From 9262d74c9a541c713e64ac6f0f13010c616a965a Mon Sep 17 00:00:00 2001 From: "mergify[bot]" <37929162+mergify[bot]@users.noreply.github.com> Date: Wed, 5 Jun 2024 19:46:50 +0200 Subject: [PATCH] Add mobile robot kinematics 101 and improve steering library docs (#954) (#1161) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit (cherry picked from commit d076ea2fe0555e8dc44cea1e3f9b4fc261ec4d1c) Co-authored-by: Christoph Fröhlich --- diff_drive_controller/doc/userdoc.rst | 2 + doc/controllers_index.rst | 7 +- doc/images/.gitignore | 1 + doc/images/ackermann_steering.drawio | 251 ++++++++++++++ doc/images/ackermann_steering.svg | 3 + doc/images/ackermann_steering_traction.drawio | 287 ++++++++++++++++ doc/images/ackermann_steering_traction.svg | 3 + doc/images/car_like_robot.drawio | 173 ++++++++++ doc/images/car_like_robot.svg | 3 + doc/images/diff_drive.drawio | 137 ++++++++ doc/images/diff_drive.svg | 3 + doc/images/double_traction.drawio | 197 +++++++++++ doc/images/double_traction.svg | 3 + doc/images/unicycle.drawio | 89 +++++ doc/images/unicycle.svg | 3 + doc/mobile_robot_kinematics.rst | 322 ++++++++++++++++++ steering_controllers_library/doc/userdoc.rst | 79 +++-- tricycle_controller/doc/userdoc.rst | 3 + 18 files changed, 1533 insertions(+), 33 deletions(-) create mode 100644 doc/images/.gitignore create mode 100644 doc/images/ackermann_steering.drawio create mode 100644 doc/images/ackermann_steering.svg create mode 100644 doc/images/ackermann_steering_traction.drawio create mode 100644 doc/images/ackermann_steering_traction.svg create mode 100644 doc/images/car_like_robot.drawio create mode 100644 doc/images/car_like_robot.svg create mode 100644 doc/images/diff_drive.drawio create mode 100644 doc/images/diff_drive.svg create mode 100644 doc/images/double_traction.drawio create mode 100644 doc/images/double_traction.svg create mode 100644 doc/images/unicycle.drawio create mode 100644 doc/images/unicycle.svg create mode 100644 doc/mobile_robot_kinematics.rst diff --git a/diff_drive_controller/doc/userdoc.rst b/diff_drive_controller/doc/userdoc.rst index f8ecd02065..2558c6e5ab 100644 --- a/diff_drive_controller/doc/userdoc.rst +++ b/diff_drive_controller/doc/userdoc.rst @@ -11,6 +11,8 @@ As input it takes velocity commands for the robot body, which are translated to Odometry is computed from hardware feedback and published. +For an introduction to mobile robot kinematics and the nomenclature used here, see :ref:`mobile_robot_kinematics`. + Other features -------------- diff --git a/doc/controllers_index.rst b/doc/controllers_index.rst index ea022e63a8..8d6480f290 100644 --- a/doc/controllers_index.rst +++ b/doc/controllers_index.rst @@ -21,18 +21,15 @@ Guidelines and Best Practices * -Controllers for Mobile Robots -***************************** +Controllers for Wheeled Mobile Robots +************************************* .. toctree:: :titlesonly: - Ackermann Steering Controller <../ackermann_steering_controller/doc/userdoc.rst> - Bicycle Steering Controller <../bicycle_steering_controller/doc/userdoc.rst> Differential Drive Controller <../diff_drive_controller/doc/userdoc.rst> Steering Controllers Library <../steering_controllers_library/doc/userdoc.rst> Tricycle Controller <../tricycle_controller/doc/userdoc.rst> - Tricycle Steering Controller <../tricycle_steering_controller/doc/userdoc.rst> Controllers for Manipulators and Other Robots ********************************************* diff --git a/doc/images/.gitignore b/doc/images/.gitignore new file mode 100644 index 0000000000..8d71bf9cf4 --- /dev/null +++ b/doc/images/.gitignore @@ -0,0 +1 @@ +*.bkp diff --git a/doc/images/ackermann_steering.drawio b/doc/images/ackermann_steering.drawio new file mode 100644 index 0000000000..d0ddb06a56 --- /dev/null +++ b/doc/images/ackermann_steering.drawio @@ -0,0 +1,251 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/images/ackermann_steering.svg b/doc/images/ackermann_steering.svg new file mode 100644 index 0000000000..1ca6ace166 --- /dev/null +++ b/doc/images/ackermann_steering.svg @@ -0,0 +1,3 @@ + + +
