Stabilizing a mobile agent under two angle constraints

Recently, angle-based formation control laws have been proposed assuming that each agent only aims at maintaining one desired angle with respect to its neighbors. To extend the angle-based formation control algorithms to more general cases, we propose for each agent to maintain simultaneously multiple prescribed angles. As a first step, we investigate how an agent can be enabled to maintain two desired angles taking three static and collinear markers as references. We first show the condition for the existence of such positions for any given two angle constraints. Then, we propose a formation control law that uses local bearing measurements with respect to the markers, under which the local convergence of the moving agent to the desired position is guaranteed while satisfying the two constraints of the desired angles. A simulation example is provided to demonstrate the correctness of the theoretical results.