Angle Rigidity and Its Usage to Stabilize Multiagent Formations in 2-D

Motivated by the challenging formation stabilization problem for mobile robotic teams wherein no distance or relative position measurements are available but each robot can only measure some of angles with respect to its neighbors in local coordinate frame, we develop notion “angle rigidity” a multipoint framework, named “angularity”, consisting set nodes embedded Euclidean space, and angle constraints among them. Different from bearings defined global use do not rely on knowledge signed according counter-clockwise direction. Here, rigidity refers property specifying that under proper constraints, angularity translate, rotate, scale as whole when one more perturbed locally. We first demonstrate this property, sharp comparison bearing other reported related frameworks literature, is since an rigid may allow flex ambiguity. then construct necessary sufficient conditions infinitesimal checking rank angularity's matrix. combinatorial condition minimal rigidity. Using developed theories, algorithm designed team achieve formation, which needed. Simulation examples advantages proposed angle-only control approach.