Harmonic-Based Optimal Motion Planning in Constrained Workspaces Using Reinforcement Learning

In this work, we propose a novel reinforcement learning algorithm to solve the optimal motion planning problem. Particular emphasis is given on the rigorous mathematical proof of safety, convergence as well as optimality w.r.t. to an integral quadratic cost function, while reinforcement learning is adopted to enable the cost function's approximation. Both offline and online solutions are proposed, and an implementation of the offline method is compared to a state-of-the-art RRT$^{\star }$ approach. This novel approach inherits the strong traits from both artificial potential fields, i.e., reactivity, as well as sampling-based methods, i.e., optimality, and opens up new paths to the age-old problem of motion planning, by merging modern tools and philosophies from various corners of the field.