Theory and methods for bearing rigidity recovery
Arman Karimian, Roberto Tron · 2017
In the bearing-based localization and formation control problem, we can uniquely determine or control the relative positions of all the agents up to a common scale if and only if the problem is rigid. The notion of rigidity therefore plays a central role. In some situations (for instance, restoring rigidity after an agent leaves a formation), it is necessary to solve the rigidity recovery problem: find a way to turn a non-rigid problem into a rigid one by adding new bearing measurements. In this paper, we first provide new theoretical insights on rigidity, and on the minimum number of additional bearing measurements necessary to ensure this property in a non-rigid problem. We then provide algorithms to select which edges to add.