Trajectory Generation for Underactuated Soft Robot Manipulators using Discrete Elastic Rod Dynamics

2026-03-23

AI Summary

Soft robots exhibit inherent compliance that is advantageous for contact-rich tasks; however, their underactuated nature poses significant challenges in dynamic modeling, hindering the generation of high-precision, dynamically feasible trajectories. To address this, this work proposes a control-oriented dynamical reformulation of the Discrete Elastic Rod (DER) model, recasting it into a control-affine form that preserves first-principles force-deformation relationships while accommodating underactuation constraints. This approach enables real-time trajectory planning that balances physical fidelity with computational efficiency. Experimental validation on a pneumatically actuated soft manipulator demonstrates that the proposed method substantially outperforms constant-curvature baselines, achieving markedly improved trajectory tracking accuracy under complex actuation conditions.

Technology Category

• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Soft robots are well suited for contact-rich tasks due to their compliance, yet this property makes accurate and tractable modeling challenging. Planning motions with dynamically-feasible trajectories requires models that capture arbitrary deformations, remain computationally efficient, and are compatible with underactuation. However, existing approaches balance these properties unevenly: continuum rod models provide physical accuracy but are computationally demanding, while reduced-order approximations improve efficiency at the cost of modeling fidelity. To address this, our work introduces a control-oriented reformulation of Discrete Elastic Rod (DER) dynamics for soft robots, and a method to generate trajectories with these dynamics. The proposed formulation yields a control-affine representation while preserving certain first-principles force-deformation relationships. As a result, the generated trajectories are both dynamically feasible and consistent with the underlying actuation assumptions. We present our trajectory generation framework and validate it experimentally on a pneumatic soft robotic limb. Hardware results demonstrate consistently improved trajectory tracking performance over a constant-curvature-based baseline, particularly under complex actuation conditions.

Problem

• trajectory generation
• underactuated soft robots
• Discrete Elastic Rod
• dynamic feasibility
• modeling fidelity

Innovation

• Discrete Elastic Rod
• soft robot
• trajectory generation
• underactuated system
• control-affine dynamics