Distributed Motion Planning for Multi-Robot Systems under Topological Constraints

2026-10-07

AI Summary

This study addresses the slow execution and suboptimality of distributed motion planning under topological braid constraints in multi-robot systems. We propose a novel approach that employs winding numbers as surrogate metrics, transforming discrete topological constraints into continuously trackable functions. This formulation enables the decoupling of global specifications into local pairwise tasks. By integrating model predictive control with a distributed consensus algorithm for progress synchronization, the proposed method overcomes the inefficiency bottleneck inherent in traditional single-generator execution. Both simulation and hardware experiments demonstrate that our approach significantly outperforms existing methods in terms of execution speed and control cost.

Abstract

Efficient and distributed coordination of mobile robots is one of the main challenges in multi-robot systems. Topological constraints, often expressed as topological braids, are a popular tool to encode complex coordination patterns between multiple mobile robots, as they offer a compact and abstract representation of the desired qualitative relation between the space-time trajectories of the robots. However, execution of joint motion plans encoded as braid-based topological constraints via distributed controllers is challenging, with existing approaches, generally based on the execution of one braid generator at a time, producing slow and suboptimal trajectories. We propose a distributed controller based on Model Predictive Control (MPC) to efficiently execute braid-based topological specifications. Rather than directly tracking the braid specification, we propose to use winding numbers, which are topological invariants for braids, as a proxy. This has the twofold benefit of converting braids into a continuous function, which can be easily tracked by an MPC controller through an appropriate term in the cost function, and of decoupling the global braid specification into a set of pairwise specifications, which can be tracked distributedly through the solution of only local MPC problems. To maintain global coordination, we propose a consensus-based progress estimation approach, which allows the robots to synchronize their motion toward the desired specification. We validate the proposed approach in simulation and in real-world experiments, where we demonstrate the effectiveness of the proposed approach and the improvement over existing approaches in terms of execution speed and control effort.

Problem

• Multi-Robot Systems
• Distributed Motion Planning
• Topological Constraints
• Braids
• Trajectory Execution

Innovation

• Distributed Motion Planning
• Model Predictive Control
• Topological Braids
• Winding Numbers
• Multi-Robot Systems