|Budget Amount *help
¥3,600,000 (Direct Cost : ¥3,600,000)
Fiscal Year 1999 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1998 : ¥2,500,000 (Direct Cost : ¥2,500,000)
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
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