shaoanlu / mppi_cbf

Colab notebooks showcasing experiments on MPPI (model predictive path integral control) and CBF (control barrier function). Utilizes jax to accelerate computation.

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
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

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

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.

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