Simultaneous Arrival Control for Distributed Multi-Robot Systems with Curvature and Constant-Speed Constraints

Abstract

The simultaneous arrival of multiple mobile robots at their respective target points is crucial for cooperative tasks such as encirclement, interception, and disaster relief. Although the problem of simultaneous arrival is inherently complex, it becomes even more challenging in multi-robot systems with curvature-constrained trajectories and constant-speed requirements that may differ among robots, along with the need for distributed, real-time, and low-communication control. These constraints are typical for a multi-robot system, such as one consisting of fixed-wing UAVs or car-like mobile robots. To address this challenge, this paper proposes a distributed switching control method based on the maximum consensus protocol. Inspired by the optimization principles and geometric properties of Dubins paths, we introduce a virtual time variable and design a hybrid control law that combines optimal control with saturated proportional control. Under the proposed control law, each robot is driven to approach the maximum virtual time among its neighbors, thereby achieving simultaneous arrival under mild conditions. Furthermore, we prove that in certain cases the proposed method achieves a theoretically optimal arrival time, and its effectiveness and robustness are validated through extensive simulations and real-world experiments.