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

TL;DR

This paper introduces a control-oriented reformulation of Discrete Elastic Rod dynamics for soft robots, enabling the generation of physically accurate, computationally efficient, and dynamically feasible trajectories validated on a pneumatic soft robotic limb.

Contribution

It presents a novel control-affine formulation of DER dynamics and a trajectory generation method tailored for underactuated soft robots, balancing accuracy and efficiency.

Findings

Improved trajectory tracking performance over baseline methods.

Validated approach on a pneumatic soft robotic limb.

Demonstrated effectiveness under complex actuation conditions.

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.