Finite-time and fixed-time formation tracking control with unknown disturbance rejection using only local bearing measurements
Hong Liang Cheah, Mohammad Deghat · Journal of the Franklin Institute · 2025
This paper proposes two formation control laws that reject unknown constant disturbances using only local bearing measurements. The first control law is developed based on finite-time input-to-state stability (FTISS) theory, ensuring that the formation error converges to a neighborhood of zero within a finite time. Then, the formation error converges to zero asymptotically. When there is no disturbance, the formation error converges to zero in finite time. The second control law employs fixed-time input-to-state stability (FXISS) theory, guaranteeing that the formation error converges to a neighborhood of zero within a fixed time, and subsequently converges to zero asymptotically. Unlike existing finite-time bearing-based formation control laws, which typically rely on the availability of a global coordinate frame and some information about the disturbances, our proposed control laws require only local bearing vector measurements. We first examine the case where leaders are stationary and then extend the results to leaders moving with an unknown constant velocity. Furthermore, when disturbances are time-varying, we show that the first control law guarantees FTISS, while the second ensures FXISS. Simulation and experimental results are provided to validate the effectiveness of the proposed control laws.