An Amended Time-Scaling Algorithm for Kino-Dynamic Trajectories

Abstract

This paper presents a computational geometry-based implementation of the time scaling algorithm, with a linear-time complexity. The proposed method involves sampling N points along a robot’s motion path and scaling their speed profiles to meet the kino-dynamic constraints at those points. The method consists of two steps. First, it decomposes the original problem into $N-1$ 2-D subproblems, and describes the feasible domain of each subproblem using a closure that does not have redundant constraints. The algorithm considers both linear and quadratic radical constraints, and the feasible domain of every subproblem is the intersection of the discretized constraints from forward, backward and central difference schemes. Second, it solves the original problem by recursively updating the domain of the subproblems twice in two oppressive directions, and guarantees optimality when constraints of every subproblem are peaked ones. Numerical experiments show that this method can not only provide the same solution as the original forward-backward algorithm in peaked-constraint cases with similar time complexity, but also be used to handle general kinodynamic trajectories with a sparse sampling strategy.