Asymptotic Optimality of a Time Optimal Path Parametrization Algorithm
This provides a theoretical guarantee for a faster algorithm in robotics and motion planning, though it is incremental as it builds on prior work.
The paper tackles the problem of proving the asymptotic optimality of a linear-time algorithm for Time Optimal Path Parametrization, showing it matches the optimal solutions from more intensive convex optimization methods for all such problems.
Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed. However, its optimality was proved for only a strict subclass of problems solved optimally by more computationally intensive approaches based on convex programming. In this paper, we prove that the same linear-time algorithm is asymptotically optimal for all problems solved optimally by convex optimization approaches. We also characterize the optimum of the Time Optimal Path Parametrization Problem, which may be of independent interest.