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It is widely recognised that compliant actuation is advantageous to robot control once high-performance, explosive tasks, such as throwing, hitting or jumping are considered. However, the benefit of intrinsic compliance comes with high control complexity. Specifically, coordinating the motion of the system through a compliant actuator and finding a task-specific impedance profile that leads to better performance is non-trivial. Here, we utilise optimal control to devise time-varying torque and stiffness profiles for highly dynamic movements in compliantly actuated robots. The proposed methodology is applied to a ballthrowing task where we demonstrate that: (i) the method is able to tailor impedance strategies to specific task objectives and system dynamics, (ii) the ability to vary stiffness can be exploited to achieve better performance in this class of movements, (iii) in systems with variable physical compliance, our methodology is able to exploit the energy storage capabilities of the actuators. We illustrate these in several numerical simulations, and in hardware experiments on a device with variable physical stiffness.