力矩受限的机器人吸引域估计方法

Estimation methods of domain of attraction for robot with bounded torques

针对力矩受限的机器人组合非线性反馈控制的局部稳定区域描述问题,研究了吸引域的估计方法.利用不变集属性和椭球性质,定义两种不同意义的最大椭球不变集来逼近吸引域,分别采用设置初始状态法和参考形状集法求解.通过带有约束的优化问题描述,所有条,件均能转化为线性矩阵不等式条件,易于求解.由于采用优化技术,能够减小吸引域估计的保守性.数值算例验证了所提方法的有效性.

To formulate the problem concerned with local stable region description of composite nonlinear feedback control for robot manipulators with bounded torques, the estimation methods of domain of attraction are studied. By using the properties of set invariance and ellipsoid, two different maximum ellipsoid invariant sets are defined as the estimation of domain of attraction, so the methods of setting initial state and reference shape set are introduced. Through the description for the constrained optimization problem, all conditions can be expressed in LMI conditions and conveniently solved. Owing to the utilization of optimization technique, both methods can reduce the conservatism of estimation. Simulation examples testify the effectiveness of the suggested methods.