Optimal Prescribed-Time Control based Reactive Planning System for Quadruped Robot Navigation

In this paper, we propose a reactive planning system for quadruped robots based on prescribed-time control. The navigation of the quadruped robot is fundamentally depicted as omnidirectional movements, while a feedback control law is formulated to address any deviations the robot may encounter. In particular, our proposed feedback control system is theoretically proven to achieve convergence within a predefined finite time that is specified by the user. To further compute the optimal convergent time and the local goal state, we present a high-level planning node encompassing terrain-aware kinodynamic search and spatiotemporal trajectory optimization, which can generate collision-free, smooth, and efficient trajectories. The effectiveness of our proposed framework is validated through both numerical simulation and real-robot experiments in indoor and outdoor environments, including scenarios with cluttered obstacles, slopes, and external disturbances.