Guaranteed-Safe MPPI Through Composite Control Barrier Functions for Efficient Sampling in Multi-Constrained Robotic Systems

We present a guaranteed-safe model predictive path integral (GS-MPPI) control algorithm that enhances sample efficiency in nonlinear systems with multiple safety constraints. The approach uses a composite control barrier function (CBF) along with MPPI to ensure all sampled trajectories are provably safe. We construct a single CBF constraint from multiple safety constraints with potentially differing relative degrees, yielding a closed-form safe control law. Integrating this into system dynamics enables MPPI to optimize exclusively over safe trajectories. The method improves computational efficiency while addressing CBFs' myopic behavior by incorporating long-term performance considerations. Simulations of a nonholonomic ground robot with position and speed constraints demonstrate the algorithm's effectiveness.