Simultaneous Arrival Control for Distributed Multi-Robot Systems with Curvature and Constant-Speed Constraints
zhouru xiao, Yang Lu, Weijia Yao, min liu, Yaonan Wang
AI summary
Problem
Coordinating multiple robots with strict curvature and constant-speed constraints to reach a target simultaneously is difficult, particularly when robots start near the target with opposing headings, while avoiding centralized control. Existing methods often neglect physical saturation limits or lack rigorous theoretical and experimental validation.
Approach
The authors introduce a virtual time variable based on Dubins path geometry and use a maximum consensus protocol to drive each robot's virtual time toward the maximum among its neighbors. A hybrid control law switches between optimal Dubins-based steering and saturated proportional control to guide the robots.
Key results
- Proves simultaneous arrival under mild conditions with rigorous convergence analysis
- Derives analytical solutions for Dubins path lengths under curvature constraints
- Achieves theoretically optimal arrival time in specific scenarios
- Validated through large-scale simulations and real quadrotor experiments with collision avoidance
Why it matters
Provides a scalable, low-overhead coordination strategy for kinematically constrained multi-robot platforms like fixed-wing UAVs in time-critical cooperative missions.
Abstract
The simultaneous arrival of multiple mobile robots at a target point is crucial for cooperation tasks such as cooperative encirclement, disaster relief, and environmental monitoring. Although the simultaneous arrival problem itself is already complex, the problem becomes more challenging when there are constraints on the robot trajectory curvatures and the speeds are required to be constant (possibly different for different robots), and the control law for robots needs to be distributed. These constraints are typical for a multi- robot system consisting of, e.g., fixed-wing UAVs. To address this challenge, this paper proposes a distributed switching control method based on the maximum consensus protocol. By exploiting the geometric properties of Dubins paths along with optimization principles, a virtual time variable is introduced, and a hybrid control law that combines optimal control with saturated proportional control is designed. Under the proposed control law, each robot is driven to approach the maximum virtual time among its neighbors, thereby achieving simulta- neous arrival under some mild conditions. Furthermore, we prove that in certain cases the proposed method attains a theoretically optimal arrival time. The approach is scalable and real-time, with low communication overhead. Its effectiveness and robustness are validated through extensive simulations and experiments.