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

研究了多连杆柔性臂的最优轨迹规划问题。针对柔性臂的振动控制，研究并应用了各种振动控制技术。然而，通过使用最优轨迹，柔性臂可以在给定的运动执行时间内从其初始位置旋转到期望位置，而不会出现大的麻烦的振动。该方法不需要在现有执行器的控制器之外增加额外的反馈控制装置，利用柔性臂的仿真模型，在考虑障碍物和伺服电机输出力矩的限制等实际约束的情况下，数值生成期望的轨迹。生成所需轨迹所需的信息仅仅是多连杆柔性臂的系统模型。通过重复计算沿每个试验轨迹旋转的柔性臂的响应，从试验轨迹中选择所需的轨迹。试验轨迹由角加速度对时间的导数组合而成。当系统的刚度较低时，试验轨迹的数目增加。然而，它很容易与几台计算机共享计算。因此，计算时间对获得期望轨迹的影响不是很大。为了验证所设计的轨迹对柔性臂减振的效果，对三连杆柔性臂进行了响应仿真。从数值结果可以看出，通过采用所需的轨迹，柔性臂的振动得到了足够的减小。

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.