Simplified Jacobian Omnidirectional Robot Simulation

This project simulates an omnidirectional robot using a simplified version of the Jacobian matrix model.

Background

The Jacobian matrix ( J ) relates the body-frame velocities to the individual wheel velocities.

For a 3-wheel configuration, the matrix is:

$$ J = \begin{bmatrix} \cos(\theta_1) / r & \sin(\theta_1) / r & L / r \\ \cos(\theta_2) / r & \sin(\theta_2) / r & L / r \\ \cos(\theta_3) / r & \sin(\theta_3) / r & L / r \\ \end{bmatrix} $$

Where:

• ($\theta_1$, $\theta_2$, $\theta_3$) are the angles of the wheels
• ($r$) is the wheel radius
• ($L$) is the distance from the robot’s center to the wheels

The wheel velocities (\mathbf{\Omega}) are calculated using:

$$ \mathbf{\Omega} = J \mathbf{V} $$

where $$\mathbf{V} = [v_x, v_y, \omega]^T$$ represents the body-frame velocities.

Features

• 3-Wheel and 4-Wheel Configurations: Choose between 3-wheel and 4-wheel setups or display both configurations side by side for comparison.
• Velocity Arrows: Visualize the velocity of each wheel dynamically calculated based on robot motion.
• Pause/Resume Functionality: Pause and resume the simulation using the spacebar.
• Customizable Omega: The robot's angular velocity (omega) can be customized through user input.

Getting Started

Prerequisites

Ensure you have the following Python packages installed: pip install numpy matplotlib

Running the Simulation

To run the simulation, execute the Python script: python jacobian_simulation.py

User Inputs

Upon running the script, you'll be prompted for the following:

1. Plot both configurations? (y/n):

   • Choose whether to display both 3-wheel and 4-wheel configurations side by side.

2. Omega (angular velocity):

   • Enter the desired angular velocity (omega). If left blank, the default value will be used.

3. Use 4 wheels? (y/n):

   • If not plotting both configurations, you'll be asked if you want to use the 4-wheel configuration.

Credits

This project was created by Michaël Guerrier (Token Thinker).

The Jacobian matrix calculations for omnidirectional platforms are based on the article: "Defining the Consistent Velocity of Omnidirectional Mobile Platforms" published by MDPI.

License

Licensed under either of:

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.