Stability and Convergence Analysis of a Decentralized Proportional-Integral Control Strategy for Collective Transport

In this paper, we study the stability and convergence properties of a decentralized proportional-integral velocity controller for collective transport by a team of point-mass robots that are rigidly attached to a payload. The controller only requires robots' velocity measurements, and the only information provided to the robots is the target speed and direction of transport. We prove that the closed-loop system with proportional control alone is exponentially stable, and we derive the system's rate of convergence to the desired transport velocity. We analyze the parameters that affect this convergence rate and characterize its dependence on the robots' distribution around the payload. We add an integral controller to the proportional controller to compensate for any drift from the desired transport path and prove asymptotic stability in this case. We validate our analytical results for the proportional controller through simulations with three different robot distributions around the payload. These simulations demonstrate that the robots' distribution has the predicted effect on the convergence rate, which influences the load's rotation and drift from the desired path during the transient phase of transport. We also confirm through simulation that the proportional-integral controller drives this drift to zero while achieving the desired transport velocity.