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The importance of Variable Stiffness Actuators (VSA) in safety and performance of robots has been extensively discussed in the last decade. It has also been shown recently that a VSA brings performance advantages with respect to common actuators. For instance, the solution of the optimal control problem of maximizing the speed of a VSA for impact maximization at a given position with free final time is achieved by applying a control policy that synchronizes stiffness changes with link speed and acceleration. This problem can be regarded as the formalization of the performance of a soccer player’s free kick. In this paper we revisit the impact maximization problem with imposing a new constraint: we want to maximize the velocity of the actuator link at a given position and fixed terminal time - applicable e.g. to maximize performance of a first-time kick. We first study the problem with fixed stiffness and show that under realistic modeling assumptions, there does exist an optimal linear spring for a given link inertia, final time and motor characteristics. Results are validated with experimental tests. We then study optimal control of VSA and show that varying the spring stiffness during the execution of the kick task substantially improves the final speed.

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