Task understanding and optimal strategies for handling flexible beams by using N-link manipulators

In this paper, task understanding and optimal strategies for handling flexible beams by using N-link manipulators are discussed. We consider the planning of the input torque and the trajectory of the manipulator as not to excite the vibration of the flexible beam. First, the equations of the motion of a general type of N-link manipulators with a flexible beam are derived. On the basis of the dynamic equations, the optimal input torque, which accomplishes the desired end-position of the manipulator and the diminution of the vibration of the flexible beam, is calculated by employing an iterative numerical algorithm. As the equation of the vibration of the flexible beam implies that the acceleration of the end-point of the manipulator excites the vibration, we consider an optimal trajectory planning so as to minimize the end-point acceleration of the manipulator. The validity of the optimal input torque and the optimal trajectory are demonstrated by computer simulations and experiments for an air-driven robot arm, respectively