ICR
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ICR
Front wheel
Rear wheel
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ICR
 diff --git a/doc/images/unicycle.drawio b/doc/images/unicycle.drawio new file mode 100644 index 0000000000..49a1f44b5a --- /dev/null +++ b/doc/images/unicycle.drawio @@ -0,0 +1,89 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/images/unicycle.svg b/doc/images/unicycle.svg new file mode 100644 index 0000000000..826bbb1463 --- /dev/null +++ b/doc/images/unicycle.svg @@ -0,0 +1,3 @@ + + +
 diff --git a/doc/mobile_robot_kinematics.rst b/doc/mobile_robot_kinematics.rst new file mode 100644 index 0000000000..2ab4f1c0ee --- /dev/null +++ b/doc/mobile_robot_kinematics.rst @@ -0,0 +1,322 @@ +:github_url: https://github.com/ros-controls/ros2_controllers/blob/{REPOS_FILE_BRANCH}/doc/mobile_robot_kinematics.rst + +.. _mobile_robot_kinematics: + +Wheeled Mobile Robot Kinematics +-------------------------------------------------------------- + +.. _siciliano: https://link.springer.com/book/10.1007/978-1-84628-642-1 +.. _modern_robotics: http://modernrobotics.org/ + +This page introduces the kinematics of different wheeled mobile robots. For further reference see `Siciliano et.al - Robotics: Modelling, Planning and Control `_ and `Kevin M. Lynch and Frank C. Park - Modern Robotics: Mechanics, Planning, And Control `_. + +Wheeled mobile robots can be classified in two categories: + +Omnidirectional robots + which can move instantaneously in any direction in the plane, and + +Nonholonomic robots + which cannot move instantaneously in any direction in the plane. + +The forward integration of the kinematic model using the encoders of the wheel actuators — is referred to as **odometric localization** or **passive localization** or **dead reckoning**. We will call it just **odometry**. + +Omnidirectional Wheeled Mobile Robots +..................................... + +Robots with omniwheels or mecanum wheels. Section will be updated if controllers for these robots are implemented. + +Nonholonomic Wheeled Mobile Robots +..................................... + +Unicycle model +,,,,,,,,,,,,,,,, + +To define the coordinate systems (`ROS coordinate frame conventions `__, the coordinate systems follow the right-hand rule), consider the following simple unicycle model + +.. image:: images/unicycle.svg + :width: 550 + :align: center + :alt: Unicycle + +* :math:`x_b,y_b` is the robot's body-frame coordinate system, located at the contact point of the wheel on the ground. +* :math:`x_w,y_w` is the world coordinate system. +* :math:`x,y` are the robot's Cartesian coordinates in the world coordinate system. +* :math:`\theta` is the robot's heading angle, i.e. the orientation of the robot's :math:`x_b`-axis w.r.t. the world's :math:`x_w`-axis. + +In the following, we want to command the robot with a desired body twist + +.. math:: + + \vec{\nu}_b = \begin{bmatrix} + \vec{\omega}_{b} \\ + \vec{v}_{b} + \end{bmatrix}, + +where :math:`\vec{v}_{b}` is the linear velocity of the robot in its body-frame, and :math:`\vec\omega_{b}` is the angular velocity of the robot in its body-frame. As we consider steering robots on a flat surface, it is sufficient to give + +* :math:`v_{b,x}`, i.e. the linear velocity of the robot in direction of the :math:`x_b` axis. +* :math:`\omega_{b,z}`, i.e. the angular velocity of the robot about the :math:`x_z` axis. + +as desired system inputs. The forward