Update README.md
Jun Zeng
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README.md
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README.md
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# MPC-CBF
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Model Predictive Control with Control Barrier Functions
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We propose a control framework which unifies the model predictive control and control barrier functions. This is the reference implementation of our paper:
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### Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function
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[PDF](https://arxiv.org/abs/2007.11718) | [Code: Double Integratror](double-integrator-2D) | [Code: Car Racing](car-racing)
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*Jun Zeng, Bike Zhang and Koushil Sreenath*
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# Prerequisites
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## Matlab
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<img src="car-racing/demo.gif" height="200"/>
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#### Citing
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If you find this code useful in your work, please consider citing:
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```shell
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@article{zeng2020mpccbf,
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title={Safety-critical model predictive control with discrete-time control barrier function},
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author={Zeng, Jun and Zhang, Bike and Sreenath, Koushil},
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journal={arXiv preprint arXiv:2007.11718},
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year={2020}
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}
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```
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### Instructions
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Two independent markdown files are written to illustrate numerical examples of [double integrator](double-integrator-2D/README.md) and [racing car](car-racing/README.md).
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### Dependencies
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#### Matlab
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The packages needed for running the code are [Yalmip](https://yalmip.github.io/) and [IPOPT](https://projects.coin-or.org/Ipopt/wiki/MatlabInterface).
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We also provide the zipped version of precompiled .mex files for IPOPT in the folder `packages` in case you don't have it. Unzip that file and add those .mex files into your MATLAB path.
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# Description
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## 2D double integrator
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The 2D double integrator is assigned to reach the target position at origin while avoiding obstacles. We have three classes for different controllers: `DCLF_DCBF.m` (DCLF-DCBF), `MPC_CBF.m` (MPC-CBF) and `MPC_DC` (MPC-DC), respectively.
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Moreover, to illustrate the performance among them, we have:
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* `main.m`: Run DCLF-DCBF/MPC-CBF/MPC-DC respectively.
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* `analysis_gamma.m`: Run analysis for different hyperparameter $\gamma$.
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* `analysis_horizon.m`: Run analysis for different horizon.
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We illustrate the performance between DCLF-DCBF/MPC-DC/MPC-CBF
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| DCLF-DCBF | MPC-DC (N=8) |
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| --- | --- |
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| <img src="double-integrator-2D/figures/dclf-dcbf-avoidance.png" width="200" height="200"> | <img src="double-integrator-2D/figures/mpc-dc-avoidance.png" width="200" height="200"> |
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| MPC-CBF (N=1) | MPC-CBF (N=8) |
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| --- | --- |
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| <img src="double-integrator-2D/figures/mpc-cbf-avoidance-one-step.png" width="200" height="200"> | <img src="double-integrator-2D/figures/mpc-cbf-avoidance-several-steps.png" width="200" height="200"> |
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and also the safety performance for different numbers of horizon and hyperparameters
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| Different hyperparameter | Different horizon |
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| --- | --- |
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| <img src="double-integrator-2D/figures/benchmark-gamma.png" width="200" height="200"> | <img src="double-integrator-2D/figures/benchmark-horizon.png" width="200" height="200"> |
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## Car racing competition
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We have the speed profile and control input shown as follow,
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<img src="car-racing/lmpc-speed-norm-profile.png" width="400">
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<img src="car-racing/lmpc-deviation-profile.png" width="400">
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<img src="car-racing/lmpc-input-profile.png" width="400">
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The animation can be found on the top of this readme, we will release full code after the paper is accepted.
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# References
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This repository is based on the following:
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* Jun Zeng, Bike Zhang and Koushil Sreenath. "Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function." [[PDF]](http://arxiv.org/abs/2007.11718)
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### Car racing competition
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The source codes are mainly adapted from Ugo's LMPC code and there are some lagacy features which are not used in our paper.
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We simulate a car racing competition between several cars, and ego car's speed profile and control input are shown as follow,
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<img src="lmpc-speed-norm-profile.png" width="400">
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<img src="lmpc-deviation-profile.png" width="400">
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<img src="lmpc-input-profile.png" width="400">
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The animation can be found on the top of this readme, we will release full code after the paper is accepted.
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### 2D double integrator
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The 2D double integrator is assigned to reach the target position at origin while avoiding obstacles. We have three classes for different controllers: `DCLF_DCBF.m` (DCLF-DCBF), `MPC_CBF.m` (MPC-CBF) and `MPC_DC` (MPC-DC), respectively.
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Moreover, to illustrate the performance among them, we have:
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* `main.m`: Run DCLF-DCBF/MPC-CBF/MPC-DC respectively.
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* `analysis_gamma.m`: Run analysis for different hyperparameter $\gamma$.
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* `analysis_horizon.m`: Run analysis for different horizon.
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We illustrate the performance between DCLF-DCBF/MPC-DC/MPC-CBF
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| DCLF-DCBF | MPC-DC (N=8) |
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| --- | --- |
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| <img src="figures/dclf-dcbf-avoidance.png" width="200" height="200"> | <img src="figures/mpc-dc-avoidance.png" width="200" height="200"> |
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| MPC-CBF (N=1) | MPC-CBF (N=8) |
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| --- | --- |
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| <img src="figures/mpc-cbf-avoidance-one-step.png" width="200" height="200"> | <img src="figures/mpc-cbf-avoidance-several-steps.png" width="200" height="200"> |
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and also the safety performance for different numbers of horizon and hyperparameters
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| Different hyperparameter | Different horizon |
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| --- | --- |
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| <img src="figures/benchmark-gamma.png" width="200" height="200"> | <img src="figures/benchmark-horizon.png" width="200" height="200">
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