• Locomotion
• Optimal Control
• Soft Robotics
• Variable Stiffness

The most recent outcomes in robotics show humanoid robots able to provide a stable and robust walk on different terrain and to manage unexpected external disturbances. Nevertheless, also loco-manipulation tasks are accomplished. Although these remarkable results, human performance still remains an unreached important goal.
Aware of the key features of the biologic actuation, such as the compliance management for task accomplishment, Soft Robotics was born. The term Soft Robotics denotes the robots that include a fixed or variable compliance at the actuation level.
Variable Stiffness Actuators (VSA) that by reconfiguring the elastic transmission are able to physically change its compliance. Hence, in the robotic locomotion field, Soft Robotic places a new variable, i.e. the system compliance, which can be profitably used to achieve the human locomotion performances.
In this thesis the inherent compliance of a soft robot is exploited in the problem solving of the robot locomotion sub-phases with
the final objective of implementing a Variable Stiffness Walk (VSW). During the VSW the robot compliance is managed in function of the current requirements and robot state in order to exploit the improvements provided by the stiffness solutions. This work is organized in five parts in function of the locomotion task requirements.
In the first part the energy efficiency problem is approached. A strategy for mechanical systems that perform cyclic tasks (like locomotion) to determine the optimal stiffness value and spring pre\-load, minimizing a given cost functional, is presented. The method is applicable for fully actuated and underactuated mechanical compliant systems and also compares two of the most used soft actuators typology.
In the second part a methodology to optimize the system stiffness in function of stability and mobility criterion is provided. The study finds the optimal stiffness and pre--load which maximize the reachable workspace subject to stability constraints, limits in actuation and task space. The design of an add-on structure to implement the chosen stiffness is reported. Tests show power consumption reducing due to the application of the add-on validating the approach.
In the third part an optimal variable stiffness control for oscillation damping is presented. The objective is to reduce the mechanical energy of a soft actuator given initial conditions and terminal time. The study provides a bang bang like model dependent control law. For a particular case, a model independent control law can be obtained and suitably applied on multi degree of freedom manipulator respecting stability requirements.
In the fifth part the robust optimization method is applied to choose the robot optimal compliance in scenarios where robot-environment interaction is requested. The goal is to minimize the exchanged forces between two entities in case of uncertainty. Simulation results, provided for two different tasks, i.e. one of manipulation and the other one of locomotion, show that in case of environment uncertainties the optimal solution is obtained for a compliant choice of the robot. Moreover, the robot compliance is proportional to the uncertainty. Experimental validations are provided for both the aforementioned tasks.
In the last part of this work, a Variable Stiffness Walk (VSW) is tested. Through the locomotion pattern analysis of a known barely stable walk, a set of joint primitives are identified and then combined to implement a walk for a biped model in simulation. A stiffness strategy is then applied on the biped legs to set a soft behaviour across the impact with the ground and stiff for the rest of the gait. Results in terms of exchanged forces and COP evolution are then compared w.r.t. the case at constant stiffness. A preliminary campaign of experiments implementing the VSW on a 6 DoF Biped robot are then produced and the results analyzed.