README.md

Ackermann Steering & Pure Pursuit Using Bullet Simulator

This project simulates an Ackermann steering model combined with a Pure Pursuit path-following algorithm using PyBullet.

Features

• Simulates a vehicle with realistic Ackermann steering.
• Uses the Pure Pursuit algorithm to follow a figure-eight trajectory.
• Visualizes waypoints, the vehicle path, and lookahead points.

Installation

Ensure you have Python installed, then install the required dependencies:

pip install pybullet numpy

Running the Simulation

Run the following command:

python simulation.py

Mathematical Background

Ackermann Steering Model

Ackermann steering ensures that all wheels follow a circular path with different turning radii. The inner and outer wheels turn at different angles to minimize tire slip.

Steering Angle Computation

$$\delta_{inner} = \tan^{-1}\left(\frac{L}{R_{inner}}\right)$$
$$\delta_{outer} = \tan^{-1}\left(\frac{L}{R_{outer}}\right)$$
where:

• $$L$$ is the wheelbase
• $$R_{inner}$$ and $$R_{outer}$$ are the inner and outer turning radii

Turning Radius

$$ R_{inner} = \frac{L}{\tan(|\delta|)} $$ $$ R_{outer} = R_{inner} \pm trackWidth $$

Pure Pursuit Algorithm

Pure Pursuit calculates the required steering angle to follow a given path based on a look-ahead point.

Steering Angle Computation

$$ \gamma = \tan^{-1}\left(\frac{2 L y}{d^2}\right) $$ where:

• $$L$$ is the wheelbase
• $$y$$ is the perpendicular distance to the look-ahead point
• $$d$$ is the Euclidean distance to the look-ahead point

File Structure

.
├── simulation.py   # Python script for PyBullet simulation
├── README.md       # Project documentation

References

• Ackermann Steering
• Pure Pursuit

License

This project is licensed under the MIT License.