n", - "# Simulation parameter\n", - "Qsim = np.diag([0.2, np.deg2rad(1.0)])**2 # Sensor Noise\n", - "Rsim = np.diag([1.0, np.deg2rad(10.0)])**2 # Process Noise\n", - "\n", - "DT = 0.1 # time tick [s]\n", - "SIM_TIME = 50.0 # simulation time [s]\n", - "MAX_RANGE = 20.0 # maximum observation range\n", - "M_DIST_TH = 2.0 # Threshold of Mahalanobis distance for data association.\n", - "STATE_SIZE = 3 # State size [x,y,yaw]\n", - "LM_SIZE = 2 # LM state size [x,y]\n", - "\n", - "show_animation = True" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Algorithm Walkthrough\n", - "\n", - "At each time step, the following is done. \n", - "- predict the new state using the control functions\n", - "- update the belief in landmark positions based on the estimated state and measurements" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "def ekf_slam(xEst, PEst, u, z):\n", - " \"\"\"\n", - " Performs an iteration of EKF SLAM from the available information. \n", - " \n", - " :param xEst: the belief in last position\n", - " :param PEst: the uncertainty in last position\n", - " :param u: the control function applied to the last position \n", - " :param z: measurements at this step\n", - " :returns: the next estimated position and associated covariance\n", - " \"\"\"\n", - " S = STATE_SIZE\n", - "\n", - " # Predict\n", - " xEst, PEst, G, Fx = predict(xEst, PEst, u)\n", - " initP = np.eye(2)\n", - "\n", - " # Update\n", - " xEst, PEst = update(xEst, PEst, u, z, initP)\n", - "\n", - " return xEst, PEst\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 1- Predict\n", - "**Predict State update:** The following equations describe the predicted motion model of the robot in case we provide only the control $(v,w)$, which are the linear and angular velocity repsectively. \n", - "\n", - "$\\begin{equation*}\n", - "F=\n", - "\\begin{bmatrix}\n", - "1 & 0 & 0 \\\\\n", - "0 & 1 & 0 \\\\\n", - "0 & 0 & 1 \n", - "\\end{bmatrix}\n", - "\\end{equation*}$\n", - "\n", - "$\\begin{equation*}\n", - "B=\n", - "\\begin{bmatrix}\n", - "\\Delta t cos(\\theta) & 0\\\\\n", - "\\Delta t sin(\\theta) & 0\\\\\n", - "0 & \\Delta t\n", - "\\end{bmatrix}\n", - "\\end{equation*}$\n", - "\n", - "$\\begin{equation*}\n", - "U=\n", - "\\begin{bmatrix}\n", - "v_t\\\\\n", - "w_t\\\\\n", - "\\end{bmatrix}\n", - "\\end{equation*}$\n", - "\n", - "$\\begin{equation*}\n", - "X = FX + BU \n", - "\\end{equation*}$\n", - "\n", - "\n", - "$\\begin{equation*}\n", - "\\begin{bmatrix}\n", - "x_{t+1} \\\\\n", - "y_{t+1} \\\\\n", - "\\theta_{t+1}\n", - "\\end{bmatrix}=\n", - "\\begin{bmatrix}\n", - "1 & 0 & 0 \\\\\n", - "0 & 1 & 0 \\\\\n", - "0 & 0 & 1 \n", - "\\end{bmatrix}\\begin{bmatrix}\n", - "x_{t} \\\\\n", - "y_{t} \\\\\n", - "\\theta_{t}\n", - "\\end{bmatrix}+\n", - "\\begin{bmatrix}\n", - "\\Delta t cos(\\theta) & 0\\\\\n", - "\\Delta t sin(\\theta) & 0\\\\\n", - "0 & \\Delta t\n", - "\\end{bmatrix}\n", - "\\begin{bmatrix}\n", - "v_{t} + \\sigma_v\\\\\n", - "w_{t} + \\sigma_w\\\\\n", - "\\end{bmatrix}\n", - "\\end{equation*}$\n", - "\n", - "Notice that while $U$ is only defined by $v_t$ and $w_t$, in the actual calcuations, a $+\\sigma_v$ and \n", - "$+\\sigma_w$ appear. These values represent the error bewteen the given control inputs and the actual control \n", - "inputs. \n", - "\n", - "As a result, the simulation is set up as the following. $R$ represents the process noise which is added to the \n", - "control inputs to simulate noise experienced in the real world. A set of truth values are computed from the raw \n", - "control values while the values dead reckoning values incorporate the error into the estimation. \n", - "\n", - "$\\begin{equation*}\n", - "R=\n", - "\\begin{bmatrix}\n", - "\\sigma_v\\\\\n", - "\\sigma_w\\\\\n", - "\\end{bmatrix}\n", - "\\end{equation*}$\n", - "\n", - "$\\begin{equation*}\n", - "X_{true} = FX + B(U)\n", - "\\end{equation*}$\n", - "\n", - "$\\begin{equation*}\n", - "X_{DR} = FX + B(U + R)\n", - "\\end{equation*}$\n", - "\n", - "The implementation of the motion model prediciton code is shown in `motion_model`. The `observation` function \n", - "shows how the simulation uses (or doesn't use) the process noise `Rsim` to the find the ground truth and dead reckoning estimtates of the pose.\n", - "\n", - "**Predict covariance:** Add the state covariance to the the current uncertainty of the EKF. At each time step, the uncertainty in the system grows by the covariance of the pose, $Cx$. \n", - "\n", - "$\n", - "P = G^TPG + Cx\n", - "$\n", - "\n", - "Notice this uncertainty is only growing with respect to the pose, not the landmarks. " - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "def predict(xEst, PEst, u):\n", - " \"\"\"\n", - " Performs the prediction step of EKF SLAM\n", - " \n", - " :param xEst: nx1 state vector\n", - " :param PEst: nxn covariacne matrix\n", - " :param u: 2x1 control vector\n", - " :returns: predicted state vector, predicted covariance, jacobian of control vector, transition fx\n", - " \"\"\"\n", - " S = STATE_SIZE\n", - " G, Fx = jacob_motion(xEst[0:S], u)\n", - " xEst[0:S] = motion_model(xEst[0:S], u)\n", - " # Fx is an an identity matrix of size (STATE_SIZE)\n", - " # sigma = G*sigma*G.T + Noise\n", - " PEst[0:S, 0:S] = G.T @ PEst[0:S, 0:S] @ G + Fx.T @ Cx @ Fx\n", - " return xEst, PEst, G, Fx" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "def motion_model(x, u):\n", - " \"\"\"\n", - " Computes the motion model based on current state and input function. \n", - " \n", - " :param x: 3x1 pose estimation\n", - " :param u: 2x1 control input [v; w]\n", - " :returns: the resutling state after the control function is applied\n", - " \"\"\"\n", - " F = np.array([[1.0, 0, 0],\n", - " [0, 1.0, 0],\n", - " [0, 0, 1.0]])\n", - "\n", - " B = np.array([[DT * math.cos(x[2, 0]), 0],\n", - " [DT * math.sin(x[2, 0]), 0],\n", - " [0.0, DT]])\n", - "\n", - " x = (F @ x) + (B @ u)\n", - " return x" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 2 - Update\n", - "In the update phase, the observations of nearby landmarks are used to correct the location estimate. \n", - "\n", - "For every landmark observed, it is associated to a particular landmark in the known map. If no landmark exists \n", - "in the position surrounding the landmark, it is taken as a NEW landmark. The distance threshold for how far a \n", - "landmark must be from the next known landmark before its considered to be a new landmark is set by `M_DIST_TH`.\n", - "\n", - "With an observation associated to the appropriate landmark, the **innovation** can be calculated. Innovation \n", - "($y$) is the difference between the observation and the observation that *should* have been made if the \n", - "observation were made from the pose predicted in the predict stage.\n", - "\n", - "$\n", - "y = z_t - h(X)\n", - "$\n", - "\n", - "With the innovation calculated, the question becomes which to trust more - the observations or the predictions? \n", - "To determine this, we calculate the Kalman Gain - a percent of how much of the innovation to add to the \n", - "prediction based on the uncertainty in the predict step and the update step. \n", - "\n", - "$\n", - "K = \\bar{P_t}H_t^T(H_t\\bar{P_t}H_t^T + Q_t)^{-1}\n", - "$\n", - "In these equations, $H$ is the jacobian of the measurement function. The multiplications by $H^T$ and $H$ \n", - "represent the application of the delta to the measurement covariance. \n", - "Intuitively, this equation is applying the following from the single variate Kalman equation but in the \n", - "multivariate form, i.e. finding the ratio of the uncertianty of the process compared the measurment. \n", - "\n", - "$\n", - "K = \\frac{\\bar{P_t}}{\\bar{P_t} + Q_t}\n", - "$\n", - "\n", - "If $Q_t << \\bar{P_t}$, (i.e. the measurement covariance is low relative to the current estimate), then the \n", - "Kalman gain will be $~1$. This results in adding all of the innovation to the estimate -- and therefore \n", - "completely believing the measurement. \n", - "\n", - "However, if $Q_t >> \\bar{P_t}$ then the Kalman gain will go to 0, signaling a high trust in the process \n", - "and little trust in the measurement.\n", - "\n", - "The update is captured in the following. \n", - "\n", - "$\n", - "xUpdate = xEst + (K * y)\n", - "$\n", - "\n", - "Of course, the covariance must also be updated as well to account for the changing uncertainty. \n", - "\n", - "$\n", - "P_{t} = (I-K_tH_t)\\bar{P_t}\n", - "$" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "def update(xEst, PEst, u, z, initP):\n", - " \"\"\"\n", - " Performs the update step of EKF SLAM\n", - " \n", - " :param xEst: nx1 the predicted pose of the system and the pose of the landmarks\n", - " :param PEst: nxn the predicted covariance\n", - " :param u: 2x1 the control function \n", - " :param z: the measurements read at new position\n", - " :param initP: 2x2 an identity matrix acting as the initial covariance\n", - " :returns: the updated state and covariance for the system\n", - " \"\"\"\n", - " for iz in range(len(z[:, 0])): # for each observation\n", - " minid = search_correspond_LM_ID(xEst, PEst, z[iz, 0:2]) # associate to a known landmark\n", - "\n", - " nLM = calc_n_LM(xEst) # number of landmarks we currently know about\n", - " \n", - " if minid == nLM: # Landmark is a NEW landmark\n", - " print(\"New LM\")\n", - " # Extend state and covariance matrix\n", - " xAug = np.vstack((xEst, calc_LM_Pos(xEst, z[iz, :])))\n", - " PAug = np.vstack((np.hstack((PEst, np.zeros((len(xEst), LM_SIZE)))),\n", - " np.hstack((np.zeros((LM_SIZE, len(xEst))), initP))))\n", - " xEst = xAug\n", - " PEst = PAug\n", - " \n", - " lm = get_LM_Pos_from_state(xEst, minid)\n", - " y, S, H = calc_innovation(lm, xEst, PEst, z[iz, 0:2], minid)\n", - "\n", - " K = (PEst @ H.T) @ np.linalg.inv(S) # Calculate Kalman Gain\n", - " xEst = xEst + (K @ y)\n", - " PEst = (np.eye(len(xEst)) - (K @ H)) @ PEst\n", - " \n", - " xEst[2] = pi_2_pi(xEst[2])\n", - " return xEst, PEst\n" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "def calc_innovation(lm, xEst, PEst, z, LMid):\n", - " \"\"\"\n", - " Calculates the innovation based on expected position and landmark position\n", - " \n", - " :param lm: landmark position\n", - " :param xEst: estimated position/state\n", - " :param PEst: estimated covariance\n", - " :param z: read measurements\n", - " :param LMid: landmark id\n", - " :returns: returns the innovation y, and the jacobian H, and S, used to calculate the Kalman Gain\n", - " \"\"\"\n", - " delta = lm - xEst[0:2]\n", - " q = (delta.T @ delta)[0, 0]\n", - " zangle = math.atan2(delta[1, 0], delta[0, 0]) - xEst[2, 0]\n", - " zp = np.array([[math.sqrt(q), pi_2_pi(zangle)]])\n", - " # zp is the expected measurement based on xEst and the expected landmark position\n", - " \n", - " y = (z - zp).T # y = innovation\n", - " y[1] = pi_2_pi(y[1])\n", - " \n", - " H = jacobH(q, delta, xEst, LMid + 1)\n", - " S = H @ PEst @ H.T + Cx[0:2, 0:2]\n", - "\n", - " return y, S, H\n", - "\n", - "def jacobH(q, delta, x, i):\n", - " \"\"\"\n", - " Calculates the jacobian of the measurement function\n", - " \n", - " :param q: the range from the system pose to the landmark\n", - " :param delta: the difference between a landmark position and the estimated system position\n", - " :param x: the state, including the estimated system position\n", - " :param i: landmark id + 1\n", - " :returns: the jacobian H\n", - " \"\"\"\n", - " sq = math.sqrt(q)\n", - " G = np.array([[-sq * delta[0, 0], - sq * delta[1, 0], 0, sq * delta[0, 0], sq * delta[1, 0]],\n", - " [delta[1, 0], - delta[0, 0], - q, - delta[1, 0], delta[0, 0]]])\n", - "\n", - " G = G / q\n", - " nLM = calc_n_LM(x)\n", - " F1 = np.hstack((np.eye(3), np.zeros((3, 2 * nLM))))\n", - " F2 = np.hstack((np.zeros((2, 3)), np.zeros((2, 2 * (i - 1))),\n", - " np.eye(2), np.zeros((2, 2 * nLM - 2 * i))))\n", - "\n", - " F = np.vstack((F1, F2))\n", - "\n", - " H = G @ F\n", - "\n", - " return H" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Observation Step\n", - "The observation step described here is outside the main EKF SLAM process and is primarily used as a method of\n", - "driving the simulation. The observations funciton is in charge of calcualting how the poses of the robots change \n", - "and accumulate error over time, and the theoretical measuremnts that are expected as a result of each \n", - "measurement. \n", - "\n", - "Observations are based on the TRUE position of the robot. Error in dead reckoning and control functions are \n", - "passed along here as well. " - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "def observation(xTrue, xd, u, RFID):\n", - " \"\"\"\n", - " :param xTrue: the true pose of the system\n", - " :param xd: the current noisy estimate of the system\n", - " :param u: the current control input\n", - " :param RFID: the true position of the landmarks\n", - " \n", - " :returns: Computes the true position, observations, dead reckoning (noisy) position, \n", - " and noisy control function\n", - " \"\"\"\n", - " xTrue = motion_model(xTrue, u)\n", - "\n", - " # add noise to gps x-y\n", - " z = np.zeros((0, 3))\n", - "\n", - " for i in range(len(RFID[:, 0])): # Test all beacons, only add the ones we can see (within MAX_RANGE)\n", - "\n", - " dx = RFID[i, 0] - xTrue[0, 0]\n", - " dy = RFID[i, 1] - xTrue[1, 0]\n", - " d = math.sqrt(dx**2 + dy**2)\n", - " angle = pi_2_pi(math.atan2(dy, dx) - xTrue[2, 0])\n", - " if d <= MAX_RANGE:\n", - " dn = d + np.random.randn() * Qsim[0, 0] # add noise\n", - " anglen = angle + np.random.randn() * Qsim[1, 1] # add noise\n", - " zi = np.array([dn, anglen, i])\n", - " z = np.vstack((z, zi))\n", - "\n", - " # add noise to input\n", - " ud = np.array([[\n", - " u[0, 0] + np.random.randn() * Rsim[0, 0],\n", - " u[1, 0] + np.random.randn() * Rsim[1, 1]]]).T\n", - "\n", - " xd = motion_model(xd, ud)\n", - " return xTrue, z, xd, ud" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "def calc_n_LM(x):\n", - " \"\"\"\n", - " Calculates the number of landmarks currently tracked in the state\n", - " :param x: the state\n", - " :returns: the number of landmarks n\n", - " \"\"\"\n", - " n = int((len(x) - STATE_SIZE) / LM_SIZE)\n", - " return n\n", - "\n", - "\n", - "def jacob_motion(x, u):\n", - " \"\"\"\n", - " Calculates the jacobian of motion model. \n", - " \n", - " :param x: The state, including the estimated position of the system\n", - " :param u: The control function\n", - " :returns: G: Jacobian\n", - " Fx: STATE_SIZE x (STATE_SIZE + 2 * num_landmarks) matrix where the left side is an identity matrix\n", - " \"\"\"\n", - " \n", - " # [eye(3) [0 x y; 0 x y; 0 x y]]\n", - " Fx = np.hstack((np.eye(STATE_SIZE), np.zeros(\n", - " (STATE_SIZE, LM_SIZE * calc_n_LM(x)))))\n", - "\n", - " jF = np.array([[0.0, 0.0, -DT * u[0] * math.sin(x[2, 0])],\n", - " [0.0, 0.0, DT * u[0] * math.cos(x[2, 0])],\n", - " [0.0, 0.0, 0.0]],dtype=object)\n", - "\n", - " G = np.eye(STATE_SIZE) + Fx.T @ jF @ Fx\n", - " if calc_n_LM(x) > 0:\n", - " print(Fx.shape)\n", - " return G, Fx,\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "def calc_LM_Pos(x, z):\n", - " \"\"\"\n", - " Calcualtes the pose in the world coordinate frame of a landmark at the given measurement. \n", - "\n", - " :param x: [x; y; theta]\n", - " :param z: [range; bearing]\n", - " :returns: [x; y] for given measurement\n", - " \"\"\"\n", - " zp = np.zeros((2, 1))\n", - "\n", - " zp[0, 0] = x[0, 0] + z[0] * math.cos(x[2, 0] + z[1])\n", - " zp[1, 0] = x[1, 0] + z[0] * math.sin(x[2, 0] + z[1])\n", - " #zp[0, 0] = x[0, 0] + z[0, 0] * math.cos(x[2, 0] + z[0, 1])\n", - " #zp[1, 0] = x[1, 0] + z[0, 0] * math.sin(x[2, 0] + z[0, 1])\n", - "\n", - " return zp\n", - "\n", - "\n", - "def get_LM_Pos_from_state(x, ind):\n", - " \"\"\"\n", - " Returns the position of a given landmark\n", - " \n", - " :param x: The state containing all landmark positions\n", - " :param ind: landmark id\n", - " :returns: The position of the landmark\n", - " \"\"\"\n", - " lm = x[STATE_SIZE + LM_SIZE * ind: STATE_SIZE + LM_SIZE * (ind + 1), :]\n", - "\n", - " return lm\n", - "\n", - "\n", - "def search_correspond_LM_ID(xAug, PAug, zi):\n", - " \"\"\"\n", - " Landmark association with Mahalanobis distance.\n", - " \n", - " If this landmark is at least M_DIST_TH units away from all known landmarks, \n", - " it is a NEW landmark.\n", - " \n", - " :param xAug: The estimated state\n", - " :param PAug: The estimated covariance\n", - " :param zi: the read measurements of specific landmark\n", - " :returns: landmark id\n", - " \"\"\"\n", - "\n", - " nLM = calc_n_LM(xAug)\n", - "\n", - " mdist = []\n", - "\n", - " for i in range(nLM):\n", - " lm = get_LM_Pos_from_state(xAug, i)\n", - " y, S, H = calc_innovation(lm, xAug, PAug, zi, i)\n", - " mdist.append(y.T @ np.linalg.inv(S) @ y)\n", - "\n", - " mdist.append(M_DIST_TH) # new landmark\n", - "\n", - " minid = mdist.index(min(mdist))\n", - "\n", - " return minid\n", - "\n", - "def calc_input():\n", - " v = 1.0 # [m/s]\n", - " yawrate = 0.1 # [rad/s]\n", - " u = np.array([[v, yawrate]]).T\n", - " return u\n", - "\n", - "def pi_2_pi(angle):\n", - " return (angle + math.pi) % (2 * math.pi) - math.pi" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "def main():\n", - " print(\" start!!