Integrated Relative Localization and Leader–Follower Formation Control

This paper concentrates on the integration of relative localization and the formation control over leader–follower networks. First, we develop a consensus-like relative localization scheme for each agent to estimate the real-time relative positions of its neighbors by merely using velocity as well as distance-related measurements and local communications under the assumption that the local frames of all agents share a common orientation. It is shown that the relative position estimate exponentially converges to its true value under a persistent excitation condition on relative velocity between the two agents. Second, an integrated relative localization and a leader–follower formation control are developed by combining the proposed relative localization scheme and a complex Laplacian-based formation control scheme. It is proven that the integrated system globally asymptotically converges to a stationary similar formation in the case of error-free initial relative position estimates while globally uniformly bounds in a neighborhood of the prescribed formation in the case with initial relative position estimation errors. Furthermore, based on the two degrees of freedom of similar formation on translation, the integrated scheme is also generalized to achieve moving similar formation control. Finally, simulations are presented to illustrate the effectiveness of our theoretical results.