Shape and orientation control of moving formation in multi-agent systems without global reference frame

In this paper, distance-based formation control laws for the multi-agent systems are proposed when the reference velocity is unknown to the followers. Especially, not only the shape but the orientation of formation is also controlled. Each agent measures only the relative positions of neighbors with respect to their own local coordinate system. The local coordinate systems in each agent are not aligned and unknown to the other agents; thus the control laws are completely decentralized. Using the measured local information, the unknown reference velocity is estimated by applying an adaptive method. The shape and orientation of formation are controlled based on the estimated reference velocity. The stability and convergence of the system are analyzed mathematically and verified through numerical simulation.