We investigate a path planning algorithm for generating robust and safe paths, which satisfy mission requirements specified in linear temporal logic (LTL). When robots are deployed to perform a mission, there can be disturbances which can cause mission failures or collisions with obstacles. Hence, a path planning algorithm needs to consider safety and robustness against possible disturbances. We present a robust path planning algorithm, which maximizes the probability of success in accomplishing a given mission by considering disturbances in robot dynamics while minimizing the moving distance of a robot. The proposed method can guarantee the safety of the planned trajectory by incorporating an LTL formula and chance constraints in a hierarchical manner. A high-level planner generates a discrete plan satisfying the mission requirements specified in LTL. A low-level planner builds a sampling-based RRT search tree to minimize both the mission failure probability and the moving distance while guaranteeing the probability of collision with obstacles to be below a specified threshold. We validate the robustness and safety of paths generated by the algorithm in simulation and experiments using a quadrotor.
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