This article studies the trajectory tracking of nonholonomic mobile robots by using geometric control methods, with extension to consensus tracking and formation tracking. Different from the system model given in the Euclidean space, we establish the dynamics of mobile robots on the tangent bundle of the Lie group, which is a global and unique description independent of local coordinates. Firstly, the tracking control of one leader with one follower is considered, which is converted to the stabilization of two relative subsystems by designing an adjoint system. Then, the controller is extended to consensus tracking of multiple robots connected by a directed acyclic graph, where the convex combination on nonlinear manifolds is introduced to construct a virtual leader for each follower. Next, the relation between consensus control and formation control is established, and a new transformed system is constructed so as to derive the formation tracking controller from the consensus result. Finally, simulation examples are presented to verify the effectiveness of the proposed controllers.

中文翻译：

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基于特殊欧氏群几何控制的非完整移动机器人轨迹跟踪

本文利用几何控制方法研究非完整移动机器人的轨迹跟踪，扩展到一致性跟踪和编队跟踪。与欧氏空间中给出的系统模型不同，我们在李群切丛上建立了移动机器人的动力学，这是一个独立于局部坐标的全局唯一描述。首先考虑一领导一跟随的跟踪控制，通过设计伴随系统将其转化为两个相关子系统的稳定。然后，控制器扩展到由有向无环图连接的多个机器人的共识跟踪，其中引入非线性流形上的凸组合为每个跟随者构建虚拟领导者。下一个，建立共识控制与编队控制的关系，构建新的变换系统，从共识结果推导出编队跟踪控制器。最后，给出了仿真例子来验证所提出的控制器的有效性。