Bearing-Constrained Leader-Follower Formation of Single-Integrators with Disturbance Rejection: Adaptive Variable-Structure Approaches

This paper studies the problem of stabilizing a leader-follower formation specified by a set of bearing constraints and being disturbed by unknown uniformly bounded disturbance. A set of leaders are positioned at the desired positions, while each follower agent is modeled by a single integrator with disturbance of which the upper bound is unavailable for the control design. Adaptive variable-structure formation control laws using only displacements or bearing vectors are provided to stabilize the agents to a desired formation. Thanks to the adaptive mechanism, the control laws require neither the information of the bearing Laplacian nor the directions and the upper bounds of the disturbance. It is further proved that when the leaders are moving with the same bounded uniformly continuous velocity, the moving target formation can still be achieved under the proposed control laws. Simulation results are also given to support the stability analysis.