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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.

Bicycle Python
  Example

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.

Bicycle MATLAB Example Path

Bicycle MATLAB Example State Bicycle MATLAB Example Input

Acknowledgements

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

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