Kinodynamic planning in a structured and time-varying 2-D workspace

This paper deals with a trajectory planning problem that we call the ‘highway problem’. It consists in planning a time-optimal trajectory for a mobile which is travelling in a structured workspace amidst moving obstacles and is subject to constraints on its velocity and acceleration. By structured workspace, we mean that there exists lanes characterized by one-dimensional curves along which the mobile is able to move. The mobile has to follow a lane but it may also shift from its lane to an adjacent one. This paper presents an efficient method which determines an approximate time-optimal solution to the highway problem. The approach consists in discretizing time and selecting the accelerations applied to the mobile among a discrete set. These hypotheses make it possible to define a grid in the mobile’s time-state space, i.e. the mobile’s state (or phase) space augmented of the time dimension. This grid is then searched in order to find a soh tion.