Avoiding Ambiguous Framework in Distance-based Formation Control Using Virtual Followers

Abstract

In this study, we develop a shape formation controller based on regular distance-based control law. As distance rigidity theory may not be successful in achieving desired shape when the control system defined under minimally rigid graph. As a matter of fact, the formation may converge to ambiguous framework when the group of mobile robots did not initialize in proper way. This is a well-known issue with distance-based formation control while there are multiple equilibrium points in the dynamics. We introduce a new controller by adding virtual constraints to the system. The performance of control system is exemplified through numerical simulations and the convergence to the desired formation for all initial conditions validated with stability analysis.