Soft Swing-up: Benchmarking Model-Based Optimal Control for Rigid-Soft Underactuated Systems
For researchers in soft robotics control, this work provides a comparative evaluation of optimal control methods on dynamic tasks, but the findings are incremental as they apply existing techniques to specific benchmarks.
This paper benchmarks three model-based optimal control strategies (Direct Collocation, Differential Dynamic Programming, Nonlinear Model Predictive Control) for dynamic swing-up tasks in rigid-soft underactuated systems, using implicit integration and warm-start to handle stiff dynamics. Results show trade-offs in performance and computational cost across three benchmark systems.
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.