Trajectory planning for multi-link flexible arms in order to achieve high-speed and little vibratory operation

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This study deals with the optimum trajectory planning for multi-link flexible arms. For the vibration control of the flexible arms, various vibration control techniques are examined and applied. However, by using the optimum trajectories, the flexible arms can rotate from its initial position to a desired location in given movement execution time without large troublesome vibrations. Moreover, additional feedback control devices besides the controller of existing actuators are not necessary.The proposed method creates the desired trajectories numerically using the simulation model of the flexible arms under the consideration of the any practical constraint such as obstacles and the limitation of servomotor output torque. The information needed for generating the desired trajectories is only the system model of the multi-link flexible arms. The desired trajectory is selected from trial trajectories by repeating the calculation of the responses of the flexible arms rotating along each trial trajectory. The trial trajectories are created by the combination of the derivative of angular acceleration with respect to time. As the stiffness of the system is lower, the number of the trial trajectories increases. However, it is easy to share the calculation with several computers. Therefore, the influence of the calculation time to obtain the desired trajectory is not very serious. In order to confirm the effect of the desired trajectories an reducing the vibrations of the flexible arms, the responses of three-link flexible arms were simulated. It can be seen from the numerical results that the vibrations of the flexible arms were reduced enough by using the desired trajectories.