• continuum soft robots
• energy shaping
• hamiltonian systems
• model-based control
• snap
• underactuated mechanical systems

Continuum soft robots are mechanical systems made with soft materials, which confer a continuously deformable structure. Their continuous dynamics leads to a large number of Degrees of Freedom, and this makes the control problem complex, especially for the model-based controller. Consequently, model-free approaches have spread widely in the soft robots field, as they allow the development of complex and efficient control laws without the necessity of knowing the structure perfectly.
However, model-based approaches are usually preferable to model-free ones, because they guarantee more robust and faster controllers. For this reason, one of the goals of the robotics community, in the field of continuum soft robots, is to design an efficient model-based control that allows the execution of dynamic tasks with soft robots. A strategy is to look at the energy properties of these systems in order to exploit their intrinsic intelligence.
In this work, a study of an under-actuated continuum soft robot modeled as an inverted pendulum with affine curvature is proposed.
A peculiar robot behavior derived from the system elasticity, which is usually referred to as a snap, is investigated. The snap defines a catapult-like behavior and is the result of how the soft robot stores and fast releases the elastic energy. First, after looking for relations between system parameters and snap, suitable input signals are defined to make a pick and place task using only the snap behavior without control input.
Secondly, an energy shaping model-based control for under-actuated systems is applied to stabilize the unstable equilibrium and control and/or exploit the snap. Then, stability conditions are discussed, and the controller's effectiveness is verified via simulations. Results are then compared with the ones obtained with baseline controllers, e.g. partial feedback linearization control and proportional derivative control to show the competitiveness of the proposed approach.
Lastly, the results of simulations are validated through simple hardware suitably realized with a harmonic steel sheet.