Bearing-Only Triangular Formation Control on the Plane and the Sphere

Abstract

We consider the problem of distributed bearing-only formation control. Each agent measures the inter-agent bearings in a local coordinate system and is tasked at maintaining a specified angular separation relative to its neighbors. The problem we consider differs from other problems in the literature since no inter-agent distance measurements are employed. Each agent's control law is distributed and based only on its locally measured bearings. A strong convergence result is established which guarantees global convergence of the formation to the desired shape while at the same time ensures that collisions are avoided naturally. We show that the control scheme is robust to agent motion failures and the presence of additional group motion inputs. Finally, we extend our system to the case where the agent's motion is restricted to a sphere.