Randomized sampling-based trajectory optimization for UAVs to satisfy linear temporal logic specifications

Abstract

We address the problem of optimal trajectory planning for a fixed wing- or quadrotor aircraft to satisfy linear temporal logic (LTL) specifications on its motion. To this end, we propose a randomized sampling-based motion planning algorithm with probabilistic guarantees of completeness and optimality. Similar to the well-known rapidly-exploring random tree (RRT⁎) algorithm, the proposed algorithm incrementally generates a tree in which edges are associated with vehicle control inputs. Random samples are taken from multiple copies of the state space, where each copy is uniquely associated with a state of the Büchi automaton that accepts the given LTL specification. To achieve significant reductions in computation time, we propose a sampling heuristic that provides a bias for growing the tree structure. This sampling heuristic preserves the completeness and optimality properties of the RRT⁎ algorithm. We provide numerical simulation results of the application of the proposed algorithm to show up to approximately 80% reductions in computation time achieved due to this sampling heuristic.