Variable-stiffness actuator is a very appealing mechatronic design that combines the efficiency of stiff actuator  in free space with the consistency of elastic actuation in contact. The control of such an actuation system remains a challenge due to its non-linearity and by the fact that it doubles the number of control inputs. In this paper, we propose an original
control strategy to compute the whole-body movement of a complex variable-stiffness robot during dynamic task execution. Operational space control is first used to compute both the joint torque and stiffness from operational references. A nonlinear model-predictive controller is then proposed to track at higher frequency these references on each joint separately. The effectiveness of this approach is then validated on two models of real actuator with adjustable stiffness, and finally on an explosive motion to make a humanoid robot jump.