kinematics of the unicycle can be calculated with + +.. math:: + \dot{x} &= v_{b,x} \cos(\theta) \\ + \dot{y} &= v_{b,x} \sin(\theta) \\ + \dot{\theta} &= \omega_{b,z} + +We will formulate the inverse kinematics to calculate the desired commands for the robot (wheel speed or steering) from the given body twist. + +Differential Drive Robot +,,,,,,,,,,,,,,,,,,,,,,,, + +Citing `Siciliano et.al - Robotics: Modelling, Planning and Control `_: + +.. code-block:: text + + A unicycle in the strict sense (i.e., a vehicle equipped with a single wheel) + is a robot with a serious problem of balance in static conditions. However, + there exist vehicles that are kinematically equivalent to a unicycle but more + stable from a mechanical viewpoint. + +One of these vehicles is the differential drive robot, which has two wheels, each of which is driven independently. + +.. image:: images/diff_drive.svg + :width: 550 + :align: center + :alt: Differential drive robot + +* :math:`w` is the wheel track (the distance between the wheels). + +**Forward Kinematics** + +The forward kinematics of the differential drive model can be calculated from the unicycle model above using + +.. math:: + v_{b,x} &= \frac{v_{right} + v_{left}}{2} \\ + \omega_{b,z} &= \frac{v_{right} - v_{left}}{w} + +**Inverse Kinematics** + +The necessary wheel speeds to achieve a desired body twist can be calculated with: + +.. math:: + + v_{left} &= v_{b,x} - \omega_{b,z} w / 2 \\ + v_{right} &= v_{b,x} + \omega_{b,z} w / 2 + + +**Odometry** + +We can use the forward kinematics equations above to calculate the robot's odometry directly from the encoder readings. + +Car-Like (Bicycle) Model +,,,,,,,,,,,,,,,,,,,,,,,, + +The following picture shows a car-like robot with two wheels, where the front wheel is steerable. This model is also known as the bicycle model. + +.. image:: images/car_like_robot.svg + :width: 550 + :align: center + :alt: Car-like robot + +* :math:`\phi` is the steering angle of the front wheel, counted positive in direction of rotation around :math:`x_z`-axis. +* :math:`v_{rear}, v_{front}` is the velocity of the rear and front wheel. +* :math:`l` is the wheelbase. + +We assume that the wheels are rolling without slipping. This means that the velocity of the contact point of the wheel with the ground is zero and the wheel's velocity points in the direction perpendicular to the wheel's axis. The **Instantaneous Center of Rotation** (ICR), i.e. the center of the circle around which the robot rotates, is located at the intersection of the lines that are perpendicular to the wheels' axes and pass through the contact points of the wheels with the ground. + +As a consequence of the no-slip condition, the velocity of the two wheels must satisfy the following constraint: + +.. math:: + v_{rear} = v_{front} \cos(\phi) + +**Forward Kinematics** + +The forward kinematics of the car-like model can be calculated with + +.. math:: + \dot{x} &= v_{b,x} \cos(\theta) \\ + \dot{y} &= v_{b,x} \sin(\theta) \\ + \dot{\theta} &= \frac{v_{b,x}}{l} \tan(\phi) + + +**Inverse Kinematics** + +The steering angle is one command input of the robot: + +.. math:: + \phi = \arctan\left(\frac{l w_{b,z}}{v_{b,x}} \right) + + +For the rear-wheel drive, the velocity of the rear wheel is the second input of the robot: + +.. math:: + v_{rear} = v_{b,x} + + +For the front-wheel drive, the velocity of the front wheel is the second input of the robot: + +.. math:: + v_{front} = \frac{v_{b,x}}{\cos(\phi)} + +**Odometry** + +We have to distinguish between two cases: Encoders on the rear wheel or on the front wheel. + +For the rear wheel case: + +.. math:: + \dot{x} &= v_{rear} \cos(\theta) \\ + \dot{y} &= v_{rear} \sin(\theta) \\ + \dot{\theta} &= \frac{v_{rear}}{l} \tan(\phi) + + +For