Contraction theory approach to generalized decentralized cyclic algorithms for global formation acquisition and control

This paper presents a new approach to distributed nonlinear formation control, inspired by recent results on properties of cyclic topologies. Tools from contraction theory are used in the analysis of nonlinear control laws that only employ local information to globally converge to a formation. Specifically, a generalization of the cyclic pursuit extended to develop properties not addressed before such as non-rotating arrays, global convergence to a specific size, and time/state varying gains. Experiments on the International Space Station using the SPHERES testbed validate their properties and effectiveness for formation flight missions where specific array geometry is a metric of interest.