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

This paper address dynamic trajectory planning, which is defined as trajectory planning for a robot subject to dynamic constraints and moving in a dynamic workspace, i.e., with moving obstacles. The authors propose the 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 by the time dimension. The constraints imposed by both the moving obstacles and the dynamic constraints can be represented by static forbidden regions of state-time space. Since a trajectory maps to a curve in state-time space, dynamic trajectory planning simply consists in finding a curve in state-time space. This concept is used 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