Stabilizing Low-Stiffness Soft Robots at Unstable Equilibria: A Model-Based Optimal Control Approach

Continuum soft robots are highly nonlinear and underactuated systems, which makes stabilizing them around unstable equilibrium points difficult. This challenge becomes even greater in low stiffness regimes, where gravitational forces dominate elastic forces. In this letter, we explore whether optimal control can address these challenges using a computa- tionally efficient method suitable for real time use. We propose a nonlinear model predictive control (NMPC) approach based on Differential Dynamic Programming (DDP), combined with an accurate reduced order Variable Strain model with analytical derivatives. This results in an efficient control framework for addressing the stabilization problem. Tested on a soft inverted pendulum and other hybrid soft rigid systems, the method outperforms traditional controllers, stabilizes more challenging configurations, and operates reliably at real time speeds (50 150 Hz), demonstrating both effectiveness and practical feasibility in experimental settings.