Formation control of a team of single-integrator agents with measurement error

This paper investigates the formation control problem for a team of single-integrator agents subject to distance measurement error. Collision, obstacle and boundary avoidance are important features of the proposed strategy. It is assumed that upper bounds exist on the magnitude of the measurement error and its derivative w.r.t. the measured distance. A decentralized navigation function is then proposed to move the agents toward a desired final configuration which is defined based on the pairwise distances of the connected agents and the characteristics of the distance measurement error. Conditions on the magnitude of the measurement error and its derivative w.r.t. the measured distance are derived under which a new formation configuration can be achieved anywhere in the space due to the measurement error. This error-dependent formation can be determined exactly if the error model is available. If such a model is not available, the maximum discrepancy in the final distances can be obtained in terms of the maximum measurement error. Moreover, the control law designed based on the navigation function ensures collision, obstacle and boundary avoidance in the workspace. The efficacy of the proposed control strategy is demonstrated by simulation.