<p>This paper studies the energy-based swing-up control of an underactuated soft inverted pendulum, a template model of soft robots with its base attached to the ground and its curvature described by an affine function. First, this paper presents a necessary and sufficient condition for the linear controllability of the robot around its upright equilibrium point (UEP). Next, without any constraint on its stiffness, this paper derives an energy-based controller to swing up the robot to its UEP, where the pendulum is in its upright position, and provides a necessary and sufficient condition such that the controller is free of singular points. Then, this paper characterizes the patterns of closed-loop equilibrium points with respect to the physical parameters of the pendulum and the gains of the derived controller, and analyzes the closed-loop motion corresponding to the special case in which desired convergence of the total mechanical energy is achieved. In such case, this paper reveals that the UEP is generically the unique closed-loop equilibrium point, and provides clarification regarding its stability. These results serve as guidelines of the design of soft robots and the tuning of control gains to achieve the desired performance of the swing-up control. Finally, this paper conducts numerical simulations to validate the theoretical results and to demonstrate the effectiveness and performance of the derived controller in swinging up the robot to its UEP from initial states far from the UEP, even under the challenging condition of very low stiffness.</p>