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受压简支梁的影响，简支梁是一个高柔度体系。推导出控制方程为非线性偏微分方程组。采用多尺度方法对系统进行了分析。结果表明，极低的刚度和库仑摩擦会产生无限多的稳定平衡态。用分叉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正确性。高频激励使这些稳定平衡点失稳，并将屈曲梁稳定到直线位置。提出了库仑摩擦的实验识别方法。此外，我们还提出了欠驱动机械手的运动控制，这是一个高柔度系统。高频激发产生各种稳定的平衡态。激励方向的改变扰动了分叉现象，实现了无状态反馈控制的欠驱动杆的位置控制。搭建了欠驱动机械手的实验装置。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。运动方程为偏微分方程式。在有源连杆的高频激励下，通过引入多个时间尺度分析了欠驱动连杆的动力学特性。在这种情况下，进行了实验，并通过实验验证了柔性欠驱动机械手的运动控制。最后，我们考虑了高顺应性系统在GRIP中的应用。夹点不会产生冲击对象，因为夹点的关节可以自由旋转。该系统采用高频励磁，实现了运动控制。

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.