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

TL;DR

This work addresses safe real-time control for nonlinear robotic systems under multiple safety constraints by marrying composite control barrier functions with model-predictive path integral control. The authors construct a composite soft-minimum R-CBF to enforce all constraints as hard safety, yielding a closed-form control $u_*(x,v)$ that minimally deviates from a desired input while guaranteeing safety. They embed this safe control into a discrete MPPI formulation, deriving an update rule via KL divergence that guides planning to explore and optimize within the guaranteed-safe set. A two-level GS-MPPI algorithm is proposed to plan over a receding horizon while applying a fast inner safety filter, resulting in trajectories that are both safe and performance-oriented. Numerical results on a nonholonomic robot with obstacles illustrate safety guarantees, improved sample efficiency, and effective long-horizon planning within the safe region.

Abstract

We present a new guaranteed-safe model predictive path integral (GS-MPPI) control algorithm that enhances sample efficiency in nonlinear systems with multiple safety constraints. The approach use a composite control barrier function (CBF) along with MPPI to ensure all sampled trajectories are provably safe. We first construct a single CBF constraint from multiple safety constraints with potentially differing relative degrees, using it to create a safe closed-form control law. This safe control is then integrated into the system dynamics, allowing MPPI to optimize over exclusively safe trajectories. The method not only improves computational efficiency but also addresses the myopic behavior often associated with CBFs by incorporating long-term performance considerations. We demonstrate the algorithm's effectiveness through simulations of a nonholonomic ground robot subject to position and speed constraints, showcasing safety and performance.

Figures (4)

• Figure 1: Block diagram of the Guaranteed-Safe Model Predictive Path Integral (MPPI) control architecture, illustrating the interaction between the Safety Filter, Safe System, and MPPI Planner components.
• Figure 2: Safe set and closed-loop trajectories using Algorithms \ref{['alg:mppi']} and \ref{['alg:mppi_cbf']}
• Figure 3: $q_{\rm x}$, $q_{\rm y}$, $\nu$, $\theta$, $u$, $v$ for $q_{{\rm d}}=[\,3 \quad 4.5\,]^\top$.
• Figure 4: $h$, $\min b_{j,i}$, and $\min h_j$ for $q_{{\rm d}}=[\,3 \quad 4.5\,]^{\rm T}$.