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
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 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.

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