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Add (empty) section for omnidirectional robots
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christophfroehlich committed Dec 31, 2023
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4 changes: 2 additions & 2 deletions doc/controllers_index.rst
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Expand Up @@ -21,8 +21,8 @@ Guidelines and Best Practices
*


Controllers for Mobile Robots
*****************************
Controllers for Wheeled Mobile Robots
*************************************

.. toctree::
:titlesonly:
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25 changes: 20 additions & 5 deletions doc/mobile_robot_kinematics.rst
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.. _mobile_robot_kinematics:

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 section introduces the kinematics of different mobile robots. The nomenclature is based on `Siciliano et.al - Robotics: Modelling, Planning and Control <siciliano_>`_.
This page introduces the kinematics of different wheeled mobile robots. For further reference see `Siciliano et.al - Robotics: Modelling, Planning and Control <siciliano_>`_ and `Kevin M. Lynch and Frank C. Park - Modern Robotics: Mechanics, Planning, And Control <modern_robotics_>`_.

.. note::
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.

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**.
Nonholonomic Wheeled Mobile Robots
.....................................

Unicycle model
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Expand All @@ -37,7 +52,7 @@ In the following, we want to command the robot with a desired body twist
\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. For reference, see, e.g., `Kevin M. Lynch and Frank C. Park - Modern Robotics: Mechanics, Planning, And Control <http://modernrobotics.org/>`__. As we consider steering robots on a flat surface, it is sufficient to give
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 :math:`x_b`-axis direction.
* :math:`\omega_{b,z}`, i.e. the angular velocity of the robot around :math:`x_z`-axis.
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