Trajectory planning in a dynamic workspace: a 'state-time space' approach

This paper addresses trajectory planning in a dynamic workspace, i.e. motion planning for a robot subject to dynamic constraints and moving in a workspace with moving obstacles. First the novel concept of state-time space is introduced, i.e. the state space of the robot augmented of the time dimension. Like configuration space which is a tool to formulate path-planning problems, state-time space is a tool to formulate trajectory planning in dynamic workspace problems. It permits us to study the different aspects of dynamic trajectory planning, i.e. moving obstacles and dynamic constraints, in a unified way. Then this new concept is applied to the case of a car-like robot subject to dynamic constraints and moving along a given path on a dynamic planar workspace. A near-time-optimal approach that searches the solution trajectory over a restricted set of canonical trajectories is presented. These canonical trajectories are defined as having discrete and piecewise constant acceleration. Under these assumptions, it is possible to transform the problem of finding the time-optimal canonical trajectory to finding the shortest path in a directed graph embedded in the state-time space.