\")\n", - "\n", - " time = 0.0\n", - "\n", - " # RFID positions [x, y]\n", - " RFID = np.array([[10.0, -2.0],\n", - " [15.0, 10.0],\n", - " [3.0, 15.0],\n", - " [-5.0, 20.0]])\n", - "\n", - " # State Vector [x y yaw v]'\n", - " xEst = np.zeros((STATE_SIZE, 1))\n", - " xTrue = np.zeros((STATE_SIZE, 1))\n", - " PEst = np.eye(STATE_SIZE)\n", - "\n", - " xDR = np.zeros((STATE_SIZE, 1)) # Dead reckoning\n", - "\n", - " # history\n", - " hxEst = xEst\n", - " hxTrue = xTrue\n", - " hxDR = xTrue\n", - "\n", - " while SIM_TIME >= time:\n", - " time += DT\n", - " u = calc_input()\n", - "\n", - " xTrue, z, xDR, ud = observation(xTrue, xDR, u, RFID)\n", - "\n", - " xEst, PEst = ekf_slam(xEst, PEst, ud, z)\n", - "\n", - " x_state = xEst[0:STATE_SIZE]\n", - "\n", - " # store data history\n", - " hxEst = np.hstack((hxEst, x_state))\n", - " hxDR = np.hstack((hxDR, xDR))\n", - " hxTrue = np.hstack((hxTrue, xTrue))\n", - "\n", - " if show_animation: # pragma: no cover\n", - " plt.cla()\n", - "\n", - " plt.plot(RFID[:, 0], RFID[:, 1], \"*k\")\n", - " plt.plot(xEst[0], xEst[1], \".r\")\n", - "\n", - " # plot landmark\n", - " for i in range(calc_n_LM(xEst)):\n", - " plt.plot(xEst[STATE_SIZE + i * 2],\n", - " xEst[STATE_SIZE + i * 2 + 1], \"xg\")\n", - "\n", - " plt.plot(hxTrue[0, :],\n", - " hxTrue[1, :], \"-b\")\n", - " plt.plot(hxDR[0, :],\n", - " hxDR[1, :], \"-k\")\n", - " plt.plot(hxEst[0, :],\n", - " hxEst[1, :], \"-r\")\n", - " plt.axis(\"equal\")\n", - " plt.grid(True)\n", - " plt.pause(0.001)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " start!!\n", - "New LM\n", - "New LM\n", - "New LM\n" - ] - }, - { - "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "/* global mpl */\n", - "window.mpl = {};\n", - "\n", - "mpl.get_websocket_type = function () {\n", - " if (typeof WebSocket !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof MozWebSocket !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert(\n", - " 'Your browser does not have WebSocket support. ' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.'\n", - " );\n", - " }\n", - "};\n", - "\n", - "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = this.ws.binaryType !== undefined;\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById('mpl-warnings');\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent =\n", - " 'This browser does not support binary websocket messages. ' +\n", - " 'Performance may be slow.';\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = document.createElement('div');\n", - " this.root.setAttribute('style', 'display: inline-block');\n", - " this._root_extra_style(this.root);\n", - "\n", - " parent_element.appendChild(this.root);\n", - "\n", - " this._init_header(this);\n", - " this._init_canvas(this);\n", - " this._init_toolbar(this);\n", - "\n", - " var fig = this;\n", - "\n", - " this.waiting = false;\n", - "\n", - " this.ws.onopen = function () {\n", - " fig.send_message('supports_binary', { value: fig.supports_binary });\n", - " fig.send_message('send_image_mode', {});\n", - " if (fig.ratio !== 1) {\n", - " fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n", - " }\n", - " fig.send_message('refresh', {});\n", - " };\n", - "\n", - " this.imageObj.onload = function () {\n", - " if (fig.image_mode === 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", - "\n", - " this.imageObj.onunload = function () {\n", - " fig.ws.close();\n", - " };\n", - "\n", - " this.ws.onmessage = this._make_on_message_function(this);\n", - "\n", - " this.ondownload = ondownload;\n", - "};\n", - "\n", - "mpl.figure.prototype._init_header = function () {\n", - " var titlebar = document.createElement('div');\n", - " titlebar.classList =\n", - " 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n", - " var titletext = document.createElement('div');\n", - " titletext.classList = 'ui-dialog-title';\n", - " titletext.setAttribute(\n", - " 'style',\n", - " 'width: 100%; text-align: center; padding: 3px;'\n", - " );\n", - " titlebar.appendChild(titletext);\n", - " this.root.appendChild(titlebar);\n", - " this.header = titletext;\n", - "};\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n", - "\n", - "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n", - "\n", - "mpl.figure.prototype._init_canvas = function () {\n", - " var fig = this;\n", - "\n", - " var canvas_div = (this.canvas_div = document.createElement('div'));\n", - " canvas_div.setAttribute(\n", - " 'style',\n", - " 'border: 1px solid #ddd;' +\n", - " 'box-sizing: content-box;' +\n", - " 'clear: both;' +\n", - " 'min-height: 1px;' +\n", - " 'min-width: 1px;' +\n", - " 'outline: 0;' +\n", - " 'overflow: hidden;' +\n", - " 'position: relative;' +\n", - " 'resize: both;'\n", - " );\n", - "\n", - " function on_keyboard_event_closure(name) {\n", - " return function (event) {\n", - " return fig.key_event(event, name);\n", - " };\n", - " }\n", - "\n", - " canvas_div.addEventListener(\n", - " 'keydown',\n", - " on_keyboard_event_closure('key_press')\n", - " );\n", - " canvas_div.addEventListener(\n", - " 'keyup',\n", - " on_keyboard_event_closure('key_release')\n", - " );\n", - "\n", - " this._canvas_extra_style(canvas_div);\n", - " this.root.appendChild(canvas_div);\n", - "\n", - " var canvas = (this.canvas = document.createElement('canvas'));\n", - " canvas.classList.add('mpl-canvas');\n", - " canvas.setAttribute('style', 'box-sizing: content-box;');\n", - "\n", - " this.context = canvas.getContext('2d');\n", - "\n", - " var backingStore =\n", - " this.context.backingStorePixelRatio ||\n", - " this.context.webkitBackingStorePixelRatio ||\n", - " this.context.mozBackingStorePixelRatio ||\n", - " this.context.msBackingStorePixelRatio ||\n", - " this.context.oBackingStorePixelRatio ||\n", - " this.context.backingStorePixelRatio ||\n", - " 1;\n", - "\n", - " this.ratio = (window.devicePixelRatio || 1) / backingStore;\n", - "\n", - " var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n", - " 'canvas'\n", - " ));\n", - " rubberband_canvas.setAttribute(\n", - " 'style',\n", - " 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n", - " );\n", - "\n", - " // Apply a ponyfill if ResizeObserver is not implemented by browser.\n", - " if (this.ResizeObserver === undefined) {\n", - " if (window.ResizeObserver !== undefined) {\n", - " this.ResizeObserver = window.ResizeObserver;\n", - " } else {\n", - " var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n", - " this.ResizeObserver = obs.ResizeObserver;\n", - " }\n", - " }\n", - "\n", - " this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n", - " var nentries = entries.length;\n", - " for (var i = 0; i < nentries; i++) {\n", - " var entry = entries[i];\n", - " var width, height;\n", - " if (entry.contentBoxSize) {\n", - " if (entry.contentBoxSize instanceof Array) {\n", - " // Chrome 84 implements new version of spec.\n", - " width = entry.contentBoxSize[0].inlineSize;\n", - " height = entry.contentBoxSize[0].blockSize;\n", - " } else {\n", - " // Firefox implements old version of spec.\n", - " width = entry.contentBoxSize.inlineSize;\n", - " height = entry.contentBoxSize.blockSize;\n", - " }\n", - " } else {\n", - " // Chrome <84 implements even older version of spec.\n", - " width = entry.contentRect.width;\n", - " height = entry.contentRect.height;\n", - " }\n", - "\n", - " // Keep the size of the canvas and rubber band canvas in sync with\n", - " // the canvas container.\n", - " if (entry.devicePixelContentBoxSize) {\n", - " // Chrome 84 implements new version of spec.\n", - " canvas.setAttribute(\n", - " 'width',\n", - " entry.devicePixelContentBoxSize[0].inlineSize\n", - " );\n", - " canvas.setAttribute(\n", - " 'height',\n", - " entry.devicePixelContentBoxSize[0].blockSize\n", - " );\n", - " } else {\n", - " canvas.setAttribute('width', width * fig.ratio);\n", - " canvas.setAttribute('height', height * fig.ratio);\n", - " }\n", - " canvas.setAttribute(\n", - " 'style',\n", - " 'width: ' + width + 'px; height: ' + height + 'px;'\n", - " );\n", - "\n", - " rubberband_canvas.setAttribute('width', width);\n", - " rubberband_canvas.setAttribute('height', height);\n", - "\n", - " // And update the size in Python. We ignore the initial 0/0 size\n", - " // that occurs as the element is placed into the DOM, which should\n", - " // otherwise not happen due to the minimum size styling.\n", - " if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n", - " fig.request_resize(width, height);\n", - " }\n", - " }\n", - " });\n", - " this.resizeObserverInstance.observe(canvas_div);\n", - "\n", - " function on_mouse_event_closure(name) {\n", - " return function (event) {\n", - " return fig.mouse_event(event, name);\n", - " };\n", - " }\n", - "\n", - " rubberband_canvas.addEventListener(\n", - " 'mousedown',\n", - " on_mouse_event_closure('button_press')\n", - " );\n", - " rubberband_canvas.addEventListener(\n", - " 'mouseup',\n", - " on_mouse_event_closure('button_release')\n", - " );\n", - " rubberband_canvas.addEventListener(\n", - " 'dblclick',\n", - " on_mouse_event_closure('dblclick')\n", - " );\n", - " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband_canvas.addEventListener(\n", - " 'mousemove',\n", - " on_mouse_event_closure('motion_notify')\n", - " );\n", - "\n", - " rubberband_canvas.addEventListener(\n", - " 'mouseenter',\n", - " on_mouse_event_closure('figure_enter')\n", - " );\n", - " rubberband_canvas.addEventListener(\n", - " 'mouseleave',\n", - " on_mouse_event_closure('figure_leave')\n", - " );\n", - "\n", - " canvas_div.addEventListener('wheel', function (event) {\n", - " if (event.deltaY < 0) {\n", - " event.step = 1;\n", - " } else {\n", - " event.step = -1;\n", - " }\n", - " on_mouse_event_closure('scroll')(event);\n", - " });\n", - "\n", - " canvas_div.appendChild(canvas);\n", - " canvas_div.appendChild(rubberband_canvas);\n", - "\n", - " this.rubberband_context = rubberband_canvas.getContext('2d');\n", - " this.rubberband_context.strokeStyle = '#000000';\n", - "\n", - " this._resize_canvas = function (width, height, forward) {\n", - " if (forward) {\n", - " canvas_div.style.width = width + 'px';\n", - " canvas_div.style.height = height + 'px';\n", - " }\n", - " };\n", - "\n", - " // Disable right mouse context menu.\n", - " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", - " event.preventDefault();\n", - " return false;\n", - " });\n", - "\n", - " function set_focus() {\n", - " canvas.focus();\n", - " canvas_div.focus();\n", - " }\n", - "\n", - " window.setTimeout(set_focus, 100);\n", - "};\n", - "\n", - "mpl.figure.prototype._init_toolbar = function () {\n", - " var fig = this;\n", - "\n", - " var toolbar = document.createElement('div');\n", - " toolbar.classList = 'mpl-toolbar';\n", - " this.root.appendChild(toolbar);\n", - "\n", - " function on_click_closure(name) {\n", - " return function (_event) {\n", - " return fig.toolbar_button_onclick(name);\n", - " };\n", - " }\n", - "\n", - " function on_mouseover_closure(tooltip) {\n", - " return function (event) {\n", - " if (!event.currentTarget.disabled) {\n", - " return fig.toolbar_button_onmouseover(tooltip);\n", - " }\n", - " };\n", - " }\n", - "\n", - " fig.buttons = {};\n", - " var buttonGroup = document.createElement('div');\n", - " buttonGroup.classList = 'mpl-button-group';\n", - " for (var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " /* Instead of a spacer, we start a new button group. */\n", - " if (buttonGroup.hasChildNodes()) {\n", - " toolbar.appendChild(buttonGroup);\n", - " }\n", - " buttonGroup = document.createElement('div');\n", - " buttonGroup.classList = 'mpl-button-group';\n", - " continue;\n", - " }\n", - "\n", - " var button = (fig.buttons[name] = document.createElement('button'));\n", - " button.classList = 'mpl-widget';\n", - " button.setAttribute('role', 'button');\n", - " button.setAttribute('aria-disabled', 'false');\n", - " button.addEventListener('click', on_click_closure(method_name));\n", - " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", - "\n", - " var icon_img = document.createElement('img');\n", - " icon_img.src = '_images/' + image + '.png';\n", - " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", - " icon_img.alt = tooltip;\n", - " button.appendChild(icon_img);\n", - "\n", - " buttonGroup.appendChild(button);\n", - " }\n", - "\n", - " if (buttonGroup.hasChildNodes()) {\n", - " toolbar.appendChild(buttonGroup);\n", - " }\n", - "\n", - " var fmt_picker = document.createElement('select');\n", - " fmt_picker.classList = 'mpl-widget';\n", - " toolbar.appendChild(fmt_picker);\n", - " this.format_dropdown = fmt_picker;\n", - "\n", - " for (var ind in mpl.extensions) {\n", - " var fmt = mpl.extensions[ind];\n", - " var option = document.createElement('option');\n", - " option.selected = fmt === mpl.default_extension;\n", - " option.innerHTML = fmt;\n", - " fmt_picker.appendChild(option);\n", - " }\n", - "\n", - " var status_bar = document.createElement('span');\n", - " status_bar.classList = 'mpl-message';\n", - " toolbar.appendChild(status_bar);\n", - " this.message = status_bar;\n", - "};\n", - "\n", - "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", - " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", - " // which will in turn request a refresh of the image.\n", - " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", - "};\n", - "\n", - "mpl.figure.prototype.send_message = function (type, properties) {\n", - " properties['type'] = type;\n", - " properties['figure_id'] = this.id;\n", - " this.ws.send(JSON.stringify(properties));\n", - "};\n", - "\n", - "mpl.figure.prototype.send_draw_message = function () {\n", - " if (!this.waiting) {\n", - " this.waiting = true;\n", - " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", - " }\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", - " var format_dropdown = fig.format_dropdown;\n", - " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", - " fig.ondownload(fig, format);\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", - " var size = msg['size'];\n", - " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", - " fig._resize_canvas(size[0], size[1], msg['forward']);\n", - " fig.send_message('refresh', {});\n", - " }\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", - " var x0 = msg['x0'] / fig.ratio;\n", - " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", - " var x1 = msg['x1'] / fig.ratio;\n", - " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", - " x0 = Math.floor(x0) + 0.5;\n", - " y0 = Math.floor(y0) + 0.5;\n", - " x1 = Math.floor(x1) + 0.5;\n", - " y1 = Math.floor(y1) + 0.5;\n", - " var min_x = Math.min(x0, x1);\n", - " var min_y = Math.min(y0, y1);\n", - " var width = Math.abs(x1 - x0);\n", - " var height = Math.abs(y1 - y0);\n", - "\n", - " fig.rubberband_context.clearRect(\n", - " 0,\n", - " 0,\n", - " fig.canvas.width / fig.ratio,\n", - " fig.canvas.height / fig.ratio\n", - " );\n", - "\n", - " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", - " // Updates the figure title.\n", - " fig.header.textContent = msg['label'];\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", - " var cursor = msg['cursor'];\n", - " switch (cursor) {\n", - " case 0:\n", - " cursor = 'pointer';\n", - " break;\n", - " case 1:\n", - " cursor = 'default';\n", - " break;\n", - " case 2:\n", - " cursor = 'crosshair';\n", - " break;\n", - " case 3:\n", - " cursor = 'move';\n", - " break;\n", - " }\n", - " fig.rubberband_canvas.style.cursor = cursor;\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_message = function (fig, msg) {\n", - " fig.message.textContent = msg['message'];\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", - " // Request the server to send over a new figure.\n", - " fig.send_draw_message();\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", - " fig.image_mode = msg['mode'];\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", - " for (var key in msg) {\n", - " if (!(key in fig.buttons)) {\n", - " continue;\n", - " }\n", - " fig.buttons[key].disabled = !msg[key];\n", - " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", - " }\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", - " if (msg['mode'] === 'PAN') {\n", - " fig.buttons['Pan'].classList.add('active');\n", - " fig.buttons['Zoom'].classList.remove('active');\n", - " } else if (msg['mode'] === 'ZOOM') {\n", - " fig.buttons['Pan'].classList.remove('active');\n", - " fig.buttons['Zoom'].classList.add('active');\n", - " } else {\n", - " fig.buttons['Pan'].classList.remove('active');\n", - " fig.buttons['Zoom'].classList.remove('active');\n", - " }\n", - "};\n", - "\n", - "mpl.figure.prototype.updated_canvas_event = function () {\n", - " // Called whenever the canvas gets updated.\n", - " this.send_message('ack', {});\n", - "};\n", - "\n", - "// A function to construct a web socket function for onmessage handling.