Model-based Optimal Control for Rigid-Soft Underactuated Systems
Daniele Caradonna, Nikhil Nair, Anup Teejo Mathew, Daniel Feliu Talegón, Imran Afgan, Egidio Falotico, Cosimo Della Santina, Federico Renda
TL;DR
This work tackles dynamic swing-up control for underactuated rigid-soft robots by leveraging a differentiable Geometric Variable Strain (GVS) model with analytical derivatives to enable gradient-based optimization on high-DoF continuum dynamics. It introduces Box-IDDP, a method that fuses implicit integration with box-constrained DDP, and a warm-start strategy that progressively increases model fidelity from rigid to high-order soft representations. Case studies on Soft Cart-Pole, Soft Pendubot, and Soft Furuta Pendulum demonstrate the framework's ability to handle non-minimum phase behavior and complex out-of-plane deformations, while comparing Direct Collocation, Box-IDDP, and NMPC in terms of convergence, robustness, and computational efficiency. The contributions enable accurate, constrained, real-time capable optimization of rigid-soft systems and pave the way for experimental validation and broader deployment in high-DoF CSR applications.
Abstract
Continuum soft robots are inherently underactuated and subject to intrinsic input constraints, making dynamic control particularly challenging, especially in hybrid rigid-soft robots. While most existing methods focus on quasi-static behaviors, dynamic tasks such as swing-up require accurate exploitation of continuum dynamics. This has led to studies on simple low-order template systems that often fail to capture the complexity of real continuum deformations. Model-based optimal control offers a systematic solution; however, its application to rigid-soft robots is often limited by the computational cost and inaccuracy of numerical differentiation for high-dimensional models. Building on recent advances in the Geometric Variable Strain model that enable analytical derivatives, this work investigates three optimal control strategies for underactuated soft systems-Direct Collocation, Differential Dynamic Programming, and Nonlinear Model Predictive Control-to perform dynamic swing-up tasks. To address stiff continuum dynamics and constrained actuation, implicit integration schemes and warm-start strategies are employed to improve numerical robustness and computational efficiency. The methods are evaluated in simulation on three Rigid-Soft and high-order soft benchmark systems-the Soft Cart-Pole, the Soft Pendubot, and the Soft Furuta Pendulum- highlighting their performance and computational trade-offs.