全弹性平面运动机器人的高精度运动控制和振动抑制算法研究

Research on high precision motion control and vibration suppression algorithm of elastic-base flexiblejoint and flexiblelink planar motion robot

为实现对基座、关节和臂均存在弹性的空间机器人运动高精度控制及多重振动抑制,建立了基座、关节和臂全弹性空间机器人动力学模型,并采用运动有限维PD重复学习控制及振动同步抑制方案进行研究。首先,利用线性弹簧、扭转弹簧和欧拉-伯努力梁理论,假设模态法和动量守恒定律,采用拉格朗日方程建立了弹性基座、柔性关节和柔性臂空间机器人动力学模型,之后,选取反映柔性臂振动的前两阶模态及基座和关节刚性运动变量为慢变子变量,选取基座和关节弹性振动变量为快变子变量,根据奇异摄动理论将系统降维分解成慢、快变子系统。最后设计了慢变子系统的运动有限维PD重复学习控制及快变子系统的线性最优双重减振控制构成的总控制器。数值仿真结果验证了算法的有效性。

In order to achieve precise motion control and multiple vibration suppression of a space robot with elastic bases,flexiblejoints and flexiblelinks,a space robot with fully elastic base,joints and links are established.The finite dimension PD repetitive learning control and vibration synchronous control scheme are used to control the system.Combined with Linear springs,torsion springs,Euler-Bernoulli beam theory,using modal method,momentum conservation laws and Lagrange method,the dynamic equations of the space robot with a flexiblebase two flexiblelinks and two flexiblejoints are established.System variables are decomposed on two different time scales using singular perturbation technology.Improved PD repetitive algorithm is used to control robot motion and suppress links vibration in the slow time scale.Then,the vibration of the flexible base and the two joints are suppressed with the linear quadratic optimal control method in a fast time scale.The main controller is composed of slow and fast sub-controllers.Numerical simulation results verify the effectiveness of the algorithm.