\n", - "// Called in the figure constructor.\n", - "mpl.figure.prototype._make_on_message_function = function (fig) {\n", - " return function socket_on_message(evt) {\n", - " if (evt.data instanceof Blob) {\n", - " var img = evt.data;\n", - " if (img.type !== 'image/png') {\n", - " /* FIXME: We get \"Resource interpreted as Image but\n", - " * transferred with MIME type text/plain:\" errors on\n", - " * Chrome. But how to set the MIME type? It doesn't seem\n", - " * to be part of the websocket stream */\n", - " img.type = 'image/png';\n", - " }\n", - "\n", - " /* Free the memory for the previous frames */\n", - " if (fig.imageObj.src) {\n", - " (window.URL || window.webkitURL).revokeObjectURL(\n", - " fig.imageObj.src\n", - " );\n", - " }\n", - "\n", - " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", - " img\n", - " );\n", - " fig.updated_canvas_event();\n", - " fig.waiting = false;\n", - " return;\n", - " } else if (\n", - " typeof evt.data === 'string' &&\n", - " evt.data.slice(0, 21) === 'data:image/png;base64'\n", - " ) {\n", - " fig.imageObj.src = evt.data;\n", - " fig.updated_canvas_event();\n", - " fig.waiting = false;\n", - " return;\n", - " }\n", - "\n", - " var msg = JSON.parse(evt.data);\n", - " var msg_type = msg['type'];\n", - "\n", - " // Call the \"handle_{type}\" callback, which takes\n", - " // the figure and JSON message as its only arguments.\n", - " try {\n", - " var callback = fig['handle_' + msg_type];\n", - " } catch (e) {\n", - " console.log(\n", - " \"No handler for the '\" + msg_type + \"' message type: \",\n", - " msg\n", - " );\n", - " return;\n", - " }\n", - "\n", - " if (callback) {\n", - " try {\n", - " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", - " callback(fig, msg);\n", - " } catch (e) {\n", - " console.log(\n", - " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", - " e,\n", - " e.stack,\n", - " msg\n", - " );\n", - " }\n", - " }\n", - " };\n", - "};\n", - "\n", - "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", - "mpl.findpos = function (e) {\n", - " //this section is from http://www.quirksmode.org/js/events_properties.html\n", - " var targ;\n", - " if (!e) {\n", - " e = window.event;\n", - " }\n", - " if (e.target) {\n", - " targ = e.target;\n", - " } else if (e.srcElement) {\n", - " targ = e.srcElement;\n", - " }\n", - " if (targ.nodeType === 3) {\n", - " // defeat Safari bug\n", - " targ = targ.parentNode;\n", - " }\n", - "\n", - " // pageX,Y are the mouse positions relative to the document\n", - " var boundingRect = targ.getBoundingClientRect();\n", - " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", - " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", - "\n", - " return { x: x, y: y };\n", - "};\n", - "\n", - "/*\n", - " * return a copy of an object with only non-object keys\n", - " * we need this to avoid circular references\n", - " * http://stackoverflow.com/a/24161582/3208463\n", - " */\n", - "function simpleKeys(original) {\n", - " return Object.keys(original).reduce(function (obj, key) {\n", - " if (typeof original[key] !== 'object') {\n", - " obj[key] = original[key];\n", - " }\n", - " return obj;\n", - " }, {});\n", - "}\n", - "\n", - "mpl.figure.prototype.mouse_event = function (event, name) {\n", - " var canvas_pos = mpl.findpos(event);\n", - "\n", - " if (name === 'button_press') {\n", - " this.canvas.focus();\n", - " this.canvas_div.focus();\n", - " }\n", - "\n", - " var x = canvas_pos.x * this.ratio;\n", - " var y = canvas_pos.y * this.ratio;\n", - "\n", - " this.send_message(name, {\n", - " x: x,\n", - " y: y,\n", - " button: event.button,\n", - " step: event.step,\n", - " guiEvent: simpleKeys(event),\n", - " });\n", - "\n", - " /* This prevents the web browser from automatically changing to\n", - " * the text insertion cursor when the button is pressed. We want\n", - " * to control all of the cursor setting manually through the\n", - " * 'cursor' event from matplotlib */\n", - " event.preventDefault();\n", - " return false;\n", - "};\n", - "\n", - "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", - " // Handle any extra behaviour associated with a key event\n", - "};\n", - "\n", - "mpl.figure.prototype.key_event = function (event, name) {\n", - " // Prevent repeat events\n", - " if (name === 'key_press') {\n", - " if (event.key === this._key) {\n", - " return;\n", - " } else {\n", - " this._key = event.key;\n", - " }\n", - " }\n", - " if (name === 'key_release') {\n", - " this._key = null;\n", - " }\n", - "\n", - " var value = '';\n", - " if (event.ctrlKey && event.key !== 'Control') {\n", - " value += 'ctrl+';\n", - " }\n", - " else if (event.altKey && event.key !== 'Alt') {\n", - " value += 'alt+';\n", - " }\n", - " else if (event.shiftKey && event.key !== 'Shift') {\n", - " value += 'shift+';\n", - " }\n", - "\n", - " value += 'k' + event.key;\n", - "\n", - " this._key_event_extra(event, name);\n", - "\n", - " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", - " return false;\n", - "};\n", - "\n", - "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", - " if (name === 'download') {\n", - " this.handle_save(this, null);\n", - " } else {\n", - " this.send_message('toolbar_button', { name: name });\n", - " }\n", - "};\n", - "\n", - "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", - " this.message.textContent = tooltip;\n", - "};\n", - "\n", - "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n", - "// prettier-ignore\n", - "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n", - "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", - "\n", - "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", - "\n", - "mpl.default_extension = \"png\";/* global mpl */\n", - "\n", - "var comm_websocket_adapter = function (comm) {\n", - " // Create a \"websocket\"-like object which calls the given IPython comm\n", - " // object with the appropriate methods. Currently this is a non binary\n", - " // socket, so there is still some room for performance tuning.\n", - " var ws = {};\n", - "\n", - " ws.binaryType = comm.kernel.ws.binaryType;\n", - " ws.readyState = comm.kernel.ws.readyState;\n", - " function updateReadyState(_event) {\n", - " if (comm.kernel.ws) {\n", - " ws.readyState = comm.kernel.ws.readyState;\n", - " } else {\n", - " ws.readyState = 3; // Closed state.\n", - " }\n", - " }\n", - " comm.kernel.ws.addEventListener('open', updateReadyState);\n", - " comm.kernel.ws.addEventListener('close', updateReadyState);\n", - " comm.kernel.ws.addEventListener('error', updateReadyState);\n", - "\n", - " ws.close = function () {\n", - " comm.close();\n", - " };\n", - " ws.send = function (m) {\n", - " //console.log('sending', m);\n", - " comm.send(m);\n", - " };\n", - " // Register the callback with on_msg.\n", - " comm.on_msg(function (msg) {\n", - " //console.log('receiving', msg['content']['data'], msg);\n", - " var data = msg['content']['data'];\n", - " if (data['blob'] !== undefined) {\n", - " data = {\n", - " data: new Blob(msg['buffers'], { type: data['blob'] }),\n", - " };\n", - " }\n", - " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", - " ws.onmessage(data);\n", - " });\n", - " return ws;\n", - "};\n", - "\n", - "mpl.mpl_figure_comm = function (comm, msg) {\n", - " // This is the function which gets called when the mpl process\n", - " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", - "\n", - " var id = msg.content.data.id;\n", - " // Get hold of the div created by the display call when the Comm\n", - " // socket was opened in Python.\n", - " var element = document.getElementById(id);\n", - " var ws_proxy = comm_websocket_adapter(comm);\n", - "\n", - " function ondownload(figure, _format) {\n", - " window.open(figure.canvas.toDataURL());\n", - " }\n", - "\n", - " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", - "\n", - " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", - " // web socket which is closed, not our websocket->open comm proxy.\n", - " ws_proxy.onopen();\n", - "\n", - " fig.parent_element = element;\n", - " fig.cell_info = mpl.find_output_cell(\"
\");\n", - " if (!fig.cell_info) {\n", - " console.error('Failed to find cell for figure', id, fig);\n", - " return;\n", - " }\n", - " fig.cell_info[0].output_area.element.on(\n", - " 'cleared',\n", - " { fig: fig },\n", - " fig._remove_fig_handler\n", - " );\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_close = function (fig, msg) {\n", - " var width = fig.canvas.width / fig.ratio;\n", - " fig.cell_info[0].output_area.element.off(\n", - " 'cleared',\n", - " fig._remove_fig_handler\n", - " );\n", - " fig.resizeObserverInstance.unobserve(fig.canvas_div);\n", - "\n", - " // Update the output cell to use the data from the current canvas.\n", - " fig.push_to_output();\n", - " var dataURL = fig.canvas.toDataURL();\n", - " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", - " // the notebook keyboard shortcuts fail.\n", - " IPython.keyboard_manager.enable();\n", - " fig.parent_element.innerHTML =\n", - " '';\n", - " fig.close_ws(fig, msg);\n", - "};\n", - "\n", - "mpl.figure.prototype.close_ws = function (fig, msg) {\n", - " fig.send_message('closing', msg);\n", - " // fig.ws.close()\n", - "};\n", - "\n", - "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", - " // Turn the data on the canvas into data in the output cell.\n", - " var width = this.canvas.width / this.ratio;\n", - " var dataURL = this.canvas.toDataURL();\n", - " this.cell_info[1]['text/html'] =\n", - " '';\n", - "};\n", - "\n", - "mpl.figure.prototype.updated_canvas_event = function () {\n", - " // Tell IPython that the notebook contents must change.\n", - " IPython.notebook.set_dirty(true);\n", - " this.send_message('ack', {});\n", - " var fig = this;\n", - " // Wait a second, then push the new image to the DOM so\n", - " // that it is saved nicely (might be nice to debounce this).\n", - " setTimeout(function () {\n", - " fig.push_to_output();\n", - " }, 1000);\n", - "};\n", - "\n", - "mpl.figure.prototype._init_toolbar = function () {\n", - " var fig = this;\n", - "\n", - " var toolbar = document.createElement('div');\n", - " toolbar.classList = 'btn-toolbar';\n", - " this.root.appendChild(toolbar);\n", - "\n", - " function on_click_closure(name) {\n", - " return function (_event) {\n", - " return fig.toolbar_button_onclick(name);\n", - " };\n", - " }\n", - "\n", - " function on_mouseover_closure(tooltip) {\n", - " return function (event) {\n", - " if (!event.currentTarget.disabled) {\n", - " return fig.toolbar_button_onmouseover(tooltip);\n", - " }\n", - " };\n", - " }\n", - "\n", - " fig.buttons = {};\n", - " var buttonGroup = document.createElement('div');\n", - " buttonGroup.classList = 'btn-group';\n", - " var button;\n", - " for (var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " /* Instead of a spacer, we start a new button group. */\n", - " if (buttonGroup.hasChildNodes()) {\n", - " toolbar.appendChild(buttonGroup);\n", - " }\n", - " buttonGroup = document.createElement('div');\n", - " buttonGroup.classList = 'btn-group';\n", - " continue;\n", - " }\n", - "\n", - " button = fig.buttons[name] = document.createElement('button');\n", - " button.classList = 'btn btn-default';\n", - " button.href = '#';\n", - " button.title = name;\n", - " button.innerHTML = '';\n", - " button.addEventListener('click', on_click_closure(method_name));\n", - " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", - " buttonGroup.appendChild(button);\n", - " }\n", - "\n", - " if (buttonGroup.hasChildNodes()) {\n", - " toolbar.appendChild(buttonGroup);\n", - " }\n", - "\n", - " // Add the status bar.\n", - " var status_bar = document.createElement('span');\n", - " status_bar.classList = 'mpl-message pull-right';\n", - " toolbar.appendChild(status_bar);\n", - " this.message = status_bar;\n", - "\n", - " // Add the close button to the window.\n", - " var buttongrp = document.createElement('div');\n", - " buttongrp.classList = 'btn-group inline pull-right';\n", - " button = document.createElement('button');\n", - " button.classList = 'btn btn-mini btn-primary';\n", - " button.href = '#';\n", - " button.title = 'Stop Interaction';\n", - " button.innerHTML = '';\n", - " button.addEventListener('click', function (_evt) {\n", - " fig.handle_close(fig, {});\n", - " });\n", - " button.addEventListener(\n", - " 'mouseover',\n", - " on_mouseover_closure('Stop Interaction')\n", - " );\n", - " buttongrp.appendChild(button);\n", - " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", - " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", - "};\n", - "\n", - "mpl.figure.prototype._remove_fig_handler = function (event) {\n", - " var fig = event.data.fig;\n", - " if (event.target !== this) {\n", - " // Ignore bubbled events from children.\n", - " return;\n", - " }\n", - " fig.close_ws(fig, {});\n", - "};\n", - "\n", - "mpl.figure.prototype._root_extra_style = function (el) {\n", - " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", - "};\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function (el) {\n", - " // this is important to make the div 'focusable\n", - " el.setAttribute('tabindex', 0);\n", - " // reach out to IPython and tell the keyboard manager to turn it's self\n", - " // off when our div gets focus\n", - "\n", - " // location in version 3\n", - " if (IPython.notebook.keyboard_manager) {\n", - " IPython.notebook.keyboard_manager.register_events(el);\n", - " } else {\n", - " // location in version 2\n", - " IPython.keyboard_manager.register_events(el);\n", - " }\n", - "};\n", - "\n", - "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager) {\n", - " manager = IPython.keyboard_manager;\n", - " }\n", - "\n", - " // Check for shift+enter\n", - " if (event.shiftKey && event.which === 13) {\n", - " this.canvas_div.blur();\n", - " // select the cell after this one\n", - " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", - " IPython.notebook.select(index + 1);\n", - " }\n", - "};\n", - "\n", - "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", - " fig.ondownload(fig, null);\n", - "};\n", - "\n", - "mpl.find_output_cell = function (html_output) {\n", - " // Return the cell and output element which can be found *uniquely* in the notebook.\n", - " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", - " // IPython event is triggered only after the cells have been serialised, which for\n", - " // our purposes (turning an active figure into a static one), is too late.\n", - " var cells = IPython.notebook.get_cells();\n", - " var ncells = cells.length;\n", - " for (var i = 0; i < ncells; i++) {\n", - " var cell = cells[i];\n", - " if (cell.cell_type === 'code') {\n", - " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", - " var data = cell.output_area.outputs[j];\n", - " if (data.data) {\n", - " // IPython >= 3 moved mimebundle to data attribute of output\n", - " data = data.data;\n", - " }\n", - " if (data['text/html'] === html_output) {\n", - " return [cell, data, j];\n", - " }\n", - " }\n", - " }\n", - " }\n", - "};\n", - "\n", - "// Register the function which deals with the matplotlib target/channel.\n", - "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel !== null) {\n", - " IPython.notebook.kernel.comm_manager.register_target(\n", - " 'matplotlib',\n", - " mpl.mpl_figure_comm\n", - " );\n", - "}\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "New LM\n" - ] - } - ], - "source": [ - "%matplotlib notebook\n", - "%matplotlib notebook\n", - "main()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.7" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/SLAM/FastSLAM1/FastSLAM1.ipynb b/SLAM/FastSLAM1/FastSLAM1.ipynb deleted file mode 100644 index 60faed6e882..00000000000 --- a/SLAM/FastSLAM1/FastSLAM1.ipynb +++ /dev/null @@ -1,676 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## FastSLAM1.0" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "execution_count": 1, - "metadata": { - "image/png": { - "width": 600 - } - }, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.display import Image\n", - "Image(filename=\"animation.png\",width=600)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Simulation\n", - "\n", - "This is a feature based SLAM example using FastSLAM 1.0.\n", - "\n", - "The blue line is ground truth, the black line is dead reckoning, the red\n", - "line is the estimated trajectory with FastSLAM.\n", - "\n", - "The red points are particles of FastSLAM.\n", - "\n", - "Black points are landmarks, blue crosses are estimated landmark\n", - "positions by FastSLAM.\n", - "\n", - "\n", - "![gif](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/FastSLAM1/animation.gif)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Introduction\n", - "\n", - "FastSLAM algorithm implementation is based on particle filters and belongs to the family of probabilistic SLAM approaches. It is used with feature-based maps (see gif above) or with occupancy grid maps.