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