Global analysis of energy-based swing-up control for soft robot

In this paper, we explore the energy-based swing-up control for a soft robot equipped with an actuated constant curvature soft pendulum and an unactuated rotational base joint. The aim is to swing the robot up towards its upright equilibrium point (UEP) with the pendulum at an upright position. We establish a necessary and sufficient condition to protect the control law from singularities and demonstrate the robot's potential motion towards a homoclinic orbit or a closed-loop equilibrium point. After examining the robot's closed-loop equilibrium points, we generate formulae to compute all such points and introduce two conditions concerning control parameters, eliminating all but the UEP and downward equilibrium point (DEP) with the robot in a downward position. We prove the instability of the equilibrium points with negative gravitational potential energy. This obviates the need for one of the two conditions concerning such equilibrium points. We also prove the robot's linear controllability at the UEP. Our obtained results reveal that, regardless of its initial state, the soft robot can be swung-up towards its UEP using the energy-based controller, provided that it meets the proposed control parameter conditions, and can subsequently be balanced around the UEP using a locally stabilizing controller. Our simulation investigations validate the presented theoretical results.(c) 2023 Published by Elsevier Ltd.