Convergence of Distance-based Formations in Case of Failure of Sensing Distances: Rigidity Theory Perspective

Abstract

This paper discusses how to achieve convergence of formations in the case where the formations lose distance information under distance-based formation control in 2-dimensional space. In particular, the rigidity theories are employed to analyze such a special case. Two methods based on the rigidity theories are presented: the first method is to make use of the property of distance rigidity; the second method is to design a switching algorithm by merging a distance-based system with a bearing-based system. In the switching algorithm, a bearing-based control law is substituted for a distance-based control law when several or all agents in a system fail in sensing inter-agent distances. This switched system is analyzed from the perspective of the distance rigidity theory and the bearing rigidity theory. We finally provide simulation examples to validate the main results studied in this paper. Copyright (C) 2021 The Authors.