Regionally Growing Random Trees: A synergistic motion planning and control algorithm for dynamic systems

Nonlinearities, differential constraints, and input limitations preclude the use of regular feedback control algorithms in a range of complex dynamic systems. This article introduces the concept of Regionally Growing Random Trees (RGRT) as a powerful tool that synergistically combines motion planning and control tasks. RGRT is a forest of Dynamics-based Rapidly Expanding Trees (DRETs) that grow in the state-space of a dynamic system without requiring any distance function or explicit solutions of the differential equations of motion. The growth of multiple DRETs results in paths between the tree roots and forms a roadmap which is utilized in a planning algorithm to find a feasible path between a current state and a goal state. A path tracking algorithm is then used to convert the open-loop commands of the planner into a feedback controller, which provides robustness against disturbances and modeling errors. The RGRT motion planning and control scheme allows complete utilization (instead of avoidance) of system nonlinearities, which provides solutions for overcoming actuator constraints and eliminates the limitations imposed on the system by traditional feedback control approaches.