\n", - "\n", - "As it is shown, the particle filter differs from EKF by representing the robot's estimation through a set of particles. Each single particle has an independent belief, as it holds the pose $(x, y, \\theta)$ and an array of landmark locations $[(x_1, y_1), (x_2, y_2), ... (x_n, y_n)]$ for n landmarks.\n", - "\n", - "* The blue line is the true trajectory\n", - "* The red line is the estimated trajectory\n", - "* The red dots represent the distribution of particles\n", - "* The black line represent dead reckoning tracjectory\n", - "* The blue x is the observed and estimated landmarks\n", - "* The black x is the true landmark\n", - "\n", - "I.e. Each particle maintains a deterministic pose and n-EKFs for each landmark and update it with each measurement." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Algorithm walkthrough\n", - "\n", - "The particles are initially drawn from a uniform distribution the represent the initial uncertainty.\n", - "At each time step we do:\n", - "\n", - "* Predict the pose for each particle by using $u$ and the motion model (the landmarks are not updated). \n", - "* Update the particles with observations $z$, where the weights are adjusted based on how likely the particle to have the correct pose given the sensor measurement\n", - "* Resampling such that the particles with the largest weights survive and the unlikely ones with the lowest weights die out.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 1- Predict\n", - "The following equations and code snippets we can see how the particles distribution evolves in case we provide only the control $(v,w)$, which are the linear and angular velocity respectively. \n", - "\n", - "$\\begin{equation*}\n", - "F=\n", - "\\begin{bmatrix}\n", - "1 & 0 & 0 \\\\\n", - "0 & 1 & 0 \\\\\n", - "0 & 0 & 1 \n", - "\\end{bmatrix}\n", - "\\end{equation*}$\n", - "\n", - "$\\begin{equation*}\n", - "B=\n", - "\\begin{bmatrix}\n", - "\\Delta t cos(\\theta) & 0\\\\\n", - "\\Delta t sin(\\theta) & 0\\\\\n", - "0 & \\Delta t\n", - "\\end{bmatrix}\n", - "\\end{equation*}$\n", - "\n", - "$\\begin{equation*}\n", - "X = FX + BU \n", - "\\end{equation*}$\n", - "\n", - "\n", - "$\\begin{equation*}\n", - "\\begin{bmatrix}\n", - "x_{t+1} \\\\\n", - "y_{t+1} \\\\\n", - "\\theta_{t+1}\n", - "\\end{bmatrix}=\n", - "\\begin{bmatrix}\n", - "1 & 0 & 0 \\\\\n", - "0 & 1 & 0 \\\\\n", - "0 & 0 & 1 \n", - "\\end{bmatrix}\\begin{bmatrix}\n", - "x_{t} \\\\\n", - "y_{t} \\\\\n", - "\\theta_{t}\n", - "\\end{bmatrix}+\n", - "\\begin{bmatrix}\n", - "\\Delta t cos(\\theta) & 0\\\\\n", - "\\Delta t sin(\\theta) & 0\\\\\n", - "0 & \\Delta t\n", - "\\end{bmatrix}\n", - "\\begin{bmatrix}\n", - "v_{t} + \\sigma_v\\\\\n", - "w_{t} + \\sigma_w\\\\\n", - "\\end{bmatrix}\n", - "\\end{equation*}$\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The following snippets playsback the recorded trajectory of each particle.\n", - "\n", - "To get the insight of the motion model change the value of $R$ and re-run the cells again. As R is the parameters that indicates how much we trust that the robot executed the motion commands.\n", - "\n", - "It is interesting to notice also that only motion will increase the uncertainty in the system as the particles start to spread out more. If observations are included the uncertainty will decrease and particles will converge to the correct estimate." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# CODE SNIPPET #\n", - "import numpy as np\n", - "import math\n", - "from copy import deepcopy\n", - "# Fast SLAM covariance\n", - "Q = np.diag([3.0, np.deg2rad(10.0)])**2\n", - "R = np.diag([1.0, np.deg2rad(20.0)])**2\n", - "\n", - "# Simulation parameter\n", - "Qsim = np.diag([0.3, np.deg2rad(2.0)])**2\n", - "Rsim = np.diag([0.5, np.deg2rad(10.0)])**2\n", - "OFFSET_YAWRATE_NOISE = 0.01\n", - "\n", - "DT = 0.1 # time tick [s]\n", - "SIM_TIME = 50.0 # simulation time [s]\n", - "MAX_RANGE = 20.0 # maximum observation range\n", - "M_DIST_TH = 2.0 # Threshold of Mahalanobis distance for data association.\n", - "STATE_SIZE = 3 # State size [x,y,yaw]\n", - "LM_SIZE = 2 # LM srate size [x,y]\n", - "N_PARTICLE = 100 # number of particle\n", - "NTH = N_PARTICLE / 1.5 # Number of particle for re-sampling\n", - "\n", - "class Particle:\n", - "\n", - " def __init__(self, N_LM):\n", - " self.w = 1.0 / N_PARTICLE\n", - " self.x = 0.0\n", - " self.y = 0.0\n", - " self.yaw = 0.0\n", - " # landmark x-y positions\n", - " self.lm = np.zeros((N_LM, LM_SIZE))\n", - " # landmark position covariance\n", - " self.lmP = np.zeros((N_LM * LM_SIZE, LM_SIZE))\n", - "\n", - "def motion_model(x, u):\n", - " F = np.array([[1.0, 0, 0],\n", - " [0, 1.0, 0],\n", - " [0, 0, 1.0]])\n", - "\n", - " B = np.array([[DT * math.cos(x[2, 0]), 0],\n", - " [DT * math.sin(x[2, 0]), 0],\n", - " [0.0, DT]])\n", - " x = F @ x + B @ u\n", - " \n", - " x[2, 0] = pi_2_pi(x[2, 0])\n", - " return x\n", - " \n", - "def predict_particles(particles, u):\n", - " for i in range(N_PARTICLE):\n", - " px = np.zeros((STATE_SIZE, 1))\n", - " px[0, 0] = particles[i].x\n", - " px[1, 0] = particles[i].y\n", - " px[2, 0] = particles[i].yaw\n", - " ud = u + (np.random.randn(1, 2) @ R).T # add noise\n", - " px = motion_model(px, ud)\n", - " particles[i].x = px[0, 0]\n", - " particles[i].y = px[1, 0]\n", - " particles[i].yaw = px[2, 0]\n", - "\n", - " return particles\n", - "\n", - "def pi_2_pi(angle):\n", - " return (angle + math.pi) % (2 * math.pi) - math.pi\n", - "\n", - "# END OF SNIPPET\n", - "\n", - "N_LM = 0 \n", - "particles = [Particle(N_LM) for i in range(N_PARTICLE)]\n", - "time= 0.0\n", - "v = 1.0 # [m/s]\n", - "yawrate = 0.1 # [rad/s]\n", - "u = np.array([v, yawrate]).reshape(2, 1)\n", - "history = []\n", - "while SIM_TIME >= time:\n", - " time += DT\n", - " particles = predict_particles(particles, u)\n", - " history.append(deepcopy(particles))\n" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "3f279cf1dcaf4ec886c01942c36e601d", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(IntSlider(value=0, description='t', max=499), Output()), _dom_classes=('widget-interact'…" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# from IPython.html.widgets import *\n", - "from ipywidgets import *\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "\n", - "# playback the recorded motion of the particles\n", - "def plot_particles(t=0):\n", - " x = []\n", - " y = []\n", - " for i in range(len(history[t])):\n", - " x.append(history[t][i].x)\n", - " y.append(history[t][i].y)\n", - " plt.figtext(0.15,0.82,'t = ' + str(t))\n", - " plt.plot(x, y, '.r')\n", - " plt.axis([-20,20, -5,25])\n", - "\n", - "interact(plot_particles, t=(0,len(history)-1,1));" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 2- Update\n", - "\n", - "For the update step it is useful to observe a single particle and the effect of getting a new measurements on the weight of the particle.\n", - "\n", - "As mentioned earlier, each particle maintains $N$ $2x2$ EKFs to estimate the landmarks, which includes the EKF process described in the EKF notebook. The difference is the change in the weight of the particle according to how likely the measurement is.\n", - "\n", - "The weight is updated according to the following equation: \n", - "\n", - "$\\begin{equation*}\n", - "w_i = |2\\pi Q|^{\\frac{-1}{2}} exp\\{\\frac{-1}{2}(z_t - \\hat z_i)^T Q^{-1}(z_t-\\hat z_i)\\}\n", - "\\end{equation*}$\n", - "\n", - "Where, $w_i$ is the computed weight, $Q$ is the measurement covariance, $z_t$ is the actual measurment and $\\hat z_i$ is the predicted measurement of particle $i$.\n", - "\n", - "To experiment this, a single particle is initialized then passed an initial measurement, which results in a relatively average weight. However, setting the particle coordinate to a wrong value to simulate wrong estimation will result in a very low weight. The lower the weight the less likely that this particle will be drawn during resampling and probably will die out." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "initial weight 1.0\n", - "weight after landmark intialization 1.0\n", - "weight after update 0.023098460073039763\n", - "weight after wrong prediction 7.951154575772496e-07\n" - ] - } - ], - "source": [ - "# CODE SNIPPET #\n", - "def observation(xTrue, xd, u, RFID):\n", - "\n", - " # calc true state\n", - " xTrue = motion_model(xTrue, u)\n", - "\n", - " # add noise to range observation\n", - " z = np.zeros((3, 0))\n", - " for i in range(len(RFID[:, 0])):\n", - "\n", - " dx = RFID[i, 0] - xTrue[0, 0]\n", - " dy = RFID[i, 1] - xTrue[1, 0]\n", - " d = math.sqrt(dx**2 + dy**2)\n", - " angle = pi_2_pi(math.atan2(dy, dx) - xTrue[2, 0])\n", - " if d <= MAX_RANGE:\n", - " dn = d + np.random.randn() * Qsim[0, 0] # add noise\n", - " anglen = angle + np.random.randn() * Qsim[1, 1] # add noise\n", - " zi = np.array([dn, pi_2_pi(anglen), i]).reshape(3, 1)\n", - " z = np.hstack((z, zi))\n", - "\n", - " # add noise to input\n", - " ud1 = u[0, 0] + np.random.randn() * Rsim[0, 0]\n", - " ud2 = u[1, 0] + np.random.randn() * Rsim[1, 1] + OFFSET_YAWRATE_NOISE\n", - " ud = np.array([ud1, ud2]).reshape(2, 1)\n", - "\n", - " xd = motion_model(xd, ud)\n", - "\n", - " return xTrue, z, xd, ud\n", - "\n", - "def update_with_observation(particles, z):\n", - " for iz in range(len(z[0, :])):\n", - "\n", - " lmid = int(z[2, iz])\n", - "\n", - " for ip in range(N_PARTICLE):\n", - " # new landmark\n", - " if abs(particles[ip].lm[lmid, 0]) <= 0.01:\n", - " particles[ip] = add_new_lm(particles[ip], z[:, iz], Q)\n", - " # known landmark\n", - " else:\n", - " w = compute_weight(particles[ip], z[:, iz], Q)\n", - " particles[ip].w *= w\n", - " particles[ip] = update_landmark(particles[ip], z[:, iz], Q)\n", - "\n", - " return particles\n", - "\n", - "def compute_weight(particle, z, Q):\n", - " lm_id = int(z[2])\n", - " xf = np.array(particle.lm[lm_id, :]).reshape(2, 1)\n", - " Pf = np.array(particle.lmP[2 * lm_id:2 * lm_id + 2])\n", - " zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q)\n", - " dx = z[0:2].reshape(2, 1) - zp\n", - " dx[1, 0] = pi_2_pi(dx[1, 0])\n", - "\n", - " try:\n", - " invS = np.linalg.inv(Sf)\n", - " except np.linalg.linalg.LinAlgError:\n", - " print(\"singuler\")\n", - " return 1.0\n", - "\n", - " num = math.exp(-0.5 * dx.T @ invS @ dx)\n", - " den = 2.0 * math.pi * math.sqrt(np.linalg.det(Sf))\n", - " w = num / den\n", - "\n", - " return w\n", - "\n", - "def compute_jacobians(particle, xf, Pf, Q):\n", - " dx = xf[0, 0] - particle.x\n", - " dy = xf[1, 0] - particle.y\n", - " d2 = dx**2 + dy**2\n", - " d = math.sqrt(d2)\n", - "\n", - " zp = np.array(\n", - " [d, pi_2_pi(math.atan2(dy, dx) - particle.yaw)]).reshape(2, 1)\n", - "\n", - " Hv = np.array([[-dx / d, -dy / d, 0.0],\n", - " [dy / d2, -dx / d2, -1.0]])\n", - "\n", - " Hf = np.array([[dx / d, dy / d],\n", - " [-dy / d2, dx / d2]])\n", - "\n", - " Sf = Hf @ Pf @ Hf.T + Q\n", - "\n", - " return zp, Hv, Hf, Sf\n", - "\n", - "def add_new_lm(particle, z, Q):\n", - "\n", - " r = z[0]\n", - " b = z[1]\n", - " lm_id = int(z[2])\n", - "\n", - " s = math.sin(pi_2_pi(particle.yaw + b))\n", - " c = math.cos(pi_2_pi(particle.yaw + b))\n", - "\n", - " particle.lm[lm_id, 0] = particle.x + r * c\n", - " particle.lm[lm_id, 1] = particle.y + r * s\n", - "\n", - " # covariance\n", - " Gz = np.array([[c, -r * s],\n", - " [s, r * c]])\n", - "\n", - " particle.lmP[2 * lm_id:2 * lm_id + 2] = Gz @ Q @ Gz.T\n", - "\n", - " return particle\n", - "\n", - "def update_KF_with_cholesky(xf, Pf, v, Q, Hf):\n", - " PHt = Pf @ Hf.T\n", - " S = Hf @ PHt + Q\n", - "\n", - " S = (S + S.T) * 0.5\n", - " SChol = np.linalg.cholesky(S).T\n", - " SCholInv = np.linalg.inv(SChol)\n", - " W1 = PHt @ SCholInv\n", - " W = W1 @ SCholInv.T\n", - "\n", - " x = xf + W @ v\n", - " P = Pf - W1 @ W1.T\n", - "\n", - " return x, P\n", - "\n", - "def update_landmark(particle, z, Q):\n", - "\n", - " lm_id = int(z[2])\n", - " xf = np.array(particle.lm[lm_id, :]).reshape(2, 1)\n", - " Pf = np.array(particle.lmP[2 * lm_id:2 * lm_id + 2, :])\n", - "\n", - " zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q)\n", - "\n", - " dz = z[0:2].reshape(2, 1) - zp\n", - " dz[1, 0] = pi_2_pi(dz[1, 0])\n", - "\n", - " xf, Pf = update_KF_with_cholesky(xf, Pf, dz, Q, Hf)\n", - "\n", - " particle.lm[lm_id, :] = xf.T\n", - " particle.lmP[2 * lm_id:2 * lm_id + 2, :] = Pf\n", - "\n", - " return particle\n", - "\n", - "# END OF CODE SNIPPET #\n", - "\n", - "\n", - "\n", - "# Setting up the landmarks\n", - "RFID = np.array([[10.0, -2.0],\n", - " [15.0, 10.0]])\n", - "N_LM = RFID.shape[0]\n", - "\n", - "# Initialize 1 particle\n", - "N_PARTICLE = 1\n", - "particles = [Particle(N_LM) for i in range(N_PARTICLE)]\n", - "\n", - "xTrue = np.zeros((STATE_SIZE, 1))\n", - "xDR = np.zeros((STATE_SIZE, 1))\n", - "\n", - "print(\"initial weight\", particles[0].w)\n", - "\n", - "xTrue, z, _, ud = observation(xTrue, xDR, u, RFID)\n", - "# Initialize landmarks\n", - "particles = update_with_observation(particles, z)\n", - "print(\"weight after landmark intialization\", particles[0].w)\n", - "particles = update_with_observation(particles, z)\n", - "print(\"weight after update \", particles[0].w)\n", - "\n", - "particles[0].x = -10\n", - "particles = update_with_observation(particles, z)\n", - "print(\"weight after wrong prediction\", particles[0].w)\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 3- Resampling\n", - "\n", - "In the reseampling steps a new set of particles are chosen from the old set. This is done according to the weight of each particle. \n", - "\n", - "The figure shows 100 particles distributed uniformly between [-0.5, 0.5] with the weights of each particle distributed according to a Gaussian funciton. \n", - "\n", - "The resampling picks \n", - "\n", - "$i \\in 1,...,N$ particles with probability to pick particle with index $i ∝ \\omega_i$, where $\\omega_i$ is the weight of that particle\n", - "\n", - "\n", - "To get the intuition of the resampling step we will look at a set of particles which are initialized with a given x location and weight. After the resampling the particles are more concetrated in the location where they had the highest weights. This is also indicated by the indices \n" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# CODE SNIPPET #\n", - "def normalize_weight(particles):\n", - "\n", - " sumw = sum([p.w for p in particles])\n", - "\n", - " try:\n", - " for i in range(N_PARTICLE):\n", - " particles[i].w /= sumw\n", - " except ZeroDivisionError:\n", - " for i in range(N_PARTICLE):\n", - " particles[i].w = 1.0 / N_PARTICLE\n", - "\n", - " return particles\n", - "\n", - " return particles\n", - "\n", - "\n", - "def resampling(particles):\n", - " \"\"\"\n", - " low variance re-sampling\n", - " \"\"\"\n", - "\n", - " particles = normalize_weight(particles)\n", - "\n", - " pw = []\n", - " for i in range(N_PARTICLE):\n", - " pw.append(particles[i].w)\n", - "\n", - " pw = np.array(pw)\n", - "\n", - " Neff = 1.0 / (pw @ pw.T) # Effective particle number\n", - " # print(Neff)\n", - "\n", - " if Neff < NTH: # resampling\n", - " wcum = np.cumsum(pw)\n", - " base = np.cumsum(pw * 0.0 + 1 / N_PARTICLE) - 1 / N_PARTICLE\n", - " resampleid = base + np.random.rand(base.shape[0]) / N_PARTICLE\n", - "\n", - " inds = []\n", - " ind = 0\n", - " for ip in range(N_PARTICLE):\n", - " while ((ind < wcum.shape[0] - 1) and (resampleid[ip] > wcum[ind])):\n", - " ind += 1\n", - " inds.append(ind)\n", - "\n", - " tparticles = particles[:]\n", - " for i in range(len(inds)):\n", - " particles[i].x = tparticles[inds[i]].x\n", - " particles[i].y = tparticles[inds[i]].y\n", - " particles[i].yaw = tparticles[inds[i]].yaw\n", - " particles[i].w = 1.0 / N_PARTICLE\n", - "\n", - " return particles, inds\n", - "# END OF SNIPPET #\n", - "\n", - "\n", - "\n", - "def gaussian(x, mu, sig):\n", - " return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))\n", - "N_PARTICLE = 100\n", - "particles = [Particle(N_LM) for i in range(N_PARTICLE)]\n", - "x_pos = []\n", - "w = []\n", - "for i in range(N_PARTICLE):\n", - " particles[i].x = np.linspace(-0.5,0.5,N_PARTICLE)[i]\n", - " x_pos.append(particles[i].x)\n", - " particles[i].w = gaussian(i, N_PARTICLE/2, N_PARTICLE/20)\n", - " w.append(particles[i].w)\n", - " \n", - "\n", - "# Normalize weights\n", - "sw = sum(w)\n", - "for i in range(N_PARTICLE):\n", - " w[i] /= sw\n", - "\n", - "particles, new_indices = resampling(particles)\n", - "x_pos2 = []\n", - "for i in range(N_PARTICLE):\n", - " x_pos2.append(particles[i].x)\n", - " \n", - "# Plot results\n", - "fig, ((ax1,ax2,ax3)) = plt.subplots(nrows=3, ncols=1)\n", - "fig.tight_layout()\n", - "ax1.plot(x_pos,np.ones((N_PARTICLE,1)), '.r', markersize=2)\n", - "ax1.set_title(\"Particles before resampling\")\n", - "ax1.axis((-1, 1, 0, 2))\n", - "ax2.plot(w)\n", - "ax2.set_title(\"Weights distribution\")\n", - "ax3.plot(x_pos2,np.ones((N_PARTICLE,1)), '.r')\n", - "ax3.set_title(\"Particles after resampling\")\n", - "ax3.axis((-1, 1, 0, 2))\n", - "fig.subplots_adjust(hspace=0.8)\n", - "plt.show()\n", - "\n", - "plt.figure()\n", - "plt.hist(new_indices)\n", - "plt.xlabel(\"Particles indices to be resampled\")\n", - "plt.ylabel(\"# of time index is used\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "\n", - "http://www.probabilistic-robotics.org/\n", - "\n", - "http://ais.informatik.uni-freiburg.de/teaching/ws12/mapping/pdf/slam10-fastslam.pdf" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.5" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/SLAM/FastSLAM1/animation.png b/SLAM/FastSLAM1/animation.png deleted file mode 100644 index 86c2950f709e3a0b97fa7b5509ae9951b7f8e883..0000000000000000000000000000000000000000 GIT binary patch literal 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files -graphSLAM_formulation.