Multi‐vehicle formation in a controllable force field with non‐identical controller gains

In this brief, a non‐identical gain based control design scheme is proposed to stabilise balanced collective formation in multi‐vehicle systems, modelled with non‐holonomic unicycle dynamics. Balanced collective formation refers to a situation in which the vehicles' motion causes their positional centroid to become stationary. This study mainly focuses on achieving stable balanced collective formation about the prescribed location of the collective centroid along with desired orientations of the vehicles. It is assumed that the vehicles are moving in a force field which is controlled externally. The proposed control algorithm consists of two controls – one of the controls, pertaining to the external force field, is directly applied to the system, and assumes the same value for all the vehicles. While the other control, which operates with heterogeneous gains, provides the steering force to the vehicles and is derived using Lyapunov analysis. Theoretical findings are validated through numerical simulations.