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). We show that C-CLF-CBF-RRT is computationally efficient for linear systems with polytopic and ellipsoidal constraints, and establish its probabilistic completeness. We showcase the performance of C-CLF-CBF-RRT in different simulation and hardware experiments.

@article{mestres2025_2410.08364,
  title={ Safe and Dynamically-Feasible Motion Planning using Control Lyapunov and Barrier Functions },
  author={ Pol Mestres and Carlos Nieto-Granda and Jorge Cortés },
  journal={arXiv preprint arXiv:2410.08364},
  year={ 2025 }
}