* -!graphSLAM_formulation.tex diff --git a/SLAM/GraphBasedSLAM/LaTeX/graphSLAM.bib b/SLAM/GraphBasedSLAM/LaTeX/graphSLAM.bib deleted file mode 100644 index 4d3b71ae50c..00000000000 --- a/SLAM/GraphBasedSLAM/LaTeX/graphSLAM.bib +++ /dev/null @@ -1,30 +0,0 @@ -@article{blanco2010tutorial, - title={A tutorial on ${SE}(3)$ transformation parameterizations and on-manifold optimization}, - author={Blanco, Jose-Luis}, - journal={University of Malaga, Tech. Rep}, - volume={3}, - year={2010}, - publisher={Citeseer} -} - -@article{grisetti2010tutorial, - title={A tutorial on graph-based {SLAM}}, - author={Grisetti, Giorgio and Kummerle, Rainer and Stachniss, Cyrill and Burgard, Wolfram}, - journal={IEEE Intelligent Transportation Systems Magazine}, - volume={2}, - number={4}, - pages={31--43}, - year={2010}, - publisher={IEEE} -} - -@article{thrun2006graph, - title={The graph {SLAM} algorithm with applications to large-scale mapping of urban structures}, - author={Thrun, Sebastian and Montemerlo, Michael}, - journal={The International Journal of Robotics Research}, - volume={25}, - number={5-6}, - pages={403--429}, - year={2006}, - publisher={SAGE Publications} -} diff --git a/SLAM/GraphBasedSLAM/LaTeX/graphSLAM_formulation.tex b/SLAM/GraphBasedSLAM/LaTeX/graphSLAM_formulation.tex deleted file mode 100644 index 25f02cd3bde..00000000000 --- a/SLAM/GraphBasedSLAM/LaTeX/graphSLAM_formulation.tex +++ /dev/null @@ -1,175 +0,0 @@ -\documentclass{article} - -\usepackage{amsfonts} -\usepackage{amsmath,amssymb,amsfonts} -\usepackage{textcomp} -\usepackage{fullpage} -\usepackage{setspace} -\usepackage{float} -\usepackage{cite} -\usepackage{graphicx} -\usepackage{caption} -\usepackage{subcaption} -\usepackage[pdfborder={0 0 0}, pdfpagemode=UseNone, pdfstartview=FitH]{hyperref} - -\DeclareMathOperator*{\argmax}{arg\,max} -\DeclareMathOperator*{\argmin}{arg\,min} - -\def\keyterm{\textit} - -\newcommand{\transp}{{\scriptstyle{\mathsf{T}}}} - - - -\begin{document} - -\title{Graph SLAM Formulation} -\author{Jeff Irion} -\date{} - -\maketitle -\vspace{3em} - - -\section{Problem Formulation} - -Let a robot's trajectory through its environment be represented by a sequence of $N$ poses: $\mathbf{p}_1, \mathbf{p}_2, \ldots, \mathbf{p}_N$. Each pose lies on a manifold: $\mathbf{p}_i \in \mathcal{M}$. Simple examples of manifolds used in Graph SLAM include 1-D, 2-D, and 3-D space, i.e., $\mathbb{R}$, $\mathbb{R}^2$, and $\mathbb{R}^3$. These environments are \keyterm{rectilinear}, meaning that there is no concept of orientation. By contrast, in $SE(2)$ problem settings a robot's pose consists of its location in $\mathbb{R}^2$ and its orientation $\theta$. Similarly, in $SE(3)$ a robot's pose consists of its location in $\mathbb{R}^3$ and its orientation, which can be represented via Euler angles, quaternions, or $SO(3)$ rotation matrices. - -As the robot explores its environment, it collects a set of $M$ measurements $\mathcal{Z} = \{\mathbf{z}_j\}$. Examples of such measurements include odometry, GPS, and IMU data. Given a set of poses $\mathbf{p}_1, \ldots, \mathbf{p}_N$, we can compute the estimated measurement $\hat{\mathbf{z}}_j(\mathbf{p}_1, \ldots, \mathbf{p}_N)$. We can then compute the \keyterm{residual} $\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j)$ for measurement $j$. The formula for the residual depends on the type of measurement. As an example, let $\mathbf{z}_1$ be an odometry measurement that was collected when the robot traveled from $\mathbf{p}_1$ to $\mathbf{p}_2$. The expected measurement and the residual are computed as -% -\begin{align*} - \hat{\mathbf{z}}_1(\mathbf{p}_1, \mathbf{p}_2) &= \mathbf{p}_2 \ominus \mathbf{p}_1 \\ - \mathbf{e}_1(\mathbf{z}_1, \hat{\mathbf{z}}_1) &= \mathbf{z}_1 \ominus \hat{\mathbf{z}}_1 = \mathbf{z}_1 \ominus (\mathbf{p}_2 \ominus \mathbf{p}_1), -\end{align*} -% -where the $\ominus$ operator indicates inverse pose composition. We model measurement $\mathbf{z}_j$ as having independent Gaussian noise with zero mean and covariance matrix $\Omega_j^{-1}$; we refer to $\Omega_j$ as the \keyterm{information matrix} for measurement $j$. That is, -\begin{equation} - p(\mathbf{z}_j \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) = \eta_j \exp \left( (-\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^\transp \Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) \right), \label{eq:observation_probability} -\end{equation} -where $\eta_j$ is the normalization constant. - -The objective of Graph SLAM is to find the maximum likelihood set of poses given the measurements $\mathcal{Z} = \{\mathbf{z}_j\}$; in other words, we want to find -% -\begin{equation*} - \argmax_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) -\end{equation*} -% -Using Bayes' rule, we can write this probability as -% -\begin{align} - p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) &= \frac{p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) p(\mathbf{p}_1, \ldots, \mathbf{p}_N) }{ p(\mathcal{Z}) } \notag \\ - &\propto p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N), \label{eq:bayes} -\end{align} -% -since $p(\mathcal{Z})$ is a constant (albeit, an unknown constant) and we assume that $p(\mathbf{p}_1, \ldots, \mathbf{p}_N)$ is uniformly distributed \cite{thrun2006graph}. Therefore, we can use \eqref{eq:observation_probability} and \eqref{eq:bayes} to simplify the Graph SLAM optimization as follows: -% -\begin{align*} - \argmax_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) &= \argmax_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) \\ - &= \argmax_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \prod_{j=1}^M p(\mathbf{z}_j \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) \\ - &= \argmax_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \prod_{j=1}^M \exp \left( -(\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^\transp \Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) \right) \\ - &= \argmin_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \sum_{j=1}^M (\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^\transp \Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j). -\end{align*} -% -We define -% -\begin{equation*} - \chi^2 := \sum_{j=1}^M (\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^\transp \Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j), -\end{equation*} -% -and this is what we seek to minimize. - - -\section{Dimensionality and Pose Representation} - -Before proceeding further, it is helpful to discuss the dimensionality of the problem. We have: -\begin{itemize} - \item A set of $N$ poses $\mathbf{p}_1, \mathbf{p}_2, \ldots, \mathbf{p}_N$, where each pose lies on the manifold $\mathcal{M}$ - \begin{itemize} - \item Each pose $\mathbf{p}_i$ is represented as a vector in (a subset of) $\mathbb{R}^d$. For example: - \begin{itemize} - \item[$\circ$] An $SE(2)$ pose is typically represented as $(x, y, \theta)$, and thus $d = 3$. - \item[$\circ$] An $SE(3)$ pose is typically represented as $(x, y, z, q_x, q_y, q_z, q_w)$, where $(x, y, z)$ is a point in $\mathbb{R}^3$ and $(q_x, q_y, q_z, q_w)$ is a \keyterm{quaternion}, and so $d = 7$. For more information about $SE(3)$ parameterizations and pose transformations, see \cite{blanco2010tutorial}. - \end{itemize} - \item We also need to be able to represent each pose compactly as a vector in (a subset of) $\mathbb{R}^c$. - \begin{itemize} - \item[$\circ$] Since an $SE(2)$ pose has three degrees of freedom, the $(x, y, \theta)$ representation is again sufficient and $c=3$. - \item[$\circ$] An $SE(3)$ pose only has six degrees of freedom, and we can represent it compactly as $(x, y, z, q_x, q_y, q_z)$, and thus $c=6$. - \end{itemize} - \item We use the $\boxplus$ operator to indicate pose composition when one or both of the poses are represented compactly. The output can be a pose in $\mathcal{M}$ or a vector in $\mathbb{R}^c$, as required by context. - \end{itemize} - \item A set of $M$ measurements $\mathcal{Z} = \{\mathbf{z}_1, \mathbf{z}_2, \ldots, \mathbf{z}_M\}$ - \begin{itemize} - \item Each measurement's dimensionality can be unique, and we will use $\bullet$ to denote a ``wildcard'' variable. - \item Measurement $\mathbf{z}_j \in \mathbb{R}^\bullet$ has an associated information matrix $\Omega_j \in \mathbb{R}^{\bullet \times \bullet}$ and residual function $\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) = \mathbf{e}_j(\mathbf{z}_j, \mathbf{p}_1, \ldots, \mathbf{p}_N) \in \mathbb{R}^\bullet$. - \item A measurement could, in theory, constrain anywhere from 1 pose to all $N$ poses. In practice, each measurement usually constrains only 1 or 2 poses. - \end{itemize} -\end{itemize} - - -\section{Graph SLAM Algorithm} - -The ``Graph'' in Graph SLAM refers to the fact that we view the problem as a graph. The graph has a set $\mathcal{V}$ of $N$ vertices, where each vertex $v_i$ has an associated pose $\mathbf{p}_i$. Similarly, the graph has a set $\mathcal{E}$ of $M$ edges, where each edge $e_j$ has an associated measurement $\mathbf{z}_j$. In practice, the edges in this graph are either unary (i.e., a loop) or binary. (Note: $e_j$ refers to the edge in the graph associated with measurement $\mathbf{z}_j$, whereas $\mathbf{e}_j$ refers to the residual function associated with $\mathbf{z}_j$.) For more information about the Graph SLAM algorithm, see \cite{grisetti2010tutorial}. - -We want to optimize -% -\begin{equation*} - \chi^2 = \sum_{e_j \in \mathcal{E}} \mathbf{e}_j^\transp \Omega_j \mathbf{e}_j. -\end{equation*} -% -Let $\mathbf{x}_i \in \mathbb{R}^c$ be the compact representation of pose $\mathbf{p}_i \in \mathcal{M}$, and let -% -\begin{equation*} - \mathbf{x} := \begin{bmatrix} \mathbf{x}_1 \\ \mathbf{x}_2 \\ \vdots \\ \mathbf{x}_N \end{bmatrix} \in \mathbb{R}^{cN} -\end{equation*} -% -We will solve this optimization problem iteratively. Let -% -\begin{equation} - \mathbf{x}^{k+1} := \mathbf{x}^k \boxplus \Delta \mathbf{x}^k = \begin{bmatrix} \mathbf{x}_1 \boxplus \Delta \mathbf{x}_1 \\ \mathbf{x}_2 \boxplus \Delta \mathbf{x}_2 \\ \vdots \\ \mathbf{x}_N \boxplus \Delta \mathbf{x}_2 \end{bmatrix} \label{eq:update} -\end{equation} -% -The $\chi^2$ error at iteration $k+1$ is -\begin{equation} - \chi_{k+1}^2 = \sum_{e_j \in \mathcal{E}} \underbrace{\left[ \mathbf{e}_j(\mathbf{x}^{k+1}) \right]^\transp}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\mathbf{e}_j(\mathbf{x}^{k+1})}_{\bullet \times 1}. \label{eq:chisq_at_kplusone} -\end{equation} -% -We will linearize the residuals as: -% -\begin{align} - \mathbf{e}_j(\mathbf{x}^{k+1}) &= \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k) \notag \\ - &\approx \mathbf{e}_j(\mathbf{x}^{k}) + \frac{\partial}{\partial \Delta \mathbf{x}^k} \left[ \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k) \right] \Delta \mathbf{x}^k \notag \\ - &= \mathbf{e}_j(\mathbf{x}^{k}) + \left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right) \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \Delta \mathbf{x}^k. \label{eq:linearization} -\end{align} -% -Plugging \eqref{eq:linearization} into \eqref{eq:chisq_at_kplusone}, we get: -% -\small -\begin{align} - \chi_{k+1}^2 &\approx \ \ \ \ \ \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x}^k)]^\transp}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\mathbf{e}_j(\mathbf{x}^k)}_{\bullet \times 1} \notag \\ - &\hphantom{\approx} \ \ \ + \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x^k}) ]^\transp }_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \underbrace{\Delta \mathbf{x}^k}_{cN \times 1} \notag \\ - &\hphantom{\approx} \ \ \ + \sum_{e_j \in \mathcal{E}} \underbrace{(\Delta \mathbf{x}^k)^\transp}_{1 \times cN} \underbrace{ \left( \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \right)^\transp}_{cN \times dN} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)^\transp}_{dN \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \underbrace{\Delta \mathbf{x}^k}_{cN \times 1} \notag \\ - &= \chi_k^2 + 2 \mathbf{b}^\transp \Delta \mathbf{x}^k + (\Delta \mathbf{x}^k)^\transp H \Delta \mathbf{x}^k, \notag -\end{align} -\normalsize -% -where -% -\begin{align*} - \mathbf{b}^\transp &= \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x^k}) ]^\transp }_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \\ - H &= \sum_{e_j \in \mathcal{E}} \underbrace{ \left( \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \right)^\transp}_{cN \times dN} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)^\transp}_{dN \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN}. -\end{align*} -% -Using this notation, we obtain the optimal update as -% -\begin{equation} - \Delta \mathbf{x}^k = -H^{-1} \mathbf{b}. \label{eq:deltax} -\end{equation} -% -We apply this update to the poses via \eqref{eq:update} and repeat until convergence. - - - -\bibliographystyle{acm} -\bibliography{graphSLAM}{} - -\end{document} diff --git a/SLAM/GraphBasedSLAM/graphSLAM_SE2_example.ipynb b/SLAM/GraphBasedSLAM/graphSLAM_SE2_example.ipynb deleted file mode 100644 index cd3d9fd5dbd..00000000000 --- a/SLAM/GraphBasedSLAM/graphSLAM_SE2_example.ipynb +++ /dev/null @@ -1,332 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from graphslam.graph import Graph\n", - "from graphslam.load import load_g2o_se2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Introduction\n", - "\n", - "For a complete derivation of the Graph SLAM algorithm, please see [graphSLAM_formulation.pdf](./graphSLAM_formulation.pdf). \n", - "\n", - "This notebook illustrates the iterative optimization of a real-world $SE(2)$ dataset. The code can be found in the `graphslam` folder. For simplicity, numerical differentiation is used in lieu of analytic Jacobians. This code originated from the [python-graphslam](https://github.com/JeffLIrion/python-graphslam) repo, which is a full-featured Graph SLAM solver. The dataset in this example is used with permission from Luca Carlone and was downloaded from his [website](https://lucacarlone.mit.edu/datasets/). " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# The Dataset" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of edges: 1483\n", - "Number of vertices: 1228\n" - ] - } - ], - "source": [ - "g = load_g2o_se2(\"data/input_INTEL.g2o\")\n", - "\n", - "print(\"Number of edges: {}\".format(len(g._edges)))\n", - "print(\"Number of vertices: {}\".format(len(g._vertices)))" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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UhqCA2z4y3LCB6O23Wbbq358ng1lHUvIaH2zCk+qcNM3/TjiEX4ux9HIl5xTD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RpstvfdV/V9PP00ricqbH1fJyPiOuzxcKkiC4aLDrx8uh4uDpJJeniy8JHG8+35PCRVD2fMJiaa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\nnQRuCt4U4/PCC8pjvv/+9I97+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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "g.plot(title=r\"Original ($\\chi^2 = {:.0f}$)\".format(g.calc_chi2()))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Each edge in this dataset is a constraint that compares the measured $SE(2)$ transformation between two poses to the expected $SE(2)$ transformation between them, as computed using the current pose estimates. These edges can be classified into two categories:\n", - "\n", - "1. Odometry edges constrain two consecutive vertices, and the measurement for the $SE(2)$ transformation comes directly from odometry data.\n", - "2. Scan-matching edges constrain two non-consecutive vertices. These scan matches can be computed using, for example, 2-D LiDAR data or landmarks; the details of how these contstraints are determined is beyond the scope of this example. This is often referred to as *loop closure* in the Graph SLAM literature.\n", - "\n", - "We can easily parse out the two different types of edges present in this dataset and plot them." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "def parse_edges(g):\n", - " \"\"\"Split the graph `g` into two graphs, one with only odometry edges and the other with only scan-matching edges.