RRT* Based Optimal Trajectory Generation with Linear Temporal Logic Specifications under Kinodynamic Constraints

Abstract: In this paper, we present a novel RRT*-based strategy for generating kinodynamically feasible paths that satisfy temporal logic specifications. Our approach integrates a robustness metric for Linear Temporal Logics (LTL) with the system's motion constraints, ensuring that the resulting trajectories are both optimal and executable. We introduce a cost function that recursively computes the robustness of temporal logic specifications while penalizing time and control effort, striking a balance between path feasibility and logical correctness. We validate our approach with simulations and real-world experiments in complex environments, demonstrating its effectiveness in producing robust and practical motion plans. This work represents a significant step towards expanding the applicability of motion planning algorithms to more complex, real-world scenarios.