Learning Free Terminal Time Optimal Closed-loop Control of Manipulators

This paper presents a novel approach to learning free terminal time closed-loop control for robotic manipulation tasks, enabling dynamic adjustment of task duration and control inputs to enhance performance. We extend the supervised learning approach, namely solving selected optimal open-loop problems and utilizing them as training data for a policy network, to the free terminal time scenario. Three main challenges are addressed in this extension. First, we introduce a marching scheme that enhances the solution quality and increases the success rate of the open-loop solver by gradually refining time discretization. Second, we extend the QRnet in [1] to the free terminal time setting to address discontinuity and improve stability at the terminal state. Third, we present a more automated version of the initial value problem (IVP) enhanced sampling method from previous work [2] to adaptively update the training dataset, significantly improving its quality. By integrating these techniques, we develop a closed-loop policy that operates effectively over a broad domain with varying optimal time durations, achieving near globally optimal total costs. The appendix and videos are available at https://deepoptimalcontrol.github.io/FreeTimeManipulator.