https://github.com/shaoanlu/mppi_cbf

Colab notebooks showcasing experiments on MPPI (model predictive path integral control) and CBF (control barrier function). Utilizes jax to accelerate computation.
https://github.com/shaoanlu/mppi_cbf

control-barrier-functions jax model-predictive-control mppi safety-filter

Last synced: 6 months ago
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Colab notebooks showcasing experiments on MPPI (model predictive path integral control) and CBF (control barrier function). Utilizes jax to accelerate computation.

• Host: GitHub
• URL: https://github.com/shaoanlu/mppi_cbf
• Owner: shaoanlu
• License: mit
• Created: 2023-10-11T16:13:36.000Z (almost 2 years ago)
• Default Branch: main
• Last Pushed: 2025-02-25T10:13:26.000Z (8 months ago)
• Last Synced: 2025-04-03T01:13:27.496Z (6 months ago)
• Topics: control-barrier-functions, jax, model-predictive-control, mppi, safety-filter
• Language: Jupyter Notebook
• Homepage:
• Size: 34.5 MB
• Stars: 64
• Watchers: 2
• Forks: 14
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# mppi_cbf_playground

Colab notebooks of personal experiments with MPPI and CBF. Each notebook is stand-alone and can be executed immediately in Colab without extra setup.

## Content

| Nominal Controller | Safety Filter               | Model                                   | Colab Link                                                                                                                                                                                             |

| ------------------ | --------------------------- | --------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |

| CLF-QP               | CBF-QP                    | Omnidirectioal Robot                             | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/shaoanlu/mppi_cbf_playground/blob/main/omnirobot_numpy_composite_clfcbf.ipynb)         |

| MPPI               | CBF cost                    | Unicycle car                             | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/shaoanlu/mppi_cbf_playground/blob/main/bicycle_mppi_cbf_shielding.ipynb)         |

|                    | CBF-QP                      | Unicycle car                             | Same as above                                                                                                                                                                                          |

|                    | Nonlinear predictive filter | Unicycle car                             | Same as above                                                                                                                                                                                          |

| MPPI               | CBF cost                    | Planar quadrotor                        | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/shaoanlu/mppi_cbf_playground/blob/main/planar_quadrotor_mppi_cbf.ipynb)          |

| [Sequential QP](https://hybrid-robotics.berkeley.edu/publications/ACC2016_Safety_Control_Planar_Quadrotor.pdf)         | CLF-CBF-QP                    | Planar quadrotor | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/shaoanlu/mppi_cbf_playground/blob/main/planar_quadrotor_cbf_clf_qp.ipynb) |

| MPPI               | CBF cost                    | Planar quadrotor with a suspended payload | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/shaoanlu/mppi_cbf_playground/blob/main/planar_quadrotor_pendulum_mppi_cbf.ipynb) |

## Demonstrations

### Demo 1: bicycle car

The following animations are simulation result of MPPI controller for obstacle avoidance.

- Left: w/ CBF as a cost term in MPPI.

- Middle: w/ a CBFQP safety filter.

- Right: w/ a nonlinear predictive safety filter.



    



### Demo 2: planar quadrotor with MPPI controller

The following animations are simulation result of MPPI controller with CBF cost for obstacle avoidance.

- Left: w/ CBF as a cost term in MPPI.

- Right: w/ CBF as a cost term in MPPI. A suspended payload is attached to the quadrotor.



   



### Demo 3: plannar quadrotor with CLF-CBF-QP controller

The following figures show a closed-loop simulation result of sequential CLF-QP controller w/ and w/o CBF as a constraint.



  



### Demo 4: Closed-form solution of CLF-CBF-QP controller

The following figures show a simulation result of CLF-QP controller w/ a safety filter using composite CBF.



  



### Note for implementations

- The terminal cost in MPPI is significant. It enhances the quality of the control sequence's prior, thereby preventing the controller from inadvertently deviating the system from its target position.

- The discrete CBF cost aligns well with sampling-based predictive controllers, introducing only minimal additional computation.

- The guarantees provided by CBF-QP diminish with discretization.

### References

1. Yin, Ji, et al. "Shield Model Predictive Path Integral: A Computationally Efficient Robust MPC Approach Using Control Barrier Functions." arXiv preprint arXiv:2302.11719 (2023). https://arxiv.org/abs/2302.11719

2. Ames, Aaron D., et al. "Control barrier functions: Theory and applications." 2019 18th European control conference (ECC). IEEE, 2019. https://arxiv.org/abs/1903.11199

3. Wu, Guofan, and Koushil Sreenath. "Safety-critical control of a planar quadrotor." 2016 American control conference (ACC). IEEE, 2016.