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In control theory, reactive methods have been widely celebrated owing to their success in providing robust, provably convergent solutions to control problems. Even though such methods have long been formulated for motion planning, optimality has largely been left untreated through reactive means, with the community focusing on discrete/graph-based solutions. Although the latter exhibit certain advantages (completeness, complicated state-spaces), the recent rise in Reinforcement Learning (RL), provides novel ways to address the limitations of reactive methods. The goal of this paper is to treat the reactive optimal motion planning problem through an RL framework. A policy iteration RL scheme is formulated in a consistent manner with the control-theoretic results, thus utilizing the advantages of each approach in a complementary way; RL is employed to construct the optimal input without necessitating the solution of a hard, non-linear partial differential equation. Conversely, safety, convergence and policy improvement are guaranteed through control theoretic arguments. The proposed method is validated in simulated synthetic workspaces, and compared against reactive methods as well as a PRM and an RRT⋆ approach. The proposed method outperforms or closely matches the latter methods, indicating the near global optimality of the former, while providing a solution for planning from anywhere within the workspace to the goal position. |
