Path Planning Using Wasserstein Distributionally Robust Deep Q-learning

We investigate the problem of risk averse robot path planning using the deep reinforcement learning and distributionally robust optimization perspectives. Our problem formulation involves modelling the robot as a stochastic linear dynamical system, assuming that a collection of process noise samples is available. We cast the risk averse motion planning problem as a Markov decision process and propose a continuous reward function design that explicitly takes into account the risk of collision with obstacles while encouraging the robot's motion towards the goal. We learn the risk-averse robot control actions through Lipschitz approximated Wasserstein distributionally robust deep Q-learning to hedge against the noise uncertainty. The learned control actions result in a safe and risk averse trajectory from the source to the goal, avoiding all the obstacles. Various supporting numerical simulations are presented to demonstrate our proposed approach.