Safe and Dynamically-Feasible Motion Planning using Control Lyapunov and Barrier Functions

This article considers the problem of designing motion planning algorithms for control-affine systems that generate collision-free paths from an initial to a final destination and can be executed using safe and dynamically feasible controllers. We introduce the compatible control lyapunov function control barrier function rapidly exploring random tree (C-CLF-CBF-RRT) algorithm, which produces paths with such properties and leverages rapidly exploring random trees (RRTs), control Lyapunov functions (CLFs), and control barrier functions (CBFs). For linear systems with polytopic and ellipsoidal constraints, C-CLF-CBF-RRT requires solving a quadratically constrained quadratic program at every iteration of the algorithm, which can be done efficiently. We prove the probabilistic completeness of C-CLF-CBF-RRT and showcase its performance in simulation and hardware experiments.