Bearing-only formation control using sign-elevation angle rigidity for avoiding formation ambiguities

Flip, flex, and reflection ambiguities, which can arise in bearing-only formation control with elevation angle rigid configurations, are addressed in this paper. Elevation angle rigidity achieves formation control in agents’ local co-ordinate system using bearing-only sensors, without any orientation synchronization or estimation algorithm. Considering elevation angle constraints to determine the formation shape, and then using a gradient based control law offers the benefit of a co-ordinate free control. However, flip, flex, and reflection ambiguities might be present in the final formation shape. To tackle this, we first develop sign-elevation angle rigidity theory to uniquely (locally) characterize formation shapes upto a translation and rotation using elevation angle and signed area/volume constraints. Thereafter, a formation control law is proposed (for 2-D and 3-D) using bearing-only information for single integrator systems, and local exponential stability is proved for formation tracking error. Finally, simulations validate the presented results.