A space-time RRT algorithm for time-dependent objectives

A new Rapidly-exploring Random Tree (RRT) algorithm variant is proposed for dealing with time-dependent motion planning problems in complex environments. The algorithm takes into account the time- varying nature of the goal region, the constraints, and the system dynamics, and it provides solutions that are guaranteed to converge to minimal-time solution. The proposed algorithm is based on the original RRT algorithm, and it utilizes a novel set of methods for generating asymptomatically-optimal trajectories for systems subject to complex differential constraints. The algorithm is evaluated in a simulation study involving a Dubins car-like vehicle, which represents a crude description of the dynamics of an aerial vehicle.