the front wheel case: + +.. math:: + \dot{x} &= v_{front} \cos(\theta) \cos(\phi)\\ + \dot{y} &= v_{front} \sin(\theta) \cos(\phi)\\ + \dot{\theta} &= \frac{v_{front}}{l} \sin(\phi) + + +Double-Traction Axle +,,,,,,,,,,,,,,,,,,,,, + +The following image shows a car-like robot with three wheels, with two independent traction wheels at the rear. + +.. image:: images/double_traction.svg + :width: 550 + :align: center + :alt: A car-like robot with two traction wheels at the rear + +* :math:`w_r` is the wheel track of the rear axle. + +**Forward Kinematics** + +The forward kinematics is the same as the car-like model above. + +**Inverse Kinematics** + +The turning radius of the robot is + +.. math:: + R_b = \frac{l}{\tan(\phi)} + +Then the velocity of the rear wheels must satisfy these conditions to avoid skidding + +.. math:: + v_{rear,left} &= v_{b,x}\frac{R_b - w_r/2}{R_b}\\ + v_{rear,right} &= v_{b,x}\frac{R_b + w_r/2}{R_b} + +**Odometry** + +The calculation of :math:`v_{b,x}` from two encoder measurements of the traction axle is overdetermined. +If there is no slip and the encoders are ideal, + +.. math:: + v_{b,x} = v_{rear,left} \frac{R_b}{R_b - w_r/2} = v_{rear,right} \frac{R_b}{R_b + w_r/2} + +holds. But to get a more robust solution, we take the average of both , i.e., + +.. math:: + v_{b,x} = 0.5 \left(v_{rear,left} \frac{R_b}{R_b - w_r/2} + v_{rear,right} \frac{R_b}{R_b + w_r/2}\right). + + +Ackermann Steering +,,,,,,,,,,,,,,,,,,,,, + +The following image shows a four-wheeled robot with two independent steering wheels in the front. + +.. image:: images/ackermann_steering.svg + :width: 550 + :align: center + :alt: A car-like robot with two steering wheels at the front + +* :math:`w_f` is the wheel track of the front axle, measured between the two kingpins. + +To prevent the front wheels from slipping, the steering angle of the front wheels cannot be equal. +This is the so-called **Ackermann steering**. + +.. note:: + Ackermann steering can also be achieved by a `mechanical linkage between the two front wheels `__. In this case the robot has only one steering input, and the steering angle of the two front wheels is mechanically coupled. The inverse kinematics of the robot will then be the same as in the car-like model above. + +**Forward Kinematics** + +The forward kinematics is the same as for the car-like model above. + +**Inverse Kinematics** + +The turning radius of the robot is + +.. math:: + R_b = \frac{l}{\tan(\phi)} + +Then the steering angles of the front wheels must satisfy these conditions to avoid skidding + +.. math:: + \phi_{left} &= \arctan\left(\frac{l}{R_b - w_f/2}\right) &= \arctan\left(\frac{2l\sin(\phi)}{2l\cos(\phi) - w_f\sin(\phi)}\right)\\ + \phi_{right} &= \arctan\left(\frac{l}{R_b + w_f/2}\right) &= \arctan\left(\frac{2l\sin(\phi)}{2l\cos(\phi) + w_f\sin(\phi)}\right) + +**Odometry** + +The calculation of :math:`\phi` from two angle measurements of the steering axle is overdetermined. +If there is no slip and the measurements are ideal, + +.. math:: + \phi = \arctan\left(\frac{l\tan(\phi_{left})}{l + w_f/2 \tan(\phi_{left})}\right) = \arctan\left(\frac{l\tan(\phi_{right})}{l - w_f/2 \tan(\phi_{right})}\right) + +holds. But to get a more robust solution, we take the average of both , i.e., + +.. math:: + \phi = 0.5 \left(\arctan\left(\frac{l\tan(\phi_{left})}{l + w_f/2 \tan(\phi_{left})}\right) + \arctan\left(\frac{l\tan(\phi_{right})}{l - w_f/2 \tan(\phi_{right})}\right)\right). + +Ackermann Steering with Traction +,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, + +The following image shows a four-wheeled car-like robot with two independent steering wheels at the front, which are also driven independently. + +.. image:: images/ackermann_steering_traction.svg + :width: 550 + :align: center + :alt: A car-like robot with two steering wheels at the front, which are also independently driven. + +* :math:`d_{kp}` is the distance from the kingpin to the contact point of the front wheel with the ground. + +**Forward Kinematics** + +The forward kinematics is the same as the car-like model above. + +**Inverse Kinematics** + +To avoid slipping of the front wheels, the velocity of the front wheels cannot be equal and + +.. math:: + \frac{v_{front,left}}{R_{left}} = \frac{v_{front,right}}{R_{right}} = \frac{v_{b,x}}{R_b} + +with turning radius of the robot and the left/right front wheel + +.. math:: + R_b &= \frac{l}{\tan(\phi)} \\ + R_{left} &= \frac{l-d_{kp}\sin(\phi_{left})}{\sin(\phi_{left})}\\ + R_{right} &= \frac{l+d_{kp}\sin(\phi_{right})}{\sin(\phi_{right})}. + +This results in the following inverse kinematics equations + +.. math:: + v_{front,left} &= \frac{v_{b,x}(l-d_{kp}\sin(\phi_{left}))}{R_b\sin(\phi_{left})}\\ + v_{front,right} &= \frac{v_{b,x}(l+d_{kp}\sin(\phi_{right}))}{R_b\sin(\phi_{right})} + +with the steering angles of the front wheels from the Ackermann steering equations above. + +**Odometry** + +The calculation of :math:`v_{b,x}` from two encoder measurements of the traction axle is again overdetermined. +If there is no slip and the encoders are ideal, + +.. math:: + v_{b,x} = v_{front,left} \frac{R_b\sin(\phi_{left})}{l-d_{kp}\sin(\phi_{left})} = v_{front,right} \frac{R_b\sin(\phi_{right})}{l+d_{kp}\sin(\phi_{right})} + +holds. But to get a more robust solution, we take the average of both , i.e., + +.. math:: + v_{b,x} = 0.5 \left( v_{front,left} \frac{R_b\sin(\phi_{left})}{l-d_{kp}\sin(\phi_{left})} + v_{front,right} \frac{R_b\sin(\phi_{right})}{l+d_{kp}\sin(\phi_{right})}\right). diff --git a/steering_controllers_library/doc/userdoc.rst b/steering_controllers_library/doc/userdoc.rst index 0155bc5fd8..a52e34c120 100644 --- a/steering_controllers_library/doc/userdoc.rst +++ b/steering_controllers_library/doc/userdoc.rst @@ -5,17 +5,25 @@ steering_controllers_library ============================= -Library with shared functionalities for mobile robot controllers with steering drive (2 degrees of freedom). +.. _steering_controller_status_msg: https://github.com/ros-controls/control_msgs/blob/master/control_msgs/msg/SteeringControllerStatus.msg +.. _odometry_msg: https://github.com/ros2/common_interfaces/blob/{DISTRO}/nav_msgs/msg/Odometry.msg +.. _twist_msg: https://github.com/ros2/common_interfaces/blob/{DISTRO}/geometry_msgs/msg/TwistStamped.msg +.. _tf_msg: https://github.com/ros2/geometry2/blob/{DISTRO}/tf2_msgs/msg/TFMessage.msg + +Library with shared functionalities for mobile robot controllers with steering drives, with so-called non-holonomic constraints. + The library implements generic odometry and update methods and defines the main interfaces. -Nomenclature used for the controller is used from `wikipedia `_. +The update methods only use inverse kinematics, it does not implement any feedback control loops like path-tracking controllers etc. + +For an introduction to mobile robot kinematics and the nomenclature used here, see :ref:`mobile_robot_kinematics`. Execution logic of the controller ---------------------------------- -The controller uses velocity input, i.e., stamped Twist messages where linear ``x`` and angular ``z`` components are used. -Angular component under +The controller uses velocity input, i.e., stamped `twist messages `_ where linear ``x`` and angular ``z`` components are used. Values in other components are ignored. + In the chain mode the controller provides two reference interfaces, one for linear velocity and one for steering angle position. Other relevant features are: @@ -24,65 +32,80 @@ Other relevant