Abstract:

For the fixed-time formation control of electrically driven nonholonomic mobile robots in the presence of disturbances, a state space dynamic model of leader-follower formation including actuator dynamics is introduced. The formation controller is designed in two steps. Multivariable fixed-time controller is designed for kinematics model of leader-follower formation. In order to achieve velocity tracking under disturbances, a multivariable super-twisting continuous fixed-time voltage controller for the follower robot is designed through auxiliary input at the dynamics level. The proposed algorithm overcomes disturbances caused by the follower robot in formation, and ensures that the follower and the leader reach the desired formation and the follower follows the desired speed at a fixed time. The designed continuous control eliminates the chattering phenomenon of switch control. The fixed time of system convergence is given in advance by parameter design, which is independent of the initial state of the system. Stability of the control system is proved using the Lyapunov theory. The effectiveness of the proposed algorithm is verified by experimental simulation.

Key words: multivariable fixed-time control, formation control, multivariable super-twisting algorithm, electrically driven, state space dynamic model, nonholonomic mobile robot

摘要：

针对扰动下电驱动非完整移动机器人固定时间编队控制问题，通过引入包含驱动器动力学的领航者-跟随者状态空间动力学模型，分两步对编队控制器进行了设计。对领航者跟随者编队运动学模型进行了多变量固定时间控制设计。在动力学层面，为实现扰动下的速度跟踪，通过辅助输入设计了一种跟随者机器人多变量超螺旋固定时间连续电压控制器。所提算法使机器人编队克服了跟随者机器人所受干扰，确保了跟随者机器人与领航者在固定时间达到期望队形，跟随者在固定时间内跟随期望速度，设计的连续控制消除了开关控制的抖振现象。通过参数设计提前给定系统收敛的固定时间，与系统初始状态无关。基于Lyapunov方法进行了系统稳定性分析。通过仿真对算法进行了验证。

关键词: 多变量固定时间控制, 编队控制, 多变量超螺旋算法, 电驱动, 状态空间动力学模型, 非完整移动机器人