Colab notebooks of personal experiments with MPPI and CBF. Each notebook is stand-alone and can be executed immediately in Colab without extra setup.
| Nominal Controller | Safety Filter | Model | Colab Link |
|---|---|---|---|
| MPPI | CBF cost | Bicycle car |  |
| CBF-QP | Bicycle car | Same as above | |
| Nonlinear predictive filter | Bicycle car | Same as above | |
| MPPI | CBF cost | Planar quadrotor | |
| Sequential QP | CLF-CBF-QP | Planar quadrotor | |
| MPPI | CBF cost | Planar quadrotor with suspended payload | |
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.
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.
The following figures show a closed-loop simulation result of sequential CLF-QP controller w/ and w/o CBF as a constraint.
- 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.
- 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
- 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
- Wu, Guofan, and Koushil Sreenath. "Safety-critical control of a planar quadrotor." 2016 American control conference (ACC). IEEE, 2016.