This paper proposes a multivariable fixed-time leader-follower formation control method for a group of nonholonomic mobile robots, which has the ability to estimate multiple uncertainties. Firstly, based on the state space model of the leader-follower formation, a multivariable fixed-time formation kinematics controller is designed. Secondly, to overcome uncertainties existing in the nonholonomic mobile robot system, such as load change, friction, external disturbance, a multivariable fixed-time torque controller based on the fixed-time disturbance observer at the dynamic level is designed. The designed torque controller is cascaded with the formation controller and finally realizes accurate estimation of the uncertain part of the system, the follower tracking of reference velocity and the desired formation of the leader and the follower in a fixed-time. The fixed-time upper bound is completely determined by the controller parameters, which is independent of the initial state of the system. The multivariable fixed-time control theory and the Lyapunov method are adopted to ensure the system stability. Finally, the effectiveness of the proposed algorithm is verified by the experimental simulation.

中文翻译：

---

基于观察者的移动机器人多变量固定时间编队控制

针对一组非完整的移动机器人，提出了一种多变量固定时间领导者从属形成控制方法，该方法具有估计多个不确定性的能力。首先，基于前随从编队的状态空间模型，设计了多变量固定时间编队运动学控制器。其次，为了克服非完整移动机器人系统中存在的诸如负载变化，摩擦，外部干扰等不确定性，设计了一种基于固定时间扰动观测器的动态多变量固定时间转矩控制器。设计的扭矩控制器与地层控制器级联，最终实现对系统不确定部分的准确估算，跟随者跟踪参考速度，并在固定时间内跟踪领导者和跟随者的期望组成。固定时间上限完全由控制器参数确定，该参数与系统的初始状态无关。采用多变量固定时间控制理论和李雅普诺夫方法来保证系统的稳定性。最后，通过实验仿真验证了所提算法的有效性。