Decentralized PD control for multi-robot collective transport to a target location using minimal information

In this paper, we propose decentralized position controllers for a team of point-mass robots that must cooperatively transport a payload to a target location. The robots have double-integrator dynamics and are rigidly attached to the payload. The controllers only require robots' measurements of their own positions and velocities, and the only information provided to the robots is the desired position of the payload's center of mass. We consider scenarios in which the robots do not know the position of the payload's center of mass and try to selfishly stabilize their own positions to the desired location, similar to the behaviors exhibited by certain species of ants when retrieving food items in groups. We propose a proportional-derivative (PD) controller that does not rely on inter-robot communication, prior information about the load dynamics and geometry, or knowledge of the number of robots and their distribution around the payload. Using a Lyapunov argument, we prove that under this control strategy, the payload's center of mass converges to a neighborhood of the desired position. Moreover, we prove that the payload's rotation is bounded, and its angular velocity converges to zero. We show that the error between the steady-state position of the payload's center of mass and its desired position depends on the robots' distribution around the payload's center of mass, with a uniform distribution resulting in the lowest steady-state error. We validate our theoretical results with simulations in MATLAB.