A General Framework for the Bearing-Based Formation Control

The bearing-based formation control has been an active research topic over the past decade. However, the existing results mainly focus on single- or double-integrator systems and assume that all the leaders move with a constant velocity. In this article, we aim to establish a general framework to handle the bearing-based formation control. The framework offers three features. First, our problem is formulated for general heterogeneous multiagent linear systems, which include high-order integrator systems as a special case. Second, the desired positions of the leaders are generated by some linear autonomous systems called exosystems. Such systems can generate a large class of signals such as polynomials of any degree with unknown coefficients or trigonometric polynomials of arbitrary amplitudes and initial phases. Hence, different leaders can have different time-varying velocities. Third, the target formation can be achieved in the presence of a large class of disturbances. A key technology of our approach is the so-called bearing-based distributed observer for an exosystem. The bearing-based distributed observer, in conjunction with the classical output regulation theory, leads to a unified approach to handling the bearing-based formation for general linear systems and for a large class of formation maneuvers.