Safe and Dynamically Feasible Motion Planning Using Control Lyapunov and Barrier Functions

This paper 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 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 (QCQP) 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.