Velocity Obstacle for Polytopic Collision Avoidance for Distributed Multi-robot Systems

TL;DR

This paper introduces a novel, computationally efficient velocity obstacle method for collision avoidance among polytopic-shaped robots in multi-robot systems, improving scalability and real-time performance.

Contribution

It extends the velocity obstacle concept to polytopic robots using a vertex-based, optimization-free construction, enabling faster and more scalable multi-robot navigation.

Findings

Outperforms existing methods in completion rate

Reduces deadlock occurrences

Decreases average travel distance

Abstract

Obstacle avoidance for multi-robot navigation with polytopic shapes is challenging. Existing works simplify the system dynamics or consider it as a convex or non-convex optimization problem with positive distance constraints between robots, which limits real-time performance and scalability. Additionally, generating collision-free behavior for polytopic-shaped robots is harder due to implicit and non-differentiable distance functions between polytopes. In this paper, we extend the concept of velocity obstacle (VO) principle for polytopic-shaped robots and propose a novel approach to construct the VO in the function of vertex coordinates and other robot's states. Compared with existing work about obstacle avoidance between polytopic-shaped robots, our approach is much more computationally efficient as the proposed approach for construction of VO between polytopes is optimization-free. Based on VO representation for polytopic shapes, we later propose a navigation approach for distributed multi-robot systems. We validate our proposed VO representation and navigation approach in multiple challenging scenarios including large-scale randomized tests, and our approach outperforms the state of art in many evaluation metrics, including completion rate, deadlock rate, and the average travel distance.