Multi-Robot Coordination Under Physical Limitations
Tohid Kargar Tasooji, Sakineh Khodadadi
TL;DR
The paper addresses energy-efficient, distributed rendezvous for $N$ mobile robots under actuator constraints by integrating Pontryagin’s Minimum Principle with an algebraic Riccati equation–based gain design. It derives two main results: an unconstrained optimal protocol $U^*(t)=-(\mathcal{L}\otimes K)\varepsilon(t)$ with $K=R^{-1}B^T P$ where $P$ solves $P A + A^T P + Q - P B R^{-1} B^T P = 0$, and a bounded-input extension that projects the unconstrained input onto [$U_{min},U_{max}$], yielding a bang-bang control with explicit switching conditions. The approach is validated through simulations and Robotarium experiments, demonstrating robust rendezvous despite communication delays, packet loss, and wheel-velocity limits, and highlighting the trade-offs between convergence speed and control effort governed by $Q$ and $R$. These results offer a practical, scalable framework for distributed multi-robot coordination in real-world settings where physical and communication constraints are prominent.
Abstract
Multi-robot coordination is fundamental to various applications, including autonomous exploration, search and rescue, and cooperative transportation. This paper presents an optimal consensus framework for multi-robot systems (MRSs) that ensures efficient rendezvous while minimizing energy consumption and addressing actuator constraints. A critical challenge in real-world deployments is actuator limitations, particularly wheel velocity saturation, which can significantly degrade control performance. To address this issue, we incorporate Pontryagin Minimum Principle (PMP) into the control design, facilitating constrained optimization while ensuring system stability and feasibility. The resulting optimal control policy effectively balances coordination efficiency and energy consumption, even in the presence of actuation constraints. The proposed framework is validated through extensive numerical simulations and real-world experiments conducted using a team of Robotarium mobile robots. The experimental results confirm that our control strategies achieve reliable and efficient coordinated rendezvous while addressing real-world challenges such as communication delays, sensor noise, and packet loss.