This study proposes a new class of controllers for mobile manipulators subject to both undesirable forces exerted on the end-effector and unknown friction forces coming from joints directly driven by the actuators as well as undesirable forces resulting from the kinematic singularities appearing on the mechanism trajectory. Based on the suitably defined task space non-singular terminal sliding manifold (TSM) and the Lyapunov stability theory, we derive a class of estimated extended transposed Jacobian controllers which seem to be effective in counteracting the unstructured forces. Due to a redundant nature of the tasks to be accomplished, our controllers also a involve useful criterion function (energy consumption) in optimally tracking a desired trajectory. Moreover, in order to eliminate (or to alleviate) undesirable chattering effects the proposed control laws include second order sliding techniques. The numerical computations, which are carried out for a mobile manipulator consisting of a platform of (2, 0) type and a holonomic manipulator of two revolute kinematic pairs, illustrate the performance of the proposed controllers and simultaneously their minimizing properties. Numerical comparison with other control algorithms well-known in the literature is also given.

本研究为移动机械手提出了一类新的控制器，这些控制器会受到施加在末端执行器上的不利力和来自执行器直接驱动的关节的未知摩擦力以及由机械轨迹上出现的运动奇点引起的不利力的影响。基于适当定义的任务空间非奇异终端滑动流形 (TSM) 和 Lyapunov 稳定性理论，我们推导出一类估计的扩展转置雅可比控制器，它们似乎可以有效地抵消非结构化力。由于要完成的任务的冗余性，我们的控制器还涉及有用的标准函数（能耗），以最佳地跟踪所需的轨迹。而且，为了消除（或减轻）不良的颤振效应，建议的控制法则包括二阶滑动技术。对由 (2, 0) 型平台和两个旋转运动对的完整机械手组成的移动机械手进行的数值计算说明了所提出的控制器的性能，同时说明了它们的最小化特性。还给出了与文献中众所周知的其他控制算法的数值比较。