This paper is concerned with the nonlinear tracking control design for robot manipulators. In spite of the rich literature in the field, the problem has not yet been addressed adequately due to the lack of an effective control design. Using a descriptor fuzzy model-based framework, we propose a new approach to design a feedback-feedforward control scheme for robot manipulators in a general form. The goal is to guarantee a small level of an ${\mathcal{L}}_{\infty }-$ gain specification to improve the tracking performance while significantly reducing the numerical complexity for real-time implementation. Based on Lyapunov stability arguments, the control design is formulated as a convex optimization problem involving linear matrix inequalities. Numerical experiments performed with a high-fidelity manipulator benchmark model, embedded in the Simscape Multibody^TM environment, demonstrate the effectiveness of the proposed control solution over existing standard approaches.

本文涉及机器人机械手的非线性跟踪控制设计。尽管该领域文献丰富，但由于缺乏有效的控制设计，该问题尚未得到充分解决。使用基于描述符模糊模型的框架，我们提出了一种新的方法来设计一般形式的机器人机械手的反馈前馈控制方案。目的是确保少量的${\mathcal{大号}}_{\infty }-$增益规范，以改善跟踪性能，同时大大降低实时实现的数值复杂度。基于Lyapunov稳定性参数，将控制设计公式化为涉及线性矩阵不等式的凸优化问题。使用嵌入在Simscape Multibody ^TM环境中的高保真机械手基准模型执行的数值实验证明了所提出的控制解决方案相对于现有标准方法的有效性。