Analysis and Control of High Compliance Systems with Coulomb Friction

首先，我们展示了轻微的库仑摩擦对压缩力下简支梁的影响，这是一个高柔度系统。推导了控制方程为非线性偏微分方程。采用多尺度的方法对系统进行了分析。结果表明，极低的刚度和库仑摩擦可产生无限数量的稳定平衡态。用分岔理论对这些现象进行了识别。并通过实验验证了理论结果的有效性。高频激励使这些稳定平衡点失稳，使屈曲梁稳定到直线位置。同时，提出了库仑摩擦的实验识别方法。在此基础上，提出了一种欠驱动高柔度机械臂的运动控制方法。高频激励产生多种稳定的平衡态。励磁方向的改变扰动了分岔现象，实现了欠驱动环节的位置控制，无需状态反馈控制。搭建了欠驱动机械手实验装置。实验验证了该控制方法的有效性。此外，我们还考虑了欠驱动连杆是柔性的情况。运动方程是偏微分方程。在主动连杆的高频激励下，通过引入多时间尺度分析欠驱动连杆的动力学特性。在此情况下，进行了实验，实验验证了柔性欠驱动机械臂的运动控制。最后，我们考虑了高柔度系统在握把中的应用。由于握把的关节是自由旋转的，所以握把不会给物体造成冲击。该系统采用高频激励，实现运动控制。

First, we show the effects of slight Coulomb friction on a simply supported beam under compressive force, which is a high compliance system. The governing equation, which is a nonlinear partial differential equation, is deduced. By the method of multiple scales, the system is analyzed. As a result it is clarified that very low stiffness and Coulomb friction produces infinite number of stable equilibrium states. The phenomena are identified by bifurcation theory. And the validity of the theoretical result is experimentally confirmed. The high- frequency excitation destabilizes these stable equilibrium points and stabilizes the buckled beam to the straight position. Also, experimental identification method for Coulomb friction is proposed. Furthermore, we propose a motion control of an underactuated manipulator, which is high compliance system. The high frequency excitation produces variety of stable equilibrium states. The change of the excitation direction perturbs the bifurcation phenomena and carries out the position control of the under actuated link without state feedback control. Experimental apparatus of the underactuated manipulator is constructed. The validity of the proposed control method is experimentally confirmed. Furthermore, we consider the case when the underactuated link is flexible. The equation of motion is partial differential equation. Under high-frequency excitation of the active link, the dynamics of the underactuated link is analyzed by introducing multiple time scales. Also, in this case, experiments are conducted and the motion control of flexible underactuated manipulator is experimentally confirmed. Finally, we consider the application of the high compliance system for grip. The grip does not give impact objects because the joint of the grip is freely rotated. This system uses high frequency excitation and carries out motion control.