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Mobile-Manipulation

A repository for my final project in the course Mobile Manipulations (ME449) at Northwestern University.
Please visit my website for more information about this project.

Table of Contents

Overview

This project is the final project in the course Robotic Manipulation at Northwestern University. In this project, I wrote a software that plans a trajectory for the end-effector of the youBot mobile manipulator, performs an odometry as the chassis moves, and performs feedback control to drive the youBot to pick up a block at a specified location, carry it to a desired location, and put it down in the V-REP simulation software.
The project description can be found here.

The project covers the following topics:

  1. Generate the kinematics simulator of the youBot - an omnidirectional mobile robot with a 5-DOF robotic arm.
  2. Plan the end-effector's trajectory between waypoints.
  3. Apply feedback control to drive the robot in the desired trajectory.
  4. Simulate the planned trajectory in CoppeliaSim.

Package Description

This project contains 3 milestones, and was implemented in the code Full_Program.py. The main code calls the 3 milestone sub-code:

  1. Next_State.py - Milestone 1 code. This code uses a function NextState(), that compute the configuration of the robot in the next time step.
  2. Trajectory_Generator.py - Milestone 2 code. This code uses a function TrajectoryGenerator(), that generates the reference trajectory for the end-effector frame {e}.
  3. Feedback_Control.py - Milestone 3 code. This code uses a function FeedbackControl(), that calculates the kinematic task-space feedforward plus feedback control law.

The code also uses functions from the Modern Robotics library. This library can be downloaded from this git repository - https://github.com/NxRLab/ModernRobotics (See "Usage and Configuration instructions" section for instructions).

Usage and Configuration Instructions

  1. To run the program, download the modern robotics library (the python version) from https://github.com/NxRLab/ModernRobotics/tree/master/packages/Python, by running:
pip install modern_robotics
  1. Run the Full_Program.py code.

Results

The results for this project can be split into 3 categories:

  1. Best results - Planning and executing a motion without overshoot or steady-state error.
  2. Overshoot results - Planning and executing a motion with overshoot but without steady-state error.
  3. NewTast results - Planning and executing the trajectory with different start and finish configuration.

Motion planning with different initial and final cube location

In this part, I simulated the controlled motion with different initial and final cube location, and different initial robot's configuration.

  1. For the default initial and final configurations, I used the following conditions:

    Initial robot's configuration:

    (0.1, -0.2, 0, 0, 0, 0.2, -1.6, 0, 0, 0, 0, 0, 0)

    Initial cube configuration:

    [1, 0, 0,     1],
[0, 1, 0,     0],
[0, 0, 1, 0.025],
[0, 0, 0,     1]

    Final cube configuration:

    [ 0, 1, 0,     0],
[-1, 0, 0,    -1],
[ 0, 0, 1, 0.025],
[ 0, 0, 0,     1]

    The simulated controlled motion with the following condition is:

  2. For the different initial and final configurations, I used the following conditions:

    Initial robot's configuration:

    (pi/6, -0.5, 0, 0, 0, 0.2, -1.6, 0, 0, 0, 0, 0, 0)

    Initial cube location:

    [1, 0, 0,     1],
[0, 1, 0,     1],
[0, 0, 1, 0.025],
[0, 0, 0,     1]

    Final cube location:

    [ 0, 1, 0,     1],
[-1, 0, 0,    -1],
[ 0, 0, 1, 0.025],
[ 0, 0, 0,     1]

    The simulated controlled motion with the following condition is:

Motion planning with different control gains

In this part, I plotted the end-effector's twist error as a function of time, to explore the error's behavior when using different control gains.

  1. For PI controller with feedback gains of Kp = 20 and Ki = 5, The error plot is:

    We can see that there is no overshoot, no steady-state error, and fast settling time.

  2. For PI controller with feedback gains of Kp = 2 and Ki = 40, The error plot is:

    We can see that there is an overshoot at the beginning of the motion, no steady-state error, and fast settling time.