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.
Real-Time Model Predictive Control for the Swing-Up Problem of an Underactuated Double Pendulum
Robotics Innovation Center, German Research Center for Artificial Intelligence (DFKI GmbH)（德国人工智能研究中心机器人创新中心）；Faculty of Electrical Engineering and Informatics, City University of applied Sciences Bremen（不来梅应用技术大学电气工程与信息学院）
Real-Time Nonlinear MPC via Sequential Quadratic Programming with Structure-Exploiting ADMM and Interior-Point Methods for Underactuated Double-Pendulum Swing-Up
Multi-objective Anti-swing Trajectory Planning of Double-pendulum Tower Crane Operations using Opposition-based Evolutionary Algorithm
Nanyang Technological University（南洋理工大学）；School of Mechanical and Aerospace Engineering (MAE)（机械与航空航天工程学院）；School of Computer Science and Engineering (CSE)（计算机科学与工程学院）
Reinforcement Learning for Robust Athletic Intelligence: Lessons from the 2nd 'AI Olympics with RealAIGym' Competition
German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心（DFKI））；University of Padova（帕多瓦大学）；Korea University（高丽大学）；Mitsubishi Electric Research Lab (MERL)（三菱电机研发实验室（MERL））；Technical University of Darmstadt（达姆施塔特工业大学）；University of Bremen（不来梅大学）；Chalmers University of Technology（查尔姆斯理工大学）
