Model-based Optimal Control for Rigid-Soft Underactuated Systems

TL;DR

This paper explores model-based optimal control strategies for rigid-soft underactuated robots, addressing computational challenges and demonstrating their effectiveness in simulation for complex dynamic tasks.

Contribution

It introduces three optimal control methods tailored for high-dimensional rigid-soft systems, utilizing analytical derivatives and implicit integration for improved robustness.

Findings

Effective swing-up control demonstrated in simulations

Implicit schemes enhance numerical stability

Trade-offs between computational efficiency and control accuracy

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.