[MPC] Linear Parameter-Varying - Model Predictive Control for Racing

Motion Planning

Linear Parameter-Varying - Model Predictive Control for Racing

Published

November 4, 2023

Planning and control for autonomous racing vehicles. This project allows you to solve the autonomous racing driving problem using advanced control theory. Particularly, here it is presented a collaborative work using optimal strategies. The Model Predictive Control (MPC) strategy is used online for computing the optimal trajectory maximizing vehicle velocity but also for computing the optimal control actions that make the vehicle to follow the computed references. All the algorithms are solved in real time employing the Operator Splitting Quadratic Program (OSQP) solver.

The vehicle model

The planning-control-estimation diagram shows the interconnection between:

Planning Module: Generates optimal trajectory using LPV-MPC
Control Module: Tracks the planned trajectory
Estimation Module: Provides state feedback

LPV modeling

The LPV (Linear Parameter-Varying) paradigm allows to represent a given non-linear representation into a pseudo-linear form:

This approach enables real-time optimization while maintaining the nonlinear vehicle dynamics characteristics.

The vehicle model

The model used in planning, control and estimation algorithms is the bicycle representation where the inputs are:

Front steering angle (δ): Controls the lateral motion
Rear wheel linear acceleration (a): Controls the longitudinal motion

The bicycle model captures the essential vehicle dynamics while remaining computationally efficient for real-time MPC implementation.

MPC for planning

The trajectory planning for racing is solved using the MPC technique. The cost function addresses the lap time minimization as well as the smoothness of the lateral motion by reducing as much as possible the understeer and oversteer behaviours. This algorithm is launched every 33 ms.

MPC for control

At this point an MPC is built and solved at every control iteration (33 ms) to figure out the optimal control actions (steering and rear wheel acceleration).

Test

To use this project, install it locally via:

git clone https://github.com/phatcvo/LPV-MPP-MPC-for-racing.git

To execute the code, run:

catkin_make (to create build and devel folders)
source devel/setup.bash
roslaunch barc MAIN_LAUNCH.launch

Note: This project demonstrates the LPV-MPC approach for autonomous racing vehicles with real-time trajectory planning and control.

References

Trajectory planner presented in: Alcala, E., Puig, V. & Quevedo, J. (2019). LPV-MP Planning for Autonomous Racing Vehicles considering Obstacles. Robotics and Autonomous Systems.
Controller presented in: Alcala, E., Puig, V., Quevedo, J., & Rosolia, U. (2019). Autonomous Racing using Linear Parameter Varying - Model Predictive Control (LPV-MPC). Control engineering practice.
Estimator presented in: Alcala, E., Puig, V., Quevedo, J., & Escobet, T. (2018). Gain-scheduling LPV control for autonomous vehicles including friction force estimation and compensation mechanism. IET Control Theory & Applications, 12(12), 1683-1693. (https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2017.1154).

--- title: "[MPC] Linear Parameter-Varying - Model Predictive Control for Racing" date: 2023-11-04 tags: ["MPC", "racing"] categories: ["Motion Planning"] description: "Linear Parameter-Varying - Model Predictive Control for Racing" draft: false --- Planning and control for autonomous racing vehicles. This project allows you to solve the autonomous racing driving problem using advanced control theory. Particularly, here it is presented a collaborative work using optimal strategies. The Model Predictive Control (MPC) strategy is used online for computing the optimal trajectory maximizing vehicle velocity but also for computing the optimal control actions that make the vehicle to follow the computed references. All the algorithms are solved in real time employing the Operator Splitting Quadratic Program (OSQP) solver. ### The vehicle model The planning-control-estimation diagram shows the interconnection between: ![ROS Graph](https://raw.githubusercontent.com/phatcvo/LPV-MPP-MPC-for-racing/main/ws/images/rosgraph.png) ![System Diagram](https://raw.githubusercontent.com/phatcvo/LPV-MPP-MPC-for-racing/main/ws/images/diagram.png) - **Planning Module**: Generates optimal trajectory using LPV-MPC - **Control Module**: Tracks the planned trajectory - **Estimation Module**: Provides state feedback ### LPV modeling The LPV (Linear Parameter-Varying) paradigm allows to represent a given non-linear representation into a pseudo-linear form: ![LPV Modeling](https://raw.githubusercontent.com/phatcvo/LPV-MPP-MPC-for-racing/main/ws/images/modeling.png) This approach enables real-time optimization while maintaining the nonlinear vehicle dynamics characteristics. ### The vehicle model The model used in planning, control and estimation algorithms is the bicycle representation where the inputs are: ![Vehicle Model Variables](https://raw.githubusercontent.com/phatcvo/LPV-MPP-MPC-for-racing/main/ws/images/variables_model.png) - **Front steering angle** (δ): Controls the lateral motion - **Rear wheel linear acceleration** (a): Controls the longitudinal motion The bicycle model captures the essential vehicle dynamics while remaining computationally efficient for real-time MPC implementation. ### MPC for planning The trajectory planning for racing is solved using the MPC technique. The cost function addresses the lap time minimization as well as the smoothness of the lateral motion by reducing as much as possible the understeer and oversteer behaviours. This algorithm is launched every 33 ms. ### MPC for control At this point an MPC is built and solved at every control iteration (33 ms) to figure out the optimal control actions (steering and rear wheel acceleration). ### Test To use this project, install it locally via: ``` git clone https://github.com/phatcvo/LPV-MPP-MPC-for-racing.git ``` To execute the code, run: ``` catkin_make (to create build and devel folders) source devel/setup.bash roslaunch barc MAIN_LAUNCH.launch ``` ![Kazam Screenshot](https://raw.githubusercontent.com/phatcvo/LPV-MPP-MPC-for-racing/main/ws/images/Kazam_screenshot_00000.png) *Note: This project demonstrates the LPV-MPC approach for autonomous racing vehicles with real-time trajectory planning and control.* ## References * Trajectory planner presented in: Alcala, E., Puig, V. & Quevedo, J. (2019). LPV-MP Planning for Autonomous Racing Vehicles considering Obstacles. Robotics and Autonomous Systems. * Controller presented in: Alcala, E., Puig, V., Quevedo, J., & Rosolia, U. (2019). Autonomous Racing using Linear Parameter Varying - Model Predictive Control (LPV-MPC). Control engineering practice. * Estimator presented in: Alcala, E., Puig, V., Quevedo, J., & Escobet, T. (2018). Gain-scheduling LPV control for autonomous vehicles including friction force estimation and compensation mechanism. IET Control Theory & Applications, 12(12), 1683-1693. (https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2017.1154).