Model-based Optimal Control for Rigid-Soft Underactuated Systems

2026-02-03

AI Summary

This work addresses the challenges of dynamic control in compliant, underactuated systems characterized by complex continuum dynamics, strong input constraints, and computationally expensive high-dimensional models. For the first time, it integrates a geometrically exact continuum model with analytical derivatives into multiple optimal control frameworks—including direct collocation, differential dynamic programming, and nonlinear model predictive control—enhancing computational efficiency through implicit integration and warm-start strategies. The proposed approach successfully achieves dynamic swing-up control on three high-dimensional simulation platforms: the Soft Cart-Pole, Soft Pendubot, and Soft Furuta Pendulum, demonstrating an effective trade-off between control performance and computational tractability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Intelligent Robots: Behavior Learning & Control

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• underactuated systems
• continuum soft robots
• dynamic control
• rigid-soft robots
• optimal control

Innovation

• Model-based optimal control
• Geometric Variable Strain model
• Rigid-soft robots
• Underactuated systems
• Analytical derivatives