Angle Rigidity Graph Theory and Multi-agent Formations

Motivated by the challenging formation control problem for a team of mobile vehicles in which each vehicle can only measure some of the angles towards its neighbors in its local coordinate frame, this thesis develops angle rigidity graph theory in both 2D and 3D. The angle rigidity graph theory is developed for a class of multi-point frameworks, called “angularity”, consisting of a set of nodes embedded in a Euclidean space and a set of angle constraints among them. Here angle rigidity refers to the property specifying that under proper angle constraints, the angularity can only translate, rotate or scale as a whole when one or more of its nodes are perturbed locally. Using the developed angle rigidity theory, angle-only formation control algorithms are designed for the team of mobile vehicles to achieve a desired angle rigid formation, in which only local angle measurements are needed for each vehicle.