An inverse dynamic method yielding flexible manipulator state trajectories

An inverse dynamic equation for a flexible manipulator is derived in a state form. By dividing the inverse system into the causal part and the anticausal part, one can calculate torque in the time domain for a certain end-point trajectory, as well as trajectories of all state variables. The open-loop control of the inverse dynamic method shows an excellent result in simulation. For practical applications, a control strategy adapting feedback tracking control to the inverse dynamic feedforward control is illustrated, and experimental results are presented.