Dynamic trajectory planning with dynamic constraints: A 'state-time space' approach

| This paper addresses dynamic trajectory planning which is deened as trajectory planning for a robot subject to dynamic constraints and moving in a dynamic workspace, i.e. with moving obstacles. To begin with, we propose the novel concept of state-time space as a tool to formulate dynamic trajectory planning problems. The state-time space of a robot is its state space augmented of the time dimension. It permits to study the diierent aspects of dynamic trajectory planning in a uniied way. Thus the constraints imposed by both the moving obstacles and the dynamic constraints can be represented by static forbidden regions of state-time space. Besides a trajectory maps to a curve in state-time space hence dynamic trajectory planning simply consists in nding a curve in state-time space. Then we apply this new concept in order to determine a time-optimal trajectory for a car-like robot subject to dynamic constraints and moving along a given path on a dynamic planar workspace. We present an approximate method which searches the solution trajectory over a restricted set of canonical trajectories. These canonical trajectories are deened as having piecewise constant acceleration that can only change its value at given times. Besides the acceleration is selected so as to be either minimum, null or maximum. Under these assumptions, it is possible to transform the problem of nding the time-optimal canonical trajectory to nding the shortest path in a directed graph embedded in the state-time space. Abstract | This paper addresses dynamic trajectory planning which is deened as trajectory planning for a robot subject to dynamic constraints and moving in a dynamic workspace, i.e. with moving obstacles. To begin with, we propose the novel concept of state-time space as a tool to formulate dynamic trajectory planning problems. The state-time space of a robot is its state space augmented of the time dimension. It permits to study the diierent aspects of dynamic trajectory planning in a uniied way. Thus the constraints imposed by both the moving obstacles and the dynamic constraints can be represented by static forbidden regions of state-time space. Besides a trajectory maps to a curve in state-time space hence dynamic trajectory planning simply consists in nding a curve in state-time space. Then we apply this new concept in order to determine a time-optimal trajectory for a car-like robot subject to dynamic constraints and moving along a given path on a dynamic planar workspace. We present an …