Multi-Robot Trajectory Generation via Consensus ADMM: Convex vs. Non-Convex

TL;DR

This paper compares convex and non-convex C-ADMM algorithms for multi-robot trajectory planning, demonstrating that convex approaches converge faster and are safer, while non-convex methods risk sub-optimality and safety violations.

Contribution

It introduces a convex C-ADMM framework for multi-robot trajectory planning using Buffered Voronoi Cells, and compares its performance to non-convex C-ADMM, highlighting convergence and safety benefits.

Findings

Convex C-ADMM converges 1000 iterations faster.

Non-convex C-ADMM yields sub-optimal solutions.

Non-convex C-ADMM can violate safety constraints.

Abstract

C-ADMM is a well-known distributed optimization framework due to its guaranteed convergence in convex optimization problems. Recently, C-ADMM has been studied in robotics applications such as multi-vehicle target tracking and collaborative manipulation tasks. However, few works have investigated the performance of C-ADMM applied to non-convex problems in robotics applications due to a lack of theoretical guarantees. For this project, we aim to quantitatively explore and examine the convergence behavior of non-convex C-ADMM through the scope of distributed multi-robot trajectory planning. We propose a convex trajectory planning problem by leveraging C-ADMM and Buffered Voronoi Cells (BVCs) to get around the non-convex collision avoidance constraint and compare this convex C-ADMM algorithm to a non-convex C-ADMM baseline with non-convex collision avoidance constraints. We show that the convex C-ADMM algorithm requires 1000 fewer iterations to achieve convergence in a multi-robot waypoint navigation scenario. We also confirm that the non-convex C-ADMM baseline leads to sub-optimal solutions and violation of safety constraints in trajectory generation.