• Trajectory generation
• Optimization
• Energy efficiency
• Variable Stiffness

This thesis focuses on the problem of minimizing the energy consumption to improve robots performance during desired tasks. Soft
actuation is used to reduce the energy cost for mechanical systems with n Degrees-of-Freedom (DoF), due to the capability of compliant elements of storing energy and releasing it to the system when required. I provide an analytical tool to assess the use of compliant actuation on the basis of the energy consumption. In other words, I tackle the problem of reducing the energy consumption of mechanical systems that perform different tasks by exploiting the characteristics of soft actuators. The analysis considers either constant and variable stiffness mechanisms used in systems that perform a certain task, where cyclic motions are of particular interest. For given joint trajectories, the methodology provides the optimal stiffness, in case of Series Elastic Actuators (SEAs), and both stiffness and pre-load, in case of Parallel Elastic Actuators (PEAs) that minimize the energy consumption. Several simulations and experimental tests on a single joint and a two-DoF platforms validate the analytical results obtained.
Moreover, I show that the problem of concurrently optimizing stiffness, pre-load and joint trajectories can be cast in a simpler problem
in which the optimization regards only the parameters that define the shape of the link trajectories. Experiments carried out show that the simultaneous optimization of stiffness and trajectories improves the performance of the system in terms of the energy consumption with respect to the case when only the stiffness is optimized. Additionally, I include the analytical solution of the optimal stiffness profile during a desired task. For this part of the analysis I consider the use of Variable Stiffness Actuators (VSAs). Several simulations and experiments were carried out, to show that there are cases in which it is worth to use VSA, but in other cases it may not be the best solution in terms of energy consumption.