Biconvex Optimization for Smooth Minimum-Time Trajectories around Convex Obstacles

Peter Werner, Tobia Marcucci, Daniela Rus

Keywords: minimum-time motion planning, convex optimization

TL;DR: We propose a biconvex procedure for finding smooth, minimum-time trajectories around collections of convex obstacles.

Abstract: We present an anytime approach for minimum-time motion planning around convex obstacles that computes high-quality trajectories, is reliable, and supports derivative constraints to arbitrary order. We convexify the minimum-time objective and all derivative constraints through a change of variables, and handle collision avoidance via time-varying separating planes, reducing the problem to a biconvex program. Our anytime algorithm alternates between computing maximum-margin separating planes and optimizing the trajectory. By only adding planes for obstacles that the current iterate collides with, the trajectory can jump around obstacles and escape some local minima. The method requires a collision-free path as initialization, e.g., a sequence of collision-free waypoints, and is then guaranteed to converge to a solution. On a dual-arm pallet unloading benchmark, our approach produces trajectories with comparable quality and computation times as a state-of-the-art decomposition-based planner, while being more general and substantially more robust to bad initialization.

Submission Number: 29