Distributed fixed-time orientation synchronization with application to formation control

This paper studies the formation tracking control problem in the agents' local co-ordinate frame without any special assumption, such as positive definiteness, on the initial orientation matrix. When follower agents do not have knowledge of their absolute orientation with respect to a global reference frame, formation control is difficult and special assumptions on initial orientation matrix are generally imposed for orientation synchronization. To address this, a distributed fixed time orientation synchronization law is first presented, using only relative orientation measurements, which aligns the co-ordinate frames of agents almost globally in finite time and locally in fixed time. This law is then used in cascade with an acceleration command for formation tracking control in a leader-follower set-up. Global asymptotic convergence of formation tracking error is proved for displacement based formation. For bearing-only formation control, semi-global uniformly asymptotic stability is established. Simulations illustrate the applicability of the results.