Iterative-MPC-DHOCBF

Matlab code for the paper "Iterative Convex Optimization for Model Predictive Control with Discrete-Time High-Order Control Barrier Functions", accepted by IEEE American Control Conference (ACC) 2023, Authors: Shuo Liu, Jun Zeng, Koushil Sreenath and Calin Belta [PDF]

In this paper, we propose a framework that solves the safety critical MPC problem in an iterative optimization, which is applicable for any relative-degree control barrier functions. In the proposed formulation, the nonlinear system dynamics as well as the safety constraints modeled as discrete-time high order control barrier functions (DHOCBF) are linearized at each time step. Our formulation is generally valid for any control barrier function with an arbitrary relative-degree. The advantages of fast computational performance with safety guarantee are analyzed and validated with numerical results.

Citing

If you find this project useful in your work, please consider citing following work:

@inproceedings{liu2023iterative,
  title={Iterative Convex Optimization for Model Predictive Control with Discrete-Time High-Order Control Barrier Functions},
  author={Liu, Shuo and Zeng, Jun and Sreenath, Koushil and Belta, Calin A},
  booktitle={2023 American Control Conference (ACC)},
  year={2023}
}

Instruction

There are two subfolders closedloop_performance and benchmark. closedloop_performance contains all information to generate figure 2, 3, 4 in paper and benchmark conatins code to generate data for table 1,2 in paper.

Subfolder closedloop_performance

Code Descriptions

• Closedloop_Trajectories_Hyperparameters.m includes codes to generate necessary data for figure 2-a and figure 3; "Iterative_Convergence" includes codes to generate necessary data for figure 2-b,c,d.
• Maximum_Iterations.m includes codes to generate necessary data for figure 4.
• NMPCDCBF1.m and NMPCDCBF2.m include codes related to NMPC-DHOCBF with mcbf=1 and mcbf=2 respectively and FigureGenerate.m includes codes to transfer the data into figures in paper.

Usage

• Run Closedloop_Trajectories_Hyperparameters.m, Iterative_Convergence.m and Maximum_Iterations.m and the data files are generated as MATLAB mat files.
• Run FigureGenerate.m to generate all figures in paper, which will be saved in folder closedloop_performance/figures.

Subfolder benchmark

Code Descriptions

There are four folders including the codes to generate necessary dada for table 1,2 in paper.

• gamma1_0p4gamma2_0p4 includes the codes for iMPC-DHOCBF and NMPC-DHOCBF with decay rate parameters gamma1=0.4, gamma2=0.4, mcbf=2.
• gamma1_0p4 includes the codes for iMPC-DHOCBF and NMPC-DHOCBF with decay rate parameters gamma1=0.4, mcbf=1.
• gamma1_0p6gamma2_0p6 includes the codes for iMPC-DHOCBF and NMPC-DHOCBF with decay rate parameters gamma1=0.6, gamma2=0.6, mcbf=2.
• gamma1_0p6 includes the codes for iMPC-DHOCBF and NMPC-DHOCBF with decay rate parameters gamma1=0.6, mcbf=1.

Usage

• Run InitialState.m first to generate 1000 random initial states in the mat file InitialStateData.mat, then copy it to each folder.
• In each folder, run the file test_comprehensive.m and you will see corresponding data files generated as MATLAB mat files feasibility_N.mat and timecom_N.mat which includes the information about infeasible rate and mean/variance of computing time (stored in matrices nmpcdata and impcdata) in paper from generating one time-step trajectories for iMPC-DHOCBF and NMPC-DHOCBF.

Warnings

• It may take a long time to run the file test_comprehensive.m (several hours to a day depending on your computer when the number of horizon reaches large). Instead, if you want to run the file for different number of horizon parallelly to speed up the running process, in folder test_each_horizon.m, there are six files called test_N4.m, test_N8.m, test_N12.m, test_N16.m, test_N20.m,test_N24.m which correspond to the number of horizon 4, 8, 12, 16, 20, 24 for iMPC-DHOCBF and NMPC-DHOCBF. By copying InitialStateData.mat to this folder then you can run these 6 files parallely, in order to generate same MATLAB mat files feasibility_N.mat and timecom_N.mat which includes the information about infeasible rate and mean/variance of computing time in paper from generating one time-step trajectories for iMPC-DHOCBF and NMPC-DHOCBF. You should run the file tabledata.m next and all useful data in table are stored in matrices nmpcdata and impcdata.

Post Analysis

1. For comparison of capability of generating safe optimal trajectories for different numbers of horizon and hyperparameters, please see the figure below:
2. For comparison of infeasible rate and mean/variance of computing time from generating one time-step trajectories, please see the figure below: For other figures please refer to the paper.

Dependencies

The packages needed for running the code are Yalmip and IPOPT for NMPC-DHOCBF and OSQP for iMPC-DHOCBF.