This paper studies the full-state formation control problem of multiple nonholonomic unicycle vehicles. Firstly, the formation error model is transformed into standard nonholonomic chained form, including orientation and position error subsystems. For orientation subsystem, an angular velocity control law is designed to be a cooperative term plus an exponential decay function of time, ensuring orientations reach an agreement on a common value. For position error subsystem, a time-varying output-like variable is carefully constructed to ensure a stable zero dynamics, that is, the consensus of these output variables guarantees position formation, overcoming the intrinsic underactuated control difficulty. Then, a linear velocity control law is derived to realize consensus of outputs. It is proved that the proposed distributed time-varying controller is capable of steering the vehicles to globally exponentially make into desired geometric position shape with the same orientations and vanishing velocities, provided that the communication topology is directed and having a spanning tree. The calculated convergence rates are shown dependent on controller coefficients; thus, the controller is modified to additionally reach a prescribed rate of convergence by redesigning conditions of controller parameters. Finally, two numerical simulations are implemented for five unicycle vehicles, demonstrating the effectiveness of the proposed control scheme.

中文翻译：

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保证收敛速度的非完整独轮车全局编队控制

本文研究了多辆非完整独轮车的全状态编队控制问题。首先，将编队误差模型转化为标准的非完整链式形式，包括方向和位置误差子系统。对于方向子系统，角速度控制律被设计为一个协同项加上时间的指数衰减函数，确保方向在一个共同值上达成一致。对于位置误差子系统，精心构造了一个时变类输出变量，以确保稳定的零动态，即这些输出变量的一致性保证了位置的形成，克服了固有的欠驱动控制困难。然后，推导出一个线速度控制律来实现输出的一致性。证明了所提出的分布式时变控制器能够引导车辆以全局指数方式形成具有相同方向和消失速度的所需几何位置形状，前提是通信拓扑是有向的并且具有生成树。计算出的收敛速度取决于控制器系数；因此，通过重新设计控制器参数的条件，控制器被修改以额外达到规定的收敛速度。最后，对五辆独轮车进行了两次数值模拟，证明了所提出的控制方案的有效性。前提是通信拓扑是定向的并且具有生成树。计算出的收敛速度取决于控制器系数；因此，通过重新设计控制器参数的条件，控制器被修改以额外达到规定的收敛速度。最后，对五辆独轮车进行了两次数值模拟，证明了所提出的控制方案的有效性。前提是通信拓扑是定向的并且具有生成树。计算出的收敛速度取决于控制器系数；因此，通过重新设计控制器参数的条件，控制器被修改以额外达到规定的收敛速度。最后，对五辆独轮车进行了两次数值模拟，证明了所提出的控制方案的有效性。