This paper presents a control approach to stabilize limit cycle motions along a mechanical mode of variable stiffness actuated (VSA) robots. Thereby, first a PD controller with gravity and Coriolis/centrifugal compensation shapes a desired dynamics, which is decoupled in terms of modal coordinates. Then an asymptotically stable limit cycle is generated on the link side dynamics for a selected mode. Finally, the modal control approach first introduced for rigid robots is extended to the VSA case. This is done by a joint torque controller, which decouples the torque dynamics from the link side dynamics. Stability and convergence are proven for the dynamics resulting from each feedback control. Furthermore, the energy efficiency of the proposed approach is verified by simulation and experiments on the VSA robotic arm DLR Hand Arm System.
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