In this paper, we investigate the role of variable stiffness in the reduction of the energy cost for mechanical systems that perform desired tasks. The objective is to assess the use of Variable Stiffness Actuation (VSA) by determining an optimal stiffness profile and the associated energy cost of performing a desired task. For the analysis we consider mechanical systems of n-Degrees of Freedom (DoF), using VSA. We find an analytical solution that expresses the optimal stiffness profile during the task as a function of joint trajectories. This stiffness profile can be either constant or variable in time, and it minimizes a cost function, when performing a desired task.
We calculate the cost related to the torque of the system and the additional cost of changing or keeping a stiffness actively constant. Additionally, we discuss some cases for which it is worth to change the stiffness during a task and cases for which a constant stiffness may be better solution. Furthermore, from simulations and experiments we show cases in which using a variable stiffness profile allows cost savings w.r.t. constant
stiffness. The use of variable stiffness depends on the task, i.e. on the joint trajectories and their frequency, as well as on the mechanical implementation of the actuator used.