Integral reinforcement learning-based approximate minimum time-energy path planning in an unknown environment

Path planning is a fundamental and critical task in many robotic applications. For energy-constrained robot platforms, path planning solutions are desired with minimum time arrivals and minimal energy consumption. Uncertain environments, such as wind conditions, pose challenges to the design of effective minimum time-energy path planning solutions. In this article, we develop a minimum time-energy path planning solution in continuous state and control input spaces using integral reinforcement learning (IRL). To provide a baseline solution for the performance evaluation of the proposed solution, we first develop a theoretical analysis for the minimum time-energy path planning problem in a known environment using the Pontryagin's minimum principle. We then provide an online adaptive solution in an unknown environment using IRL. This is done through transforming the minimum time-energy problem to an approximate minimum time-energy problem and then developing an IRL-based optimal control strategy. Convergence of the IRL-based optimal control strategy is proven. Simulation studies are developed to compare the theoretical analysis and the proposed IRL-based algorithm.