Approximate kinodynamic planning using L2-norm dynamic bounds

AbstractIn this paper we address the issue of kinodynamic motion planning. Given a point that moves with bounded acceleration and velocity, we wish to find the time-optimal trajectory from a start state to a goal state (a state consists of both a position and a velocity). As finding exact optimal solutions to this problem seems very hard, we present a provably good approximation algorithm using the L2 norm to bound acceleration and velocity. Our results are an extension of the earlier work of Canny, Donald, Reif, and Xavier [1], who present similar results where the dynamics bounds can be examined in each dimension independently (they use the L∞ norm to bound acceleration and velocity)