The dynamic modeling and trajectory tracking control of a mobile robot is handled by a hierarchical constraint approach in this study. When the wheeled mobile robot with complex generalized coordinates has structural constraints and motion constraints, the number of constraints is large and the properties of them are different. Therefore, it is difficult to get the dynamic model and trajectory tracking control force of the wheeled mobile robot at the same time. To solve the aforementioned problem, a creative hierarchical constraint approach based on the Udwadia–Kalaba theory is proposed. In this approach, constraints are classified into two levels, structural constraints are the first level and motion constraints are the second level. In the second level constraint, arbitrary initial conditions may cause the trajectory to diverge. Thus, we propose the asymptotic convergence criterion to deal with it. Then, the analytical dynamic equation and trajectory tracking control force of the wheeled mobile robot can be obtained simultaneously. To verify the effectiveness and accuracy of this methodology, a numerical simulation of a three-wheeled mobile robot is carried out.

在这项研究中，移动机器人的动态建模和轨迹跟踪控制是通过分层约束方法来处理的。当具有复杂广义坐标的轮式移动机器人具有结构约束和运动约束时，约束的数量很大并且它们的性质是不同的。因此，很难同时获得轮式移动机器人的动力学模型和轨迹跟踪控制力。为了解决上述问题，提出了一种基于乌德瓦迪亚-卡拉巴理论的创造性的层次约束方法。在这种方法中，约束分为两个级别，结构约束为第一级别，运动约束为运动约束是第二层。在第二级约束中，任意初始条件可能导致轨迹发散。因此，我们提出了渐近收敛准则来处理它。然后，可以同时获得轮式移动机器人的解析动力学方程和轨迹跟踪控制力。为了验证该方法的有效性和准确性，对三轮移动机器人进行了数值模拟。