Synchronization with partial state feedback on SO(n)

Abstract— In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in Rn . We propose a gradient based control law which achieves exponential local convergence to a synchronization configuration under a rank condition on a generalized Laplacian matrix. Furthermore, we discuss the case of time-varying reference vectors and provide a convergence result for this case. The latter helps reach synchronization, requiring less communication links and weaker conditions on the instantaneous reference vectors. Our methods are illustrated on an attitude synchronization problem where agents exchange only their relative positions observed in the respective body frames.

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Christian Lageman, Alain Sarlette, Rodolphe Sepulchre
• Keywords: CDC 2009, Control Systems, Partial State Information, Reference Vectors, Synchronization