LAUSR

Abstract This work demonstrates the swing-up of a custom-built spherical pendulum, which is mounted on the 7-axis industrial robot Kuka LWRIV+. The swing-up trajectory for this system with nine degrees of freedom is calculated offline in a three-step process: First, an optimal control problem for the pendulum model with fewer states and inputs is solved. Then, using the inverse kinematics of the robot model and the forward dynamics of the complete system, this trajectory is converted to a feasible starting solution for the third step, which is solving the optimal control problem for the complete system. Finally, the swing-up is shown experimentally using a two-degrees-of-freedom control structure comprising the calculated trajectory for the feedforward control and a time-variant linear quadratic regulator (LQR) as a feedback controller.