mppi_cbf

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
CLF-QP	CBF-QP (Poisson Safety Function)	Omnidirectioal Robot
MPPI	CBF cost	Unicycle car
	CBF-QP	Unicycle car	Same as above
	Nonlinear predictive filter	Unicycle car	Same as above
MPPI	CBF cost	Planar quadrotor
Sequential QP	CLF-CBF-QP	Planar quadrotor
MPPI	CBF cost	Planar quadrotor with a suspended payload

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.

Demo 5: Closed-form solution of CLF-CBF-QP controller with Poisson equation

The following figures show a simulation result of CLF-QP controller w/ a safety filter based on a Poisson equation built from a 2D occupancy map.

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.
4. Bahati, G., Bena, R. M., & Ames, A. D. (2025). Dynamic Safety in Complex Environments: Synthesizing Safety Filters with Poisson’s Equation. arXiv preprint arXiv:2505.06794.