ROBUST MOTION CONTROL OF NONHOLONOMIC FLEXIBLE ROBOT

简化机械手的机构和减轻其重量，使其能够在外层空间操作，已成为一个重要的研究课题。在这项研究中，通过使用更轻的材料，以减少重量，并通过抑制尽可能多的致动器在关节，以提供简单性，我们处理的问题，控制具有非驱动关节的多连杆机械手的运动。前一种措施引起的挠度不可忽略，然后必须考虑连杆的柔性。此外，后者意味着非完整约束条件的出现。因此，本研究的目的是开发一种方法，为运动控制的多连杆柔性臂具有关节不配备执行器。首先，在这项研究中，一个三连杆柔性臂与未驱动关节建模为一个非线性仿射系统。因为对于这个模型，我们假设手臂的质量相对较小， 关于我们 比接头处的质量大，连杆的挠度近似为静态弯曲。一种方法来解决这个非线性系统的最优定位受到极端条件下，在一般情况下，是非常困难的，其最优解的控制输入表示为一个一般函数的傅立叶基参数获得通过使用一个经典的变分方法，里兹法。然后通过应用牛顿法对该参数进行优化。此外，通过数值求解雅可比矩阵，缩短了计算时间。为了验证该方法的有效性，进行了计算机仿真。所提出的方法的有效性进行了验证，实现了一些位置的目标。此外，从分析的结果的时间历程响应的连杆的角度，输入扭矩，位移的关节和有效载荷在臂的尖端，最优轨迹的特性可以注意到。我们可以看到，在从动关节位于基部的情况下，从该关节开始，从最远的连杆开始，按顺序提供并实现连杆的姿态。此外，它清楚地表明，控制输入的振荡行为对应于自由度的数量。少

The simplicity of mechanisms and the reduction of weight in manipulators to make them feasible to be operated in outer space have become an important subject of research. In this study, by using lighter materials to reduce the weight and by suppressing as many as possible actuators at the joints to provide simplicity, we deal with the problem of controlling the motion of a multi-link manipulator possessing non-driven joints. The former of these measures causes deflections that can not be ignored and then the flexibility of the links has to be considered. In addition, the latter implies the appearing of nonholonomic constraint conditions. Therefore, the present study is aimed at developing an approach for the motion control of a multi-link flexible arm possessing joints not equipped with actuators.In first place in this study, a three-flexible-link arm with unactuated joints is modeled as a nonlinear Affine system. Since for this model we assume the mass of the arm comparatively smaller … More than the mass at the joints, the deflection of the links is approximated as a static bending. A method to solve the optimal positioning of this nonlinear system subjected to extreme conditions is, in general, very difficult; and for its optimal solution the control input is expressed as a general function of a Fourier basis parameter acquired by using a classical variational approach, the Ritz method. Then this parameter is optimized through the application of the Newton method. Additionally, the consumption of calculation time is shortened by obtaining the Jacobian using numerical procedures.In order to examine the validity of the present approach, computer simulations were carried out. The efficacy of the proposed approach was verified by achieving a number of position targets. Moreover, from the analysis of the results of the time histories response of the linksi angles, input torque, and the displacement of the joints and the payload at the tip of the arm, characteristics of optimal trajectories can be noticed. We can see, that in case the driven joint is located at the base, from this joint the posture for the links is provided and achieved in order, beginning with the farthest link. Also, it is clearly shown that the oscillating behavior of the control input corresponds with the number of degrees of freedom. Less