\n", - "\n", - " Parameters\n", - " ----------\n", - " g : graphslam.graph.Graph\n", - " The input graph\n", - "\n", - " Returns\n", - " -------\n", - " g_odom : graphslam.graph.Graph\n", - " A graph consisting of the vertices and odometry edges from `g`\n", - " g_scan : graphslam.graph.Graph\n", - " A graph consisting of the vertices and scan-matching edges from `g`\n", - "\n", - " \"\"\"\n", - " edges_odom = []\n", - " edges_scan = []\n", - " \n", - " for e in g._edges:\n", - " if abs(e.vertex_ids[1] - e.vertex_ids[0]) == 1:\n", - " edges_odom.append(e)\n", - " else:\n", - " edges_scan.append(e)\n", - "\n", - " g_odom = Graph(edges_odom, g._vertices)\n", - " g_scan = Graph(edges_scan, g._vertices)\n", - "\n", - " return g_odom, g_scan" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of odometry edges: 1227\n", - "Number of scan-matching edges: 256\n", - "\n", - "χ^2 error from odometry edges: 0.232\n", - "χ^2 error from scan-matching edges: 7191686.151\n" - ] - } - ], - "source": [ - "g_odom, g_scan = parse_edges(g)\n", - "\n", - "print(\"Number of odometry edges: {:4d}\".format(len(g_odom._edges)))\n", - "print(\"Number of scan-matching edges: {:4d}\".format(len(g_scan._edges)))\n", - "\n", - "print(\"\\nχ^2 error from odometry edges: {:11.3f}\".format(g_odom.calc_chi2()))\n", - "print(\"χ^2 error from scan-matching edges: {:11.3f}\".format(g_scan.calc_chi2()))" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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yZfp370hhD5BKYf1hEiidfD04ZxyJwZUESmcPaMmkcsGJF7CoYjtevettcsoh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Jzn1WrGAcfP/+FC+rDMEgj9mtG7NgS0tFjjqKnHXffaw3q89br56lpVNdVFSI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\nFTs2RGNhsDdQwXa9ICp46ZiyZb7fH++ePWdmZ1MQUK/5nme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ILDMMDI1YvWlrqUU4hRsj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\nxzSUft/UxKy4xGIYd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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "g_scan.plot(title=\"Scan-matching edges\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Optimization\n", - "\n", - "Initially, the pose estimates are consistent with the collected odometry measurements, and the odometry edges contribute almost zero towards the $\\chi^2$ error. However, there are large discrepancies between the scan-matching constraints and the initial pose estimates. This is not surprising, since small errors in odometry readings that are propagated over time can lead to large errors in the robot's trajectory. What makes Graph SLAM effective is that it allows incorporation of multiple different data sources into a single optimization problem." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Iteration chi^2 rel. change\n", - "--------- ----- -----------\n", - " 0 7191686.3825\n", - " 1 320031728.8624 43.500234\n", - " 2 125083004.3299 -0.609154\n", - " 3 338155.9074 -0.997297\n", - " 4 735.1344 -0.997826\n", - " 5 215.8405 -0.706393\n", - " 6 215.8405 -0.000000\n" - ] - } - ], - "source": [ - "g.optimize()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "![Graph_SLAM_optimization.gif](images/Graph_SLAM_optimization.gif)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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+QwlrklvTY+kKDiCGkUoPMfvUmSSIMJAgXgdO5GmSgAF8bOzLPc553MVY0mm4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\nYCufSwnFn34SWfgPSyKmTxI1BHu2c2prj9V0Tzuysl+P4M7RiNJJKlu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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "g.plot(title=\"Optimized\")" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "χ^2 error from odometry edges: 142.189\n", - "χ^2 error from scan-matching edges: 73.652\n" - ] - } - ], - "source": [ - "print(\"\\nχ^2 error from odometry edges: {:7.3f}\".format(g_odom.calc_chi2()))\n", - "print(\"χ^2 error from scan-matching edges: {:7.3f}\".format(g_scan.calc_chi2()))" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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Wm4l+8IHIUUfpR+rEAbaeTZhm0Qyk3tCDryFDRP4T62Az4fXgG/y2Yl36ZnV1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\nPPQDW1yzVMP/7OjRkm00kmgI5lZkMPMO8ULnEcr7OzIYklYRcUxLXMO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kWku1JLBlLdUyAkd69hQ5q0dUPqFPXl1oqalpu0pZZQbtHWkLbO97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\nXvgUCWjQIb10hNcDHOIvddM6Jvn0CsVauqSGn8Gbb5K/qjT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z^A4^1Gkzc@7m9=)c4Rk@3ypT2D$RG=27Zj;fvjbcyLa1n+O@Z4PaY5ZEHIs!fuD&- zNBQaL)Ir1S;n+cpu$W6HfrcloTuMQgJ3^{rjVnTiZ0)N~(vMN@6~*GmUA8PXzD>5G z>wUjzxx9ut#+JNVt}_R%gMP9C`n-+}2MIAP%hTG>t^#>hhJ54n(_$B{QwN3KFa-JA z?<4c7fRat;lZ7> \bar{P_t}` then the Kalman gain will go to 0, +signaling a high trust in the process and little trust in the +measurement. + +The update is captured in the following. + +:math:`xUpdate = xEst + (K * y)` + +Of course, the covariance must also be updated as well to account for +the changing uncertainty. + +:math:`P_{t} = (I-K_tH_t)\bar{P_t}` + +.. code:: ipython3 + + def update(xEst, PEst, u, z, initP): + """ + Performs the update step of EKF SLAM + + :param xEst: nx1 the predicted pose of the system and the pose of the landmarks + :param PEst: nxn the predicted covariance + :param u: 2x1 the control function + :param z: the measurements read at new position + :param initP: 2x2 an identity matrix acting as the initial covariance + :returns: the updated state and covariance for the system + """ + for iz in range(len(z[:, 0])): # for each observation + minid = search_correspond_LM_ID(xEst, PEst, z[iz, 0:2]) # associate to a known landmark + + nLM = calc_n_LM(xEst) # number of landmarks we currently know about + + if minid == nLM: # Landmark is a NEW landmark + print("New LM") + # Extend state and covariance matrix + xAug = np.vstack((xEst, calc_LM_Pos(xEst, z[iz, :]))) + PAug = np.vstack((np.hstack((PEst, np.zeros((len(xEst), LM_SIZE)))), + np.hstack((np.zeros((LM_SIZE, len(xEst))), initP)))) + xEst = xAug + PEst = PAug + + lm = get_LM_Pos_from_state(xEst, minid) + y, S, H = calc_innovation(lm, xEst, PEst, z[iz, 0:2], minid) + + K = (PEst @ H.T) @ np.linalg.inv(S) # Calculate Kalman Gain + xEst = xEst + (K @ y) + PEst = (np.eye(len(xEst)) - (K @ H)) @ PEst + + xEst[2] = pi_2_pi(xEst[2]) + return xEst, PEst + + +.. code:: ipython3 + + def calc_innovation(lm, xEst, PEst, z, LMid): + """ + Calculates the innovation based on expected position and landmark position + + :param lm: landmark position + :param xEst: estimated position/state + :param PEst: estimated covariance + :param z: read measurements + :param LMid: landmark id + :returns: returns the innovation y, and the jacobian H, and S, used to calculate the Kalman Gain + """ + delta = lm - xEst[0:2] + q = (delta.T @ delta)[0, 0] + zangle = math.atan2(delta[1, 0], delta[0, 0]) - xEst[2, 0] + zp = np.array([[math.sqrt(q), pi_2_pi(zangle)]]) + # zp is the expected measurement based on xEst and the expected landmark position + + y = (z - zp).T # y = innovation + y[1] = pi_2_pi(y[1]) + + H = jacobH(q, delta, xEst, LMid + 1) + S = H @ PEst @ H.T + Cx[0:2, 0:2] + + return y, S, H + + def jacobH(q, delta, x, i): + """ + Calculates the jacobian of the measurement function + + :param q: the range from the system pose to the landmark + :param delta: the difference between a landmark position and the estimated system position + :param x: the state, including the estimated system position + :param i: landmark id + 1 + :returns: the jacobian H + """ + sq = math.sqrt(q) + G = np.array([[-sq * delta[0, 0], - sq * delta[1, 0], 0, sq * delta[0, 0], sq * delta[1, 0]], + [delta[1, 0], - delta[0, 0], - q, - delta[1, 0], delta[0, 0]]]) + + G = G / q + nLM = calc_n_LM(x) + F1 = np.hstack((np.eye(3), np.zeros((3, 2 * nLM)))) + F2 = np.hstack((np.zeros((2, 3)), np.zeros((2, 2 * (i - 1))), + np.eye(2), np.zeros((2, 2 * nLM - 2 * i)))) + + F = np.vstack((F1, F2)) + + H = G @ F + + return H + +Observation Step +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The observation step described here is outside the main EKF SLAM process +and is primarily used as a method of driving the simulation. The +observations function is in charge of calculating how the poses of the +robots change and accumulate error over time, and the theoretical +measurements that are expected as a result of each measurement. + +Observations are based on the TRUE position of the robot. Error in dead +reckoning and control functions are passed along here as well. + +.. code:: ipython3 + + def observation(xTrue, xd, u, RFID): + """ + :param xTrue: the true pose of the system + :param xd: the current noisy estimate of the system + :param u: the current control input + :param RFID: the true position of the landmarks + + :returns: Computes the true position, observations, dead reckoning (noisy) position, + and noisy control function + """ + xTrue = motion_model(xTrue, u) + + # add noise to gps x-y + z = np.zeros((0, 3)) + + for i in range(len(RFID[:, 0])): # Test all beacons, only add the ones we can see (within MAX_RANGE) + + dx = RFID[i, 0] - xTrue[0, 0] + dy = RFID[i, 1] - xTrue[1, 0] + d = math.sqrt(dx**2 + dy**2) + angle = pi_2_pi(math.atan2(dy, dx) - xTrue[2, 0]) + if d <= MAX_RANGE: + dn = d + np.random.randn() * Qsim[0, 0] # add noise + anglen = angle + np.random.randn() * Qsim[1, 1] # add noise + zi = np.array([dn, anglen, i]) + z = np.vstack((z, zi)) + + # add noise to input + ud = np.array([[ + u[0, 0] + np.random.randn() * Rsim[0, 0], + u[1, 0] + np.random.randn() * Rsim[1, 1]]]).T + + xd = motion_model(xd, ud) + return xTrue, z, xd, ud + +.. code:: ipython3 + + def calc_n_LM(x): + """ + Calculates the number of landmarks currently tracked in the state + :param x: the state + :returns: the number of landmarks n + """ + n = int((len(x) - STATE_SIZE) / LM_SIZE) + return n + + + def jacob_motion(x, u): + """ + Calculates the jacobian of motion model. + + :param x: The state, including the estimated position of the system + :param u: The control function + :returns: G: Jacobian + Fx: STATE_SIZE x (STATE_SIZE + 2 * num_landmarks) matrix where the left side is an identity matrix + """ + + # [eye(3) [0 x y; 0 x y; 0 x y]] + Fx = np.hstack((np.eye(STATE_SIZE), np.zeros( + (STATE_SIZE, LM_SIZE * calc_n_LM(x))))) + + jF = np.array([[0.0, 0.0, -DT * u[0] * math.sin(x[2, 0])], + [0.0, 0.0, DT * u[0] * math.cos(x[2, 0])], + [0.0, 0.0, 0.0]],dtype=object) + + G = np.eye(STATE_SIZE) + Fx.T @ jF @ Fx + if calc_n_LM(x) > 0: + print(Fx.shape) + return G, Fx, + + + + +.. code:: ipython3 + + def calc_LM_Pos(x, z): + """ + Calculates the pose in the world coordinate frame of a landmark at the given measurement. + + :param x: [x; y; theta] + :param z: [range; bearing] + :returns: [x; y] for given measurement + """ + zp = np.zeros((2, 1)) + + zp[0, 0] = x[0, 0] + z[0] * math.cos(x[2, 0] + z[1]) + zp[1, 0] = x[1, 0] + z[0] * math.sin(x[2, 0] + z[1]) + #zp[0, 0] = x[0, 0] + z[0, 0] * math.cos(x[2, 0] + z[0, 1]) + #zp[1, 0] = x[1, 0] + z[0, 0] * math.sin(x[2, 0] + z[0, 1]) + + return zp + + + def get_LM_Pos_from_state(x, ind): + """ + Returns the position of a given landmark + + :param x: The state containing all landmark positions + :param ind: landmark id + :returns: The position of the landmark + """ + lm = x[STATE_SIZE + LM_SIZE * ind: STATE_SIZE + LM_SIZE * (ind + 1), :] + + return lm + + + def search_correspond_LM_ID(xAug, PAug, zi): + """ + Landmark association with Mahalanobis distance. + + If this landmark is at least M_DIST_TH units away from all known landmarks, + it is a NEW landmark. + + :param xAug: The estimated state + :param PAug: The estimated covariance + :param zi: the read measurements of specific landmark + :returns: landmark id + """ + + nLM = calc_n_LM(xAug) + + mdist = [] + + for i in range(nLM): + lm = get_LM_Pos_from_state(xAug, i) + y, S, H = calc_innovation(lm, xAug, PAug, zi, i) + mdist.append(y.T @ np.linalg.inv(S) @ y) + + mdist.append(M_DIST_TH) # new landmark + + minid = mdist.index(min(mdist)) + + return minid + + def calc_input(): + v = 1.0 # [m/s] + yawrate = 0.1 # [rad/s] + u = np.array([[v, yawrate]]).T + return u + + def pi_2_pi(angle): + return (angle + math.pi) % (2 * math.pi) - math.pi + +.. code:: ipython3 + + def main(): + print(" start!!") + + time = 0.0 + + # RFID positions [x, y] + RFID = np.array([[10.0, -2.0], + [15.0, 10.0], + [3.0, 15.0], + [-5.0, 20.0]]) + + # State Vector [x y yaw v]' + xEst = np.zeros((STATE_SIZE, 1)) + xTrue = np.zeros((STATE_SIZE, 1)) + PEst = np.eye(STATE_SIZE) + + xDR = np.zeros((STATE_SIZE, 1)) # Dead reckoning + + # history + hxEst = xEst + hxTrue = xTrue + hxDR = xTrue + + while SIM_TIME >= time: + time += DT + u = calc_input() + + xTrue, z, xDR, ud = observation(xTrue, xDR, u, RFID) + + xEst, PEst = ekf_slam(xEst, PEst, ud, z) + + x_state = xEst[0:STATE_SIZE] + + # store data history + hxEst = np.hstack((hxEst, x_state)) + hxDR = np.hstack((hxDR, xDR)) + hxTrue = np.hstack((hxTrue, xTrue)) + + if show_animation: # pragma: no cover + plt.cla() + + plt.plot(RFID[:, 0], RFID[:, 1], "*k") + plt.plot(xEst[0], xEst[1], ".r") + + # plot landmark + for i in range(calc_n_LM(xEst)): + plt.plot(xEst[STATE_SIZE + i * 2], + xEst[STATE_SIZE + i * 2 + 1], "xg") + + plt.plot(hxTrue[0, :], + hxTrue[1, :], "-b") + plt.plot(hxDR[0, :], + hxDR[1, :], "-k") + plt.plot(hxEst[0, :], + hxEst[1, :], "-r") + plt.axis("equal") + plt.grid(True) + plt.pause(0.001) + +.. code:: ipython3 + + %matplotlib notebook + main() + + +.. parsed-literal:: + + start!! + New LM + New LM + New LM + +.. image:: ekf_slam_files/ekf_slam_1_0.png + +References: +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +- `PROBABILISTIC ROBOTICS`_ + +.. _PROBABILISTIC ROBOTICS: http://www.probabilistic-robotics.org/ + +.. |4| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/EKFSLAM/animation.gif diff --git a/SLAM/EKFSLAM/animation.png b/docs/modules/slam/ekf_slam_files/ekf_slam_1_0.png similarity index 100% rename from SLAM/EKFSLAM/animation.png rename to docs/modules/slam/ekf_slam_files/ekf_slam_1_0.png diff --git a/docs/modules/slam/graphSLAM_SE2_example.rst b/docs/modules/slam/graphSLAM_SE2_example.rst new file mode 100644 index 00000000000..bcc797ba3ec --- /dev/null +++ b/docs/modules/slam/graphSLAM_SE2_example.rst @@ -0,0 +1,209 @@ +Graph SLAM for a real-world SE(2) dataset +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. code:: ipython3 + + from graphslam.graph import Graph + from graphslam.load import load_g2o_se2 + +Introduction +^^^^^^^^^^^^ + +For a complete derivation of the Graph SLAM algorithm, please see +`Graph SLAM Formulation`_. + +This notebook illustrates the iterative optimization of a real-world +:math:`SE(2)` dataset. The code can be found in the ``graphslam`` +folder. For simplicity, numerical differentiation is used in lieu of +analytic Jacobians. This code originated from the +`python-graphslam `__ +repo, which is a full-featured Graph SLAM solver. The dataset in this +example is used with permission from Luca Carlone and was downloaded +from his `website `__. + +The Dataset +^^^^^^^^^^^^ + +.. code:: ipython3 + + g = load_g2o_se2("data/input_INTEL.g2o") + + print("Number of edges: {}".format(len(g._edges))) + print("Number of vertices: {}".format(len(g._vertices))) + + +.. parsed-literal:: + + Number of edges: 1483 + Number of vertices: 1228 + + +.. code:: ipython3 + + g.plot(title=r"Original ($\chi^2 = {:.0f}$)".format(g.calc_chi2())) + + + +.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_4_0.png + + +Each edge in this dataset is a constraint that compares the measured +:math:`SE(2)` transformation between two poses to the expected +:math:`SE(2)` transformation between them, as computed using the current +pose estimates. These edges can be classified into two categories: + +1. Odometry edges constrain two consecutive vertices, and the + measurement for the :math:`SE(2)` transformation comes directly from + odometry data. +2. Scan-matching edges constrain two non-consecutive vertices. These + scan matches can be computed using, for example, 2-D LiDAR data or + landmarks; the details of how these constraints are determined is + beyond the scope of this example. This is often referred to as *loop + closure* in the Graph SLAM literature. + +We can easily parse out the two different types of edges present in this +dataset and plot them. + +.. code:: ipython3 + + def parse_edges(g): + """Split the graph `g` into two graphs, one with only odometry edges and the other with only scan-matching edges. + + Parameters + ---------- + g : graphslam.graph.Graph + The input graph + + Returns + ------- + g_odom : graphslam.graph.Graph + A graph consisting of the vertices and odometry edges from `g` + g_scan : graphslam.graph.Graph + A graph consisting of the vertices and scan-matching edges from `g` + + """ + edges_odom = [] + edges_scan = [] + + for e in g._edges: + if abs(e.vertex_ids[1] - e.vertex_ids[0]) == 1: + edges_odom.append(e) + else: + edges_scan.append(e) + + g_odom = Graph(edges_odom, g._vertices) + g_scan = Graph(edges_scan, g._vertices) + + return g_odom, g_scan + +.. code:: ipython3 + + g_odom, g_scan = parse_edges(g) + + print("Number of odometry edges: {:4d}".format(len(g_odom._edges))) + print("Number of scan-matching edges: {:4d}".format(len(g_scan._edges))) + + print("\nχ^2 error from odometry edges: {:11.3f}".format(g_odom.calc_chi2())) + print("χ^2 error from scan-matching edges: {:11.3f}".format(g_scan.calc_chi2())) + + +.. parsed-literal:: + + Number of odometry edges: 1227 + Number of scan-matching edges: 256 + + χ^2 error from odometry edges: 0.232 + χ^2 error from scan-matching edges: 7191686.151 + + +.. code:: ipython3 + + g_odom.plot(title="Odometry edges") + + + +.