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

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