Rigidity of distance-based formations with additional subtended-angle constraints

In this paper, we propose a new concept of rigidity, named weak rigidity, using distance and subtended-angle constraints. The classical rigidity of formation is used in the field of distance-based formation control as a fundamental tool to guarantee a locally unique formation shape with given inter-agent distances. We assume that there are some angle constraints in addition to the existing distance constraints. Then the formation could result in a rigid formation shape even if it is not rigid in the viewpoint of classical rigidity. Weak rigidity distinguishes whether the formation with additional angle constraints can maintain its shape. Relation between classical rigidity and weak rigidity is addressed and used to derive some useful results.