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_8_0.png + + +.. code:: ipython3 + + g_scan.plot(title="Scan-matching edges") + + + +.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_9_0.png + + +Optimization +^^^^^^^^^^^^ + +Initially, the pose estimates are consistent with the collected odometry +measurements, and the odometry edges contribute almost zero towards the +:math:`\chi^2` error. However, there are large discrepancies between the +scan-matching constraints and the initial pose estimates. This is not +surprising, since small errors in odometry readings that are propagated +over time can lead to large errors in the robot’s trajectory. What makes +Graph SLAM effective is that it allows incorporation of multiple +different data sources into a single optimization problem. + +.. code:: ipython3 + + g.optimize() + + +.. parsed-literal:: + + + Iteration chi^2 rel. change + --------- ----- ----------- + 0 7191686.3825 + 1 320031728.8624 43.500234 + 2 125083004.3299 -0.609154 + 3 338155.9074 -0.997297 + 4 735.1344 -0.997826 + 5 215.8405 -0.706393 + 6 215.8405 -0.000000 + + +.. figure:: graphSLAM_SE2_example_files/Graph_SLAM_optimization.gif + :alt: Graph_SLAM_optimization.gif + +.. code:: ipython3 + + g.plot(title="Optimized") + + + +.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_13_0.png + + +.. code:: ipython3 + + print("\nχ^2 error from odometry edges: {:7.3f}".format(g_odom.calc_chi2())) + print("χ^2 error from scan-matching edges: {:7.3f}".format(g_scan.calc_chi2())) + + +.. parsed-literal:: + + + χ^2 error from odometry edges: 142.189 + χ^2 error from scan-matching edges: 73.652 + + +.. code:: ipython3 + + g_odom.plot(title="Odometry edges") + + + +.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_15_0.png + + +.. code:: ipython3 + + g_scan.plot(title="Scan-matching edges") + + + +.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_16_0.png + diff --git a/SLAM/GraphBasedSLAM/images/Graph_SLAM_optimization.gif b/docs/modules/slam/graphSLAM_SE2_example_files/Graph_SLAM_optimization.gif similarity index 100% rename from SLAM/GraphBasedSLAM/images/Graph_SLAM_optimization.gif rename to docs/modules/slam/graphSLAM_SE2_example_files/Graph_SLAM_optimization.gif diff --git a/docs/modules/slam/graphSLAM_SE2_example_files/graphSLAM_SE2_example_13_0.png b/docs/modules/slam/graphSLAM_SE2_example_files/graphSLAM_SE2_example_13_0.png new file mode 100644 index 0000000000000000000000000000000000000000..a3fca366e4ef37bceaac5cc1e45a987bbd2d8252 GIT binary patch literal 32748 zcmY(q1yEc~&@PMyhu{PWu((@rcZc8(!GkRBPVnIFkN}IjyZa)+-QC^o?)!c9-&_CG 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b/docs/modules/slam/graphSLAM_doc.rst @@ -0,0 +1,557 @@ + +Graph SLAM +~~~~~~~~~~~~ + +.. code:: ipython3 + + import copy + import math + import itertools + import numpy as np + import matplotlib.pyplot as plt + from graph_based_slam import calc_rotational_matrix, calc_jacobian, cal_observation_sigma, \ + calc_input, observation, motion_model, Edge, pi_2_pi + + %matplotlib inline + np.set_printoptions(precision=3, suppress=True) + np.random.seed(0) + +Introduction +^^^^^^^^^^^^ + +In contrast to the probabilistic approaches for solving SLAM, such as +EKF, UKF, particle filters, and so on, the graph technique formulates +the SLAM as an optimization problem. It is mostly used to solve the full +SLAM problem in an offline fashion, i.e. optimize all the poses of the +robot after the path has been traversed. However, some variants are +available that uses graph-based approaches to perform online estimation +or to solve for a subset of the poses. + +GraphSLAM uses the motion information as well as the observations of the +environment to create least square problem that can be solved using +standard optimization techniques. + +Minimal Example +^^^^^^^^^^^^^^^ + +The following example illustrates the main idea behind graphSLAM. A +simple case of a 1D robot is considered that can only move in 1 +direction. The robot is commanded to move forward with a control input +:math:`u_t=1`, however, the motion is not perfect and the measured +odometry will deviate from the true path. At each time step the robot can +observe its environment, for this simple case as well, there is only a +single landmark at coordinates :math:`x=3`. The measured observations +are the range between the robot and landmark. These measurements are +also subjected to noise. No bearing information is required since this +is a 1D problem. + +To solve this, graphSLAM creates what is called as the system +information matrix :math:`\Omega` also referred to as :math:`H` and the +information vector :math:`\xi` also known as :math:`b`. The entries are +created based on the information of the motion and the observation. + +.. code:: ipython3 + + R = 0.2 + Q = 0.2 + N = 3 + graphics_radius = 0.1 + + odom = np.empty((N,1)) + obs = np.empty((N,1)) + x_true = np.empty((N,1)) + + landmark = 3 + # Simulated readings of odometry and observations + x_true[0], odom[0], obs[0] = 0.0, 0.0, 2.9 + x_true[1], odom[1], obs[1] = 1.0, 1.5, 2.0 + x_true[2], odom[2], obs[2] = 2.0, 2.4, 1.0 + + hxDR = copy.deepcopy(odom) + # Visualization + plt.plot(landmark,0, '*k', markersize=30) + for i in range(N): + plt.plot(odom[i], 0, '.', markersize=50, alpha=0.8, color='steelblue') + plt.plot([odom[i], odom[i] + graphics_radius], + [0,0], 'r') + plt.text(odom[i], 0.02, "X_{}".format(i), fontsize=12) + plt.plot(obs[i]+odom[i],0,'.', markersize=25, color='brown') + plt.plot(x_true[i],0,'.g', markersize=20) + plt.grid() + plt.show() + + + # Defined as a function to facilitate iteration + def get_H_b(odom, obs): + """ + Create the information matrix and information vector. This implementation is + based on the concept of virtual measurement i.e. the observations of the + landmarks are converted into constraints (edges) between the nodes that + have observed this landmark. + """ + measure_constraints = {} + omegas = {} + zids = list(itertools.combinations(range(N),2)) + H = np.zeros((N,N)) + b = np.zeros((N,1)) + for (t1, t2) in zids: + x1 = odom[t1] + x2 = odom[t2] + z1 = obs[t1] + z2 = obs[t2] + + # Adding virtual measurement constraint + measure_constraints[(t1,t2)] = (x2-x1-z1+z2) + omegas[(t1,t2)] = (1 / (2*Q)) + + # populate system's information matrix and vector + H[t1,t1] += omegas[(t1,t2)] + H[t2,t2] += omegas[(t1,t2)] + H[t2,t1] -= omegas[(t1,t2)] + H[t1,t2] -= omegas[(t1,t2)] + + b[t1] += omegas[(t1,t2)] * measure_constraints[(t1,t2)] + b[t2] -= omegas[(t1,t2)] * measure_constraints[(t1,t2)] + + return H, b + + + H, b = get_H_b(odom, obs) + print("The determinant of H: ", np.linalg.det(H)) + H[0,0] += 1 # np.inf ? + print("The determinant of H after anchoring constraint: ", np.linalg.det(H)) + + for i in range(5): + H, b = get_H_b(odom, obs) + H[(0,0)] += 1 + + # Recover the posterior over the path + dx = np.linalg.inv(H) @ b + odom += dx + # repeat till convergence + print("Running graphSLAM ...") + print("Odometry values after optimzation: \n", odom) + + plt.figure() + plt.plot(x_true, np.zeros(x_true.shape), '.', markersize=20, label='Ground truth') + plt.plot(odom, np.zeros(x_true.shape), '.', markersize=20, label='Estimation') + plt.plot(hxDR, np.zeros(x_true.shape), '.', markersize=20, label='Odom') + plt.legend() + plt.grid() + plt.show() + + + +.. image:: graphSLAM_doc_files/graphSLAM_doc_2_0.png + + +.. parsed-literal:: + + The determinant of H: 0.0 + The determinant of H after anchoring constraint: 18.750000000000007 + Running graphSLAM ... + Odometry values after optimzation: + [[-0. ] + [ 0.9] + [ 1.9]] + + + +.. image:: graphSLAM_doc_files/graphSLAM_doc_2_2.png + + +In particular, the tasks are split into 2 parts, graph construction, and +graph optimization. ### Graph Construction + +Firstly the nodes are defined +:math:`\boldsymbol{x} = \boldsymbol{x}_{1:n}` such that each node is the +pose of the robot at time :math:`t_i` Secondly, the edges i.e. the +constraints, are constructed according to the following conditions: + +- robot moves from :math:`\boldsymbol{x}_i` to + :math:`\boldsymbol{x}_j`. This edge corresponds to the odometry + measurement. Relative motion constraints (Not included in the + previous minimal example). +- Measurement constraints, this can be done in two ways: + + - The information matrix is set in such a way that it includes the + landmarks in the map as well. Then the constraints can be entered + in a straightforward fashion between a node + :math:`\boldsymbol{x}_i` and some landmark :math:`m_k` + - Through creating a virtual measurement among all the node that + have observed the same landmark. More concretely, robot observes + the same landmark from :math:`\boldsymbol{x}_i` and + :math:`\boldsymbol{x}_j`. Relative measurement constraint. The + “virtual measurement” :math:`\boldsymbol{z}_{ij}`, which is the + estimated pose of :math:`\boldsymbol{x}_j` as seen from the node + :math:`\boldsymbol{x}_i`. The virtual measurement can then be + entered in the information matrix and vector in a similar fashion + to the motion constraints. + +An edge is fully characterized by the values of the error (entry to +information vector) and the local information matrix (entry to the +system’s information vector). The larger the local information matrix +(lower :math:`Q` or :math:`R`) the values that this edge will contribute +with. + +Important Notes: + +- The addition to the information matrix and vector are added to the + earlier values. +- In the case of 2D robot, the constraints will be non-linear, + therefore, a Jacobian of the error w.r.t the states is needed when + updated :math:`H` and :math:`b`. +- The anchoring constraint is needed in order to avoid having a + singular information matri. + +Graph Optimization +^^^^^^^^^^^^^^^^^^ + +The result from this formulation yields an overdetermined system of +equations. The goal after constructing the graph is to find: +:math:`x^*=\underset{x}{\mathrm{argmin}}~\underset{ij}\Sigma~f(e_{ij})`, +where :math:`f` is some error function that depends on the edges between +to related nodes :math:`i` and :math:`j`. The derivation in the references +arrive at the solution for :math:`x^* = H^{-1}b` + +Planar Example: +^^^^^^^^^^^^^^^ + +Now we will go through an example with a more realistic case of a 2D +robot with 3DoF, namely, :math:`[x, y, \theta]^T` + +.. code:: ipython3 + + # Simulation parameter + Qsim = np.diag([0.01, np.deg2rad(0.010)])**2 # error added to range and bearing + Rsim = np.diag([0.1, np.deg2rad(1.0)])**2 # error added to [v, w] + + DT = 2.0 # time tick [s] + SIM_TIME = 100.0 # simulation time [s] + MAX_RANGE = 30.0 # maximum observation range + STATE_SIZE = 3 # State size [x,y,yaw] + + # TODO: Why not use Qsim ? + # Covariance parameter of Graph Based SLAM + C_SIGMA1 = 0.1 + C_SIGMA2 = 0.1 + C_SIGMA3 = np.deg2rad(1.0) + + MAX_ITR = 20 # Maximum iteration during optimization + timesteps = 1 + + # consider only 2 landmarks for simplicity + # RFID positions [x, y, yaw] + RFID = np.array([[10.0, -2.0, 0.0], + # [15.0, 10.0, 0.0], + # [3.0, 15.0, 0.0], + # [-5.0, 20.0, 0.0], + # [-5.0, 5.0, 0.0] + ]) + + # State Vector [x y yaw v]' + xTrue = np.zeros((STATE_SIZE, 1)) + xDR = np.zeros((STATE_SIZE, 1)) # Dead reckoning + xTrue[2] = np.deg2rad(45) + xDR[2] = np.deg2rad(45) + # history initial values + hxTrue = xTrue + hxDR = xTrue + _, z, _, _ = observation(xTrue, xDR, np.array([[0,0]]).T, RFID) + hz = [z] + + for i in range(timesteps): + u = calc_input() + xTrue, z, xDR, ud = observation(xTrue, xDR, u, RFID) + hxDR = np.hstack((hxDR, xDR)) + hxTrue = np.hstack((hxTrue, xTrue)) + hz.append(z) + + # visualize + graphics_radius = 0.3 + plt.plot(RFID[:, 0], RFID[:, 1], "*k", markersize=20) + plt.plot(hxDR[0, :], hxDR[1, :], '.', markersize=50, alpha=0.8, label='Odom') + plt.plot(hxTrue[0, :], hxTrue[1, :], '.', markersize=20, alpha=0.6, label='X_true') + + for i in range(hxDR.shape[1]): + x = hxDR[0, i] + y = hxDR[1, i] + yaw = hxDR[2, i] + plt.plot([x, x + graphics_radius * np.cos(yaw)], + [y, y + graphics_radius * np.sin(yaw)], 'r') + d = hz[i][:, 0] + angle = hz[i][:, 1] + plt.plot([x + d * np.cos(angle + yaw)], [y + d * np.sin(angle + yaw)], '.', + markersize=20, alpha=0.7) + plt.legend() + plt.grid() + plt.show() + + + +.. image:: graphSLAM_doc_files/graphSLAM_doc_4_0.png + + +.. code:: ipython3 + + # Copy the data to have a consistent naming with the .py file + zlist = copy.deepcopy(hz) + x_opt = copy.deepcopy(hxDR) + xlist = copy.deepcopy(hxDR) + number_of_nodes = x_opt.shape[1] + n = number_of_nodes * STATE_SIZE + +After the data has been saved, the graph will be constructed by looking +at each pair for nodes. The virtual measurement is only created if two +nodes have observed the same landmark at different points in time. The +next cells are a walk through for a single iteration of graph +construction -> optimization -> estimate update. + +.. code:: ipython3 + + # get all the possible combination of the different node + zids = list(itertools.combinations(range(len(zlist)), 2)) + print("Node combinations: \n", zids) + + for i in range(xlist.shape[1]): + print("Node {} observed landmark with ID {}".format(i, zlist[i][0, 3])) + + +.. parsed-literal:: + + Node combinations: + [(0, 1)] + Node 0 observed landmark with ID 0.0 + Node 1 observed landmark with ID 0.0 + + +In the following code snippet the error based on the virtual measurement +between node 0 and 1 will be created. The equations for the error is as follows: +:math:`e_{ij}^x = x_j + d_j cos(\psi_j +\theta_j) - x_i - d_i cos(\psi_i + \theta_i)` + +:math:`e_{ij}^y = y_j + d_j sin(\psi_j + \theta_j) - y_i - d_i sin(\psi_i + \theta_i)` + +:math:`e_{ij}^x = \psi_j + \theta_j - \psi_i - \theta_i` + +Where :math:`[x_i, y_i, \psi_i]` is the pose for node :math:`i` and +similarly for node :math:`j`, :math:`d` is the measured distance at +nodes :math:`i` and :math:`j`, and :math:`\theta` is the measured +bearing to the landmark. The difference is visualized with the figure in +the next cell. + +In case of perfect motion and perfect measurement the error shall be +zero since :math:`x_j + d_j cos(\psi_j + \theta_j)` should equal +:math:`x_i + d_i cos(\psi_i + \theta_i)` + +.. code:: ipython3 + + # Initialize edges list + edges = [] + + # Go through all the different combinations + for (t1, t2) in zids: + x1, y1, yaw1 = xlist[0, t1], xlist[1, t1], xlist[2, t1] + x2, y2, yaw2 = xlist[0, t2], xlist[1, t2], xlist[2, t2] + + # All nodes have valid observation with ID=0, therefore, no data association condition + iz1 = 0 + iz2 = 0 + + d1 = zlist[t1][iz1, 0] + angle1, phi1 = zlist[t1][iz1, 1], zlist[t1][iz1, 2] + d2 = zlist[t2][iz2, 0] + angle2, phi2 = zlist[t2][iz2, 1], zlist[t2][iz2, 2] + + # find angle between observation and horizontal + tangle1 = pi_2_pi(yaw1 + angle1) + tangle2 = pi_2_pi(yaw2 + angle2) + + # project the observations + tmp1 = d1 * math.cos(tangle1) + tmp2 = d2 * math.cos(tangle2) + tmp3 = d1 * math.sin(tangle1) + tmp4 = d2 * math.sin(tangle2) + + edge = Edge() + print(y1,y2, tmp3, tmp4) + # calculate the error of the virtual measurement + # node 1 as seen from node 2 throught the observations 1,2 + edge.e[0, 0] = x2 - x1 - tmp1 + tmp2 + edge.e[1, 0] = y2 - y1 - tmp3 + tmp4 + edge.e[2, 0] = pi_2_pi(yaw2 - yaw1 - tangle1 + tangle2) + + edge.d1, edge.d2 = d1, d2 + edge.yaw1, edge.yaw2 = yaw1, yaw2 + edge.angle1, edge.angle2 = angle1, angle2 + edge.id1, edge.id2 = t1, t2 + + edges.append(edge) + + print("For nodes",(t1,t2)) + print("Added edge with errors: \n", edge.e) + + # Visualize measurement projections + plt.plot(RFID[0, 0], RFID[0, 1], "*k", markersize=20) + plt.plot([x1,x2],[y1,y2], '.', markersize=50, alpha=0.8) + plt.plot([x1, x1 + graphics_radius * np.cos(yaw1)], + [y1, y1 + graphics_radius * np.sin(yaw1)], 'r') + plt.plot([x2, x2 + graphics_radius * np.cos(yaw2)], + [y2, y2 + graphics_radius * np.sin(yaw2)], 'r') + + plt.plot([x1,x1+tmp1], [y1,y1], label="obs 1 x") + plt.plot([x2,x2+tmp2], [y2,y2], label="obs 2 x") + plt.plot([x1,x1], [y1,y1+tmp3], label="obs 1 y") + plt.plot([x2,x2], [y2,y2+tmp4], label="obs 2 y") + plt.plot(x1+tmp1, y1+tmp3, 'o') + plt.plot(x2+tmp2, y2+tmp4, 'o') + plt.legend() + plt.grid() + plt.show() + + +.. parsed-literal:: + + 0.0 1.427649841628278 -2.0126109674819155 -3.524048014922737 + For nodes (0, 1) + Added edge with errors: + [[-0.02 ] + [-0.084] + [ 0. ]] + + + +.. image:: graphSLAM_doc_files/graphSLAM_doc_9_1.png + + +Since the constraints equations derived before are non-linear, +linearization is needed before we can insert them into the information +matrix and information vector. Two jacobians + +:math:`A = \frac{\partial e_{ij}}{\partial \boldsymbol{x}_i}` as +:math:`\boldsymbol{x}_i` holds