FlatVCP: Optimal Control for Kinematic Bicycle Model

This repository contains source code for the paper Optimal Control for Kinematic Bicycle Model with Continuous-time Safety Guarantees: A Sequential Second-order Cone Programming Approach. The repository contains both Python3 and MATLAB code.

If you use this code, we would appreciate it if you cited the paper as follows:

@ARTICLE{freire2022optimal,
  author={Freire, Victor and Xu, Xiangru},
  journal={IEEE Robotics and Automation Letters},
  title={Optimal Control for Kinematic Bicycle Model With Continuous-Time Safety Guarantees: A
Sequential Second-Order Cone Programming Approach},
  year={2022},
  volume={7},
  number={4},
  pages={11681-11688},
  doi={10.1109/LRA.2022.3204903}
}

For more information about our work, please visit ARC Lab@UW-Madison.

Python3

Dependencies & Installation

The repository is structured as a Python3 package. Thus, you can run the following command to install the dependencies.

pip3 install -r requirements.txt

For cvxpy, we recommend using MOSEK noting that you will need a license (free academic license available). We also tested ECOS with satisfactory performance.

Example

For a quick-start, inspect the file examples/fig_s.py and run it with:

python3 examples/fig_s.py

The output should be a trajectory file traj_figS.csv with the generated state-space trajectory and the following plot of the x-y trajectory.

Note that this example uses matplotlib for visualization.

MATLAB

Dependencies & Installation

The MATLAB implementation requires a working installation of YALMIP and we recommend using MOSEK. noting that you will need a license (free academic license available). However, any second-order cone programming solver should also work.

Also required is the B-splines Add-On by Levente Hunyadi.

You might also find the following MATHWORKS toolboxes useful/necessary:

• Optimization Toolbox
• Symbolic Math Toolbox
• Control Systems Toolbox

The package is lightweight and there is no installation beyond adding the following folders to your path:

addpath(userpath+"\FlatVCP\matlab\bspline")
addpath(userpath+"\FlatVCP\matlab\vcp_bk")

Then, you need to compile the SOCPs into YALMIP optimizer objects by running matlab/vcp_bk/vcp_bk_compile.m. This will generate vcp_bk_compiled.mat which will later be sourced to avoid re-compiling the SOCPs at each solve time.

Example

For a quick-start, inspect the file matlab/vcp_bk/vcp_bk_example.m and run it. You should see the following plots.

Acknowledgements

This work was supported by the University of Wisconsin-Madison and SAE/GM AutoDrive Challenge Series II.