Translational Drift in Formation Control Under Infeasible Configurations

Abstract

This paper investigates formation control for networks of single-integrators based solely on relative position measurements. Unlike prevalent studies, which assume feasible displacement constraints and focus on convergence conditions, we analyze the closed-loop dynamics when the desired configuration is infeasible. We show that the standard formation control law induces a translational drift whose properties are determined by the sensing topology. We further characterize this drift explicitly in terms of the spectral structure of the graph Laplacian. To eliminate this unintended motion, we propose a distributed control law that compensates for the drift and guarantees convergence to a stationary formation. Numerical simulations validate the theoretical analysis of the drift and demonstrate the effectiveness of the proposed controller. © 2017 IEEE.