Safe Motion Planning for an Uncertain Non-Holonomic System with Temporal Logic Specification

We propose a sampling-based motion planning algorithm for systems with complex dynamics and temporal logic specifications allowing to tackle sophisticated missions. By complex dynamics we refer to non-holonomy and disturbance that prevent implementation of an exact steer function. We instead construct a set of feedback motion primitives guaranteeing bounded state uncertainty (and thus safety) allowing the system to follow an arbitrarily long trajectory without replanning. The motion primitives allow to use A*-based algorithm to provably accomplish the temporal logic mission. We propose a heuristics for the A*-based algorithm via construction of backward trees. We illustrate the approach on several case studies, including simulations of a rover and fixed wing drone. We further show that construction of backward trees allows for faster re-planning compared to the state-of-the-art.