Bearing-Based Formation With Disturbance Rejection

This paper considers the problem of the bearing-based formation control with disturbance rejection for a group of agents under the leader-follower structure. The disturbances are in the form of trigonometric polynomials with arbitrary unknown amplitudes, unknown initial phases, and known or unknown frequencies. For the case of the known frequencies, we employ the canonical internal model to solve the problem, and, for the case of the unknown frequencies, we combine the canonical internal model and some distributed adaptive control technique to deal with the problem. It is noted that the existing results can only handle constant disturbances by continuous control laws or disturbances with known bounds by discontinuous control laws. The first case is a special case of our result. The second case cannot cover our results because the bounds of our disturbances are unknown. Moreover, our control law is smooth. Additionally, we also present the collision avoidance condition on the initial conditions of the closed-loop system for each case. Finally, numerical examples are used to illustrate our design.