“小误差放大,大误差饱和”函数能够提高柔性关节机器人位置的控制品质。利用这一函数,提出了比例-非线性微分加实时重力补偿(P-ND+)位置控制算法。应用Lyapunov稳定性理论和La Salle's不变性原理证明了闭环系统的全局渐近稳定性。通过仿真,采用P-ND+算法能使机械臂和关节的稳定时间从1 s减小到0.2 s左右,结果表明该算法比传统算法响应速度更快,验证了提出的非线性控制(P-ND+)相对于传统的线性(PD+)控制具有更好的控制品质。

The function which is named as “enlargement of small error and saturation of large error” has the ability to improve the performance of the control of the flexible-joint robot. Using such function, a P-ND+ position control algorithm in proposed in this paper. The global asymptotic stability of the resulting closed-loop system is proved in agreements with Lyapunov direct method and La Salle's invariability principle. Through simulation, the P-ND+ algorithm can make the stability time of the mechanical arm and joint decrease from 1 s to 0.2 s. The results show that the response time of the proposed algorithm is faster than that of the traditional algorithm, and it also verifies that the proposed nonlinear control has better control quality than the tralitional linear(PD+).