Control of a nonholonomic mobile robot: backstepping kinematics into dynamics

A dynamical extension that makes possible the integration of a kinematic controller and a torque controller for nonholonomic mobile robots is presented. A combined kinematic/torque control law is developed using backstepping and asymptotic stability is guaranteed by Lyapunov theory. Moreover, this control algorithm can be applied to the three basic nonholonomic navigation problems: tracking a reference trajectory, path following and stabilization about a desired posture. A general structure for controlling a mobile robot results that can accommodate different control techniques ranging from a conventional computed-torque controller, when all dynamics are known, to adaptive controllers.

提出了一种动态扩展，它使得非完整移动机器人的运动学控制器和转矩控制器的集成成为可能。利用反步法推导出了一种组合的运动学/转矩控制律，并通过李雅普诺夫理论保证了渐近稳定性。此外，该控制算法可应用于三个基本的非完整导航问题：跟踪参考轨迹、路径跟踪以及关于期望位姿的镇定。由此产生了一种用于控制移动机器人的通用结构，它能够适应不同的控制技术，从所有动力学已知时的常规计算转矩控制器到自适应控制器。