Robust Multi-Robot Trajectory Optimization Using Alternating Direction Method of Multiplier

TL;DR

This paper introduces a novel ADMM-based approach for multi-robot trajectory optimization that guarantees collision avoidance, preserves homotopy, and significantly speeds up computation compared to traditional methods.

Contribution

The paper presents a new ADMM framework for constrained trajectory optimization that is faster and maintains theoretical guarantees of collision avoidance and homotopy preservation.

Findings

Achieves an order of magnitude speedup over existing solvers.

Generates trajectories of comparable quality to state-of-the-art methods.

Successfully applied to multi-UAV and multi-robot arm scenarios.

Abstract

We propose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and decentralized parameter updates. Starting from a collision-free initial trajectory, our method inherits the theoretical properties of primal interior point method (P-IPM), i.e., guaranteed collision avoidance and homotopy preservation throughout optimization, while being orders of magnitude faster. We have analyzed the convergence and evaluated our method for time-optimal multi-UAV trajectory optimizations and simultaneous goal-reaching of multiple robot arms, where we take into consider kinematics-, dynamics-limits, and homotopy-preserving collision constraints. Our method highlights an order of magnitude's speedup, while generating trajectories of comparable qualities as state-of-the-art P-IPM solver.