Multi-agent formation control using angle measurements

This paper investigates the triangular and polygonal formation control problem for mobile multi-agent systems under the constraint that each agent can only take angle measurements. For triangular formations, due to the fact that the sum of three interior angles always equals π, the desired triangular shape can be obtained when any two agents achieve desired angles for which they are the corresponding vertices of the triangle. So to achieve the desired shape of a triangular formation, we propose to let one agent remain fixed and the other two agents move along their bisectors respectively with respect to their two neighbors. For convex polygonal formations, since the sum of all interior angles is constant, we are able to use a similar control strategy to achieve the desired polygonal shape. The stability of the closed-loop multi-agent systems is proved using Lyapunov theory. Finally, simulation examples illustrate the validity of the theoretic results.