Globally Stabilizing Triangularly Angle Rigid Formations

The global stabilization of planar angle rigid formations is acknowledged to be a challenging problem in the existing literature even when relative position measurements are available among neighboring agents. Inspired by an angle-induced linear constraint imposed on each triangle, this article first proposes formation control laws to achieve almost global stabilization of triangularly angle rigid formations using local relative position measurements. Compared with some other globally stable formation control systems using local relative position measurements, our approach is shown to be more computationally effective and scalable. Moreover, by additionally controlling the relative position between a pair of neighboring agents, we also propose formation control laws to globally stabilize triangularly angle rigid formations with prescribed orientation and scale. Compared with other angle-constrained formations with prescribed orientation and scale, our proposed formation control law guarantees global stability instead of almost global stability. Finally, we remark that the proposed approach can also be used to globally stabilize triangular formations specified by ratio-of-distance constraints. Simulation examples validate the effectiveness of the proposed formation control approaches.