Formation control of non-holonomic multi-agent systems under relative measurements

This paper addresses a formation control problem for multi-agent systems with non-holonomic constraints under relative measurements. To overcome the issue of non-holonomic constraints, we design a feedback controller deriving rotational and translational motions according to formation error. A special form of formation error is employed here, which depends only on relative positions in a local frame. Hence, the designed controller is distributed and relative, meaning that only relative measurements of neighbors are used. Because a clique-based function is used, not an edge-based one, the best performance is yielded of all distributed, relative, gradient-based controllers. Moreover, we derive a necessary and sufficient condition of graphs under which a desired formation is achieved by such controllers. The proposed method is valid regardless of the dimension of the space, and thus it is applicable to not only unmanned ground vehicles (UGVs) but also unmanned aerial vehicles (UAVs). The effectiveness of the proposed method is demonstrated by simulations. Copyright (C) 2020 The Authors.