A Singularity-Free Vector-Field-Based Framework for Safe Distributed Motion Coordination of Multirobot Systems

Abstract

Guiding vector-field (GVF) methods provide effective solutions for manifold-following problems by generating smooth guidance signals that steer robots toward and navigate desired geometric manifolds. Recent advances in high-dimensional GVF design have successfully eliminated singularities that arise in classical formulations. However, robots must additionally achieve obstacle avoidance, interrobot collision prevention, and cooperative coordination in practical applications. When vector-field composition is introduced, existing GVF-based approaches often fail to preserve the singularity-free property. To address this challenge, a truncated GVF and an obstacle-avoidance vector field are integrated in a high-dimensional space, enabling robots to follow the desired path while simultaneously avoiding obstacles. Based on this formulation, a unified and distributed coordination and safety framework is further developed to enable cooperative motion while simultaneously incorporating obstacle avoidance and interrobot collision prevention. Through the introduction of appropriately designed virtual coordinates, the composite GVF is shown to be system-level singularity-free in the sense of collective nonvanishing and nonpersistence of individual vector-field zeros. Rigorous theoretical analysis establishes safety under nonconflicting simultaneous safety constraints and proves conditional convergence when the avoidance terms eventually become inactive. Extensive numerical simulations and software-in-the-loop experiments validate the effectiveness of the proposed method in both single-robot and multirobot scenarios. In addition, real-world vertical takeoff and landing unmanned aerial vehicle experiments empirically demonstrate the applicability of the proposed approach in realistic flight environments.