features are: * input command timeout based on a parameter. The command for the wheels are calculated using ``odometry`` library where based on concrete kinematics traction and steering commands are calculated. -Currently implemented kinematics in corresponding packages are: + +Currently implemented kinematics +-------------------------------------------------------------- * :ref:`Bicycle ` - with one steering and one drive joints; * :ref:`Tricylce ` - with one steering and two drive joints; -* :ref:`Ackermann ` - with two seering and two drive joints. +* :ref:`Ackermann ` - with two steering and two drive joints. +.. toctree:: + :hidden: + Bicycle <../../bicycle_steering_controller/doc/userdoc.rst> + Tricylce <../../tricycle_steering_controller/doc/userdoc.rst> + Ackermann <../../ackermann_steering_controller/doc/userdoc.rst> Description of controller's interfaces -------------------------------------- References (from a preceding controller) ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, -- /linear/velocity [double], in m/s -- /angular/position [double] # in [rad] -Commands -,,,,,,,,, -``front_steering == true`` +Used when controller is in chained mode (``in_chained_mode == true``). + +- ``/linear/velocity`` double, in m/s +- ``/angular/position`` double, in rad -- /position [double] # in [rad] -- /velocity [double] # in [m/s] +Command interfaces +,,,,,,,,,,,,,,,,,,, -``front_steering == false`` +If parameter ``front_steering == true`` -- /velocity [double] # in [m/s] -- /position [double] # in [rad] +- ``/position`` double, in rad +- ``/velocity`` double, in m/s + +If parameter ``front_steering == false`` + +- ``/velocity`` double, in m/s +- ``/position`` double, in rad + +State interfaces +,,,,,,,,,,,,,,,,, -States -,,,,,,, Depending on the ``position_feedback``, different feedback types are expected * ``position_feedback == true`` --> ``TRACTION_FEEDBACK_TYPE = position`` * ``position_feedback == false`` --> ``TRACTION_FEEDBACK_TYPE = velocity`` -``front_steering == true`` +If parameter ``front_steering == true`` -- /position [double] # in [rad] -- / [double] # in [m] or [m/s] +- ``/position`` double, in rad +- ``/`` double, in m or m/s -``front_steering == false`` +If parameter ``front_steering == false`` -- / [double] # [m] or [m/s] -- /position [double] # in [rad] +- ``/`` double, in m or m/s +- ``/position`` double, in rad Subscribers ,,,,,,,,,,,, + Used when controller is not in chained mode (``in_chained_mode == false``). -- /reference [geometry_msgs/msg/TwistStamped] +- ``/reference`` [`geometry_msgs/msg/TwistStamped `_] Publishers ,,,,,,,,,,, -- /odometry [nav_msgs/msg/Odometry] -- /tf_odometry [tf2_msgs/msg/TFMessage] -- /controller_state [control_msgs/msg/SteeringControllerStatus] + +- ``/odometry`` [`nav_msgs/msg/Odometry `_] +- ``/tf_odometry`` [`tf2_msgs/msg/TFMessage `_] +- ``/controller_state`` [`control_msgs/msg/SteeringControllerStatus `_] Parameters ,,,,,,,,,,, + This controller uses the `generate_parameter_library `_ to handle its parameters. For an exemplary parameterization see the ``test`` folder of the controller's package. diff --git a/tricycle_controller/doc/userdoc.rst b/tricycle_controller/doc/userdoc.rst index 30973762fd..2ede52e1b6 100644 --- a/tricycle_controller/doc/userdoc.rst +++ b/tricycle_controller/doc/userdoc.rst @@ -10,6 +10,9 @@ Controller for mobile robots with a single double-actuated wheel, including trac Input for control are robot base_link twist commands which are translated to traction and steering commands for the tricycle drive base. Odometry is computed from hardware feedback and published. +For an introduction to mobile robot kinematics and the nomenclature used here, see :ref:`mobile_robot_kinematics`. + + Other features --------------