Hierarchical trajectory generation for a class of nonlinear systems

Trajectory generation and motion planning for nonlinear control systems is an important and difficult problem. In this paper, we provide a constructive method for hierarchical trajectory generation and hierarchical motion planning. The approach is based on the recent notion of Φ-related control systems. Given a control affine system satisfying certain assumptions, we project the trajectory planning problem onto a Φ-related control system of smaller dimension. Trajectories designed for the smaller, abstracted system are guaranteed, by construction, to be feasible for the original system. Constructive procedures are provided for refining trajectories of the coarser system to the more detailed system.