Development of redundant rigidity theory for formation control

Abstract

Multiagent formation control may proceed by ensuring that designated pairs of agents maintain a specified distance between each other, in order that the overall shape of the formation can be preserved while it translates or rotates. A minimally rigid formation is one in which loss of any one such constraint or link means that individual agent motions can occur, which do not preserve the shape of the formation. Recognizing that real-world formations may suffer link loss and even agent loss, this paper presents a systematic approach to defining a measure for redundant or nonminimal rigidity, which is the property that formation shape will still be preserved in the face of loss of a certain designated number of distance constraints or formation agents. Most of the results are concerned with advancing a deterministic measure, but this paper also indicates circumstances under which a statistical measure may be relevant. For illustration, the paper analyses a number of standard formations to establish their levels of redundancy.