the three variabls x, y, and theta. +Similarly, :math:`B = \frac{\partial e_{ij}}{\partial \boldsymbol{x}_j}` + +.. code:: ipython3 + + # Initialize the system information matrix and information vector + H = np.zeros((n, n)) + b = np.zeros((n, 1)) + x_opt = copy.deepcopy(hxDR) + + for edge in edges: + id1 = edge.id1 * STATE_SIZE + id2 = edge.id2 * STATE_SIZE + + t1 = edge.yaw1 + edge.angle1 + A = np.array([[-1.0, 0, edge.d1 * math.sin(t1)], + [0, -1.0, -edge.d1 * math.cos(t1)], + [0, 0, -1.0]]) + + t2 = edge.yaw2 + edge.angle2 + B = np.array([[1.0, 0, -edge.d2 * math.sin(t2)], + [0, 1.0, edge.d2 * math.cos(t2)], + [0, 0, 1.0]]) + + # TODO: use Qsim instead of sigma + sigma = np.diag([C_SIGMA1, C_SIGMA2, C_SIGMA3]) + Rt1 = calc_rotational_matrix(tangle1) + Rt2 = calc_rotational_matrix(tangle2) + edge.omega = np.linalg.inv(Rt1 @ sigma @ Rt1.T + Rt2 @ sigma @ Rt2.T) + + # Fill in entries in H and b + H[id1:id1 + STATE_SIZE, id1:id1 + STATE_SIZE] += A.T @ edge.omega @ A + H[id1:id1 + STATE_SIZE, id2:id2 + STATE_SIZE] += A.T @ edge.omega @ B + H[id2:id2 + STATE_SIZE, id1:id1 + STATE_SIZE] += B.T @ edge.omega @ A + H[id2:id2 + STATE_SIZE, id2:id2 + STATE_SIZE] += B.T @ edge.omega @ B + + b[id1:id1 + STATE_SIZE] += (A.T @ edge.omega @ edge.e) + b[id2:id2 + STATE_SIZE] += (B.T @ edge.omega @ edge.e) + + + print("The determinant of H: ", np.linalg.det(H)) + plt.figure() + plt.subplot(1,2,1) + plt.imshow(H, extent=[0, n, 0, n]) + plt.subplot(1,2,2) + plt.imshow(b, extent=[0, 1, 0, n]) + plt.show() + + # Fix the origin, multiply by large number gives same results but better visualization + H[0:STATE_SIZE, 0:STATE_SIZE] += np.identity(STATE_SIZE) + print("The determinant of H after origin constraint: ", np.linalg.det(H)) + plt.figure() + plt.subplot(1,2,1) + plt.imshow(H, extent=[0, n, 0, n]) + plt.subplot(1,2,2) + plt.imshow(b, extent=[0, 1, 0, n]) + plt.show() + + +.. parsed-literal:: + + The determinant of H: 0.0 + The determinant of H after origin constraint: 716.1972439134893 + + + +.. image:: graphSLAM_doc_files/graphSLAM_doc_11_1.png + + + +.. image:: graphSLAM_doc_files/graphSLAM_doc_11_2.png + + +.. code:: ipython3 + + # Find the solution (first iteration) + dx = - np.linalg.inv(H) @ b + for i in range(number_of_nodes): + x_opt[0:3, i] += dx[i * 3:i * 3 + 3, 0] + print("dx: \n",dx) + print("ground truth: \n ",hxTrue) + print("Odom: \n", hxDR) + print("SLAM: \n", x_opt) + + # performance will improve with more iterations, nodes and landmarks. + print("\ngraphSLAM localization error: ", np.sum((x_opt - hxTrue) ** 2)) + print("Odom localization error: ", np.sum((hxDR - hxTrue) ** 2)) + + +.. parsed-literal:: + + dx: + [[-0. ] + [-0. ] + [ 0. ] + [ 0.02 ] + [ 0.084] + [-0. ]] + ground truth: + [[0. 1.414] + [0. 1.414] + [0.785 0.985]] + Odom: + [[0. 1.428] + [0. 1.428] + [0.785 0.976]] + SLAM: + [[-0. 1.448] + [-0. 1.512] + [ 0.785 0.976]] + + graphSLAM localization error: 0.010729072751057656 + Odom localization error: 0.0004460978857535104 + + +The references: +^^^^^^^^^^^^^^^ + +- http://robots.stanford.edu/papers/thrun.graphslam.pdf + +- http://ais.informatik.uni-freiburg.de/teaching/ss13/robotics/slides/16-graph-slam.pdf + +- http://www2.informatik.uni-freiburg.de/~stachnis/pdf/grisetti10titsmag.pdf + +N.B. An additional step is required that uses the estimated path to +update the belief regarding the map. + diff --git a/docs/modules/slam/graphSLAM_formulation.rst b/docs/modules/slam/graphSLAM_formulation.rst new file mode 100644 index 00000000000..c673bdcbfbe --- /dev/null +++ b/docs/modules/slam/graphSLAM_formulation.rst @@ -0,0 +1,216 @@ +.. _Graph SLAM Formulation: + +Graph SLAM Formulation +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Author Jeff Irion + +Problem Formulation +^^^^^^^^^^^^^^^^^^^ + +Let a robot’s trajectory through its environment be represented by a +sequence of :math:`N` poses: +:math:`\mathbf{p}_1, \mathbf{p}_2, \ldots, \mathbf{p}_N`. Each pose lies +on a manifold: :math:`\mathbf{p}_i \in \mathcal{M}`. Simple examples of +manifolds used in Graph SLAM include 1-D, 2-D, and 3-D space, i.e., +:math:`\mathbb{R}`, :math:`\mathbb{R}^2`, and :math:`\mathbb{R}^3`. +These environments are *rectilinear*, meaning that there is no concept +of orientation. By contrast, in :math:`SE(2)` problem settings a robot’s +pose consists of its location in :math:`\mathbb{R}^2` and its +orientation :math:`\theta`. Similarly, in :math:`SE(3)` a robot’s pose +consists of its location in :math:`\mathbb{R}^3` and its orientation, +which can be represented via Euler angles, quaternions, or :math:`SO(3)` +rotation matrices. + +As the robot explores its environment, it collects a set of :math:`M` +measurements :math:`\mathcal{Z} = \{\mathbf{z}_j\}`. Examples of such +measurements include odometry, GPS, and IMU data. Given a set of poses +:math:`\mathbf{p}_1, \ldots, \mathbf{p}_N`, we can compute the estimated +measurement +:math:`\hat{\mathbf{z}}_j(\mathbf{p}_1, \ldots, \mathbf{p}_N)`. We can +then compute the *residual* +:math:`\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j)` for measurement +:math:`j`. The formula for the residual depends on the type of +measurement. As an example, let :math:`\mathbf{z}_1` be an odometry +measurement that was collected when the robot traveled from +:math:`\mathbf{p}_1` to :math:`\mathbf{p}_2`. The expected measurement +and the residual are computed as + +.. math:: + + \begin{aligned} + \hat{\mathbf{z}}_1(\mathbf{p}_1, \mathbf{p}_2) &= \mathbf{p}_2 \ominus \mathbf{p}_1 \\ + \mathbf{e}_1(\mathbf{z}_1, \hat{\mathbf{z}}_1) &= \mathbf{z}_1 \ominus \hat{\mathbf{z}}_1 = \mathbf{z}_1 \ominus (\mathbf{p}_2 \ominus \mathbf{p}_1),\end{aligned} + +where the :math:`\ominus` operator indicates inverse pose composition. +We model measurement :math:`\mathbf{z}_j` as having independent Gaussian +noise with zero mean and covariance matrix :math:`\Omega_j^{-1}`; we +refer to :math:`\Omega_j` as the *information matrix* for measurement +:math:`j`. That is, + +.. math:: + p(\mathbf{z}_j \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) = \eta_j \exp (-\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\mathsf{T}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) + :label: infomat + +where :math:`\eta_j` is the normalization constant. + +The objective of Graph SLAM is to find the maximum likelihood set of +poses given the measurements :math:`\mathcal{Z} = \{\mathbf{z}_j\}`; in +other words, we want to find + +.. math:: \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) + +Using Bayes’ rule, we can write this probability as + +.. math:: + \begin{aligned} + p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) &= \frac{p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) p(\mathbf{p}_1, \ldots, \mathbf{p}_N) }{ p(\mathcal{Z}) } \notag \\ + &\propto p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) + \end{aligned} + :label: bayes + +since :math:`p(\mathcal{Z})` is a constant (albeit, an unknown constant) +and we assume that :math:`p(\mathbf{p}_1, \ldots, \mathbf{p}_N)` is +uniformly distributed `PROBABILISTIC ROBOTICS`_. Therefore, we +can use Eq. :eq:`infomat` and and Eq. :eq:`bayes` to simplify the Graph SLAM +optimization as follows: + +.. math:: + + \begin{aligned} + \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) &= \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) \\ + &= \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \prod_{j=1}^M p(\mathbf{z}_j \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) \\ + &= \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \prod_{j=1}^M \exp \left( -(\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) \right) \\ + &= \mathop{\mathrm{arg\,min}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \sum_{j=1}^M (\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j).\end{aligned} + +We define + +.. math:: \chi^2 := \sum_{j=1}^M (\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j), + +and this is what we seek to minimize. + +Dimensionality and Pose Representation +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Before proceeding further, it is helpful to discuss the dimensionality +of the problem. We have: + +- A set of :math:`N` poses + :math:`\mathbf{p}_1, \mathbf{p}_2, \ldots, \mathbf{p}_N`, where each + pose lies on the manifold :math:`\mathcal{M}` + + - Each pose :math:`\mathbf{p}_i` is represented as a vector in (a + subset of) :math:`\mathbb{R}^d`. For example: + + - An :math:`SE(2)` pose is typically represented as + :math:`(x, y, \theta)`, and thus :math:`d = 3`. + + - An :math:`SE(3)` pose is typically represented as + :math:`(x, y, z, q_x, q_y, q_z, q_w)`, where :math:`(x, y, z)` + is a point in :math:`\mathbb{R}^3` and + :math:`(q_x, q_y, q_z, q_w)` is a *quaternion*, and so + :math:`d = 7`. For more information about :math:`SE(3)` + parameterization and pose transformations, see + [blanco2010tutorial]_. + + - We also need to be able to represent each pose compactly as a + vector in (a subset of) :math:`\mathbb{R}^c`. + + - Since an :math:`SE(2)` pose has three degrees of freedom, the + :math:`(x, y, \theta)` representation is again sufficient and + :math:`c=3`. + + - An :math:`SE(3)` pose only has six degrees of freedom, and we + can represent it compactly as :math:`(x, y, z, q_x, q_y, q_z)`, + and thus :math:`c=6`. + + - We use the :math:`\boxplus` operator to indicate pose composition + when one or both of the poses are represented compactly. The + output can be a pose in :math:`\mathcal{M}` or a vector in + :math:`\mathbb{R}^c`, as required by context. + +- A set of :math:`M` measurements + :math:`\mathcal{Z} = \{\mathbf{z}_1, \mathbf{z}_2, \ldots, \mathbf{z}_M\}` + + - Each measurement’s dimensionality can be unique, and we will use + :math:`\bullet` to denote a “wildcard” variable. + + - Measurement :math:`\mathbf{z}_j \in \mathbb{R}^\bullet` has an + associated information matrix + :math:`\Omega_j \in \mathbb{R}^{\bullet \times \bullet}` and + residual function + :math:`\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) = \mathbf{e}_j(\mathbf{z}_j, \mathbf{p}_1, \ldots, \mathbf{p}_N) \in \mathbb{R}^\bullet`. + + - A measurement could, in theory, constrain anywhere from 1 pose to + all :math:`N` poses. In practice, each measurement usually + constrains only 1 or 2 poses. + +Graph SLAM Algorithm +^^^^^^^^^^^^^^^^^^^^ + +The “Graph” in Graph SLAM refers to the fact that we view the problem as +a graph. The graph has a set :math:`\mathcal{V}` of :math:`N` vertices, +where each vertex :math:`v_i` has an associated pose +:math:`\mathbf{p}_i`. Similarly, the graph has a set :math:`\mathcal{E}` +of :math:`M` edges, where each edge :math:`e_j` has an associated +measurement :math:`\mathbf{z}_j`. In practice, the edges in this graph +are either unary (i.e., a loop) or binary. (Note: :math:`e_j` refers to +the edge in the graph associated with measurement :math:`\mathbf{z}_j`, +whereas :math:`\mathbf{e}_j` refers to the residual function associated +with :math:`\mathbf{z}_j`.) For more information about the Graph SLAM +algorithm, see [grisetti2010tutorial]_. + +We want to optimize + +.. math:: \chi^2 = \sum_{e_j \in \mathcal{E}} \mathbf{e}_j^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j. + +Let :math:`\mathbf{x}_i \in \mathbb{R}^c` be the compact representation +of pose :math:`\mathbf{p}_i \in \mathcal{M}`, and let + +.. math:: \mathbf{x} := \begin{bmatrix} \mathbf{x}_1 \\ \mathbf{x}_2 \\ \vdots \\ \mathbf{x}_N \end{bmatrix} \in \mathbb{R}^{cN} + +We will solve this optimization problem iteratively. Let + +.. math:: \mathbf{x}^{k+1} := \mathbf{x}^k \boxplus \Delta \mathbf{x}^k = \begin{bmatrix} \mathbf{x}_1 \boxplus \Delta \mathbf{x}_1 \\ \mathbf{x}_2 \boxplus \Delta \mathbf{x}_2 \\ \vdots \\ \mathbf{x}_N \boxplus \Delta \mathbf{x}_2 \end{bmatrix} + :label: update + +The :math:`\chi^2` error at iteration :math:`k+1` is + +.. math:: \chi_{k+1}^2 = \sum_{e_j \in \mathcal{E}} \underbrace{\left[ \mathbf{e}_j(\mathbf{x}^{k+1}) \right]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\mathbf{e}_j(\mathbf{x}^{k+1})}_{\bullet \times 1}. + :label: chisq_at_kplusone + +We will linearize the residuals as: + +.. math:: + \begin{aligned} + \mathbf{e}_j(\mathbf{x}^{k+1}) &= \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k) \\ + &\approx \mathbf{e}_j(\mathbf{x}^{k}) + \frac{\partial}{\partial \Delta \mathbf{x}^k} \left[ \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k) \right] \Delta \mathbf{x}^k \\ + &= \mathbf{e}_j(\mathbf{x}^{k}) + \left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right) \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \Delta \mathbf{x}^k. + \end{aligned} + :label: linearization + +Plugging :eq:`linearization` into :eq:`chisq_at_kplusone`, we get: + +.. math:: + + \begin{aligned} + \chi_{k+1}^2 &\approx \ \ \ \ \ \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x}^k)]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\mathbf{e}_j(\mathbf{x}^k)}_{\bullet \times 1} \notag \\ + &\hphantom{\approx} \ \ \ + \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x^k}) ]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \underbrace{\Delta \mathbf{x}^k}_{cN \times 1} \notag \\ + &\hphantom{\approx} \ \ \ + \sum_{e_j \in \mathcal{E}} \underbrace{(\Delta \mathbf{x}^k)^{\scriptstyle{\mathsf{T}}}}_{1 \times cN} \underbrace{ \left( \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \right)^{\scriptstyle{\mathsf{T}}}}_{cN \times dN} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)^{\scriptstyle{\mathsf{T}}}}_{dN \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \underbrace{\Delta \mathbf{x}^k}_{cN \times 1} \notag \\ + &= \chi_k^2 + 2 \mathbf{b}^{\scriptstyle{\mathsf{T}}}\Delta \mathbf{x}^k + (\Delta \mathbf{x}^k)^{\scriptstyle{\mathsf{T}}}H \Delta \mathbf{x}^k, \notag\end{aligned} + +where + +.. math:: + + \begin{aligned} + \mathbf{b}^{\scriptstyle{\mathsf{T}}}&= \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x^k}) ]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \\ + H &= \sum_{e_j \in \mathcal{E}} \underbrace{ \left( \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \right)^{\scriptstyle{\mathsf{T}}}}_{cN \times dN} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)^{\scriptstyle{\mathsf{T}}}}_{dN \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN}.\end{aligned} + +Using this notation, we obtain the optimal update as + +.. math:: \Delta \mathbf{x}^k = -H^{-1} \mathbf{b}. \label{eq:deltax} + +We apply this update to the poses via :eq:`update` and repeat until convergence. + + +.. _PROBABILISTIC ROBOTICS: http://www.probabilistic-robotics.org/ diff --git a/docs/modules/slam/slam.rst b/docs/modules/slam/slam_main.rst similarity index 75% rename from docs/modules/slam/slam.rst rename to docs/modules/slam/slam_main.rst index 981c45ada54..41210fee4ee 100644 --- a/docs/modules/slam/slam.rst +++ b/docs/modules/slam/slam_main.rst @@ -21,32 +21,12 @@ Ref: - `Introduction to Mobile Robotics: Iterative Closest Point Algorithm`_ -EKF SLAM --------- -This is an Extended Kalman Filter based SLAM example. +.. include:: ekf_slam.rst -The blue line is ground truth, the black line is dead reckoning, the red -line is the estimated trajectory with EKF SLAM. - -The green crosses are estimated landmarks. - -|4| - -Ref: - -- `PROBABILISTIC ROBOTICS`_ .. include:: FastSLAM1.rst -|5| - -Ref: - -- `PROBABILISTIC ROBOTICS`_ - -- `SLAM simulations by Tim Bailey`_ - FastSLAM 2.0 ------------ @@ -56,7 +36,8 @@ The animation has the same meanings as one of FastSLAM 1.0. |6| -Ref: +References +~~~~~~~~~~ - `PROBABILISTIC ROBOTICS`_ @@ -77,6 +58,10 @@ The black stars are landmarks for graph edge generation. |7| +.. include:: graphSLAM_doc.rst +.. include:: graphSLAM_formulation.rst +.. include:: graphSLAM_SE2_example.rst + Ref: - `A Tutorial on Graph-Based SLAM`_ @@ -85,9 +70,12 @@ Ref: .. _PROBABILISTIC ROBOTICS: http://www.probabilistic-robotics.org/ .. _SLAM simulations by Tim Bailey: http://www-personal.acfr.usyd.edu.au/tbailey/software/slam_simulations.htm .. _A Tutorial on Graph-Based SLAM: http://www2.informatik.uni-freiburg.de/~stachnis/pdf/grisetti10titsmag.pdf +.. _FastSLAM Lecture: http://ais.informatik.uni-freiburg.de/teaching/ws12/mapping/pdf/slam10-fastslam.pdf + +.. [blanco2010tutorial] Blanco, J.-L.A tutorial onSE(3) transformation parameterization and on-manifold optimization.University of Malaga, Tech. Rep 3(2010) +.. [grisetti2010tutorial] Grisetti, G., Kummerle, R., Stachniss, C., and Burgard, W.A tutorial on graph-based SLAM.IEEE Intelligent Transportation Systems Magazine 2, 4 (2010), 31–43. .. |3| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/iterative_closest_point/animation.gif -.. |4| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/EKFSLAM/animation.gif .. |5| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/FastSLAM1/animation.gif .. |6| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/FastSLAM2/animation.gif .. |7| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/GraphBasedSLAM/animation.gif