Morphologies of a sagging elastica with intrinsic sensing and actuation

📅 2025-09-22
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🤖 AI Summary
Precise shape control of soft robots under self-weight and geometric nonlinearity remains challenging due to limited sensing/actuation resolution, modeling inaccuracies, and constrained feedback capability. Method: This work proposes a distributed curvature sensing–torque actuation closed-loop control framework grounded in the elastic rod model. To characterize resolution limitations, a bandwidth-controllable filter is introduced to emulate perception–actuation fidelity; theoretical analysis reveals an inverse-square relationship between sensing–actuation gain and filter bandwidth. A precision–robustness trade-off mechanism is then established, jointly accommodating long- and short-wavelength shape features. Results: The framework yields quantitative design principles for shape control in geometrically nonlinear systems. Experiments demonstrate effective suppression of sagging deformation, with minimal shape error achieved at the optimal filter bandwidth—providing transferable theoretical insights and experimental validation for controllable deformation design in highly agile soft robotic systems.

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📝 Abstract
The morphology of a slender soft-robot can be modified by sensing its shape via sensors and exerting moments via actuators embedded along its body. The actuating moments required to morph these soft-robots to a desired shape are often difficult to compute due to the geometric non-linearity associated with the structure, the errors in modeling the experimental system, and the limitations in sensing and feedback/actuation capabilities. In this article, we explore the effect of a simple feedback strategy (actuation being proportional to the sensed curvature) on the shape of a soft-robot, modeled as an elastica. The finite number of sensors and actuators, often seen in experiments, is captured in the model via filters of specified widths. Using proportional feedback, we study the simple task of straightening the device by compensating for the sagging introduced by its self-weight. The device undergoes a hierarchy of morphological instabilities defined in the phase-space given by the gravito-bending number, non-dimensional sensing/feedback gain, and the scaled width of the filter. For complex shape-morphing tasks, given a perfect model of the device with limited sensing and actuating capabilities, we find that a trade-off arises (set by the sensor spacing & actuator size) between capturing the long and short wavelength features. We show that the error in shape-morphing is minimal for a fixed filter width when we choose an appropriate actuating gain (whose magnitude goes as a square of the filter width). Our model provides a quantitative lens to study and design slender soft devices with limited sensing and actuating capabilities for complex maneuvering applications.
Problem

Research questions and friction points this paper is trying to address.

Computing actuation moments for soft-robot shape morphing is difficult
Studying feedback strategy effects on shape using a finite sensor model
Exploring trade-offs in capturing shape features with limited capabilities
Innovation

Methods, ideas, or system contributions that make the work stand out.

Proportional feedback control using sensed curvature
Model incorporating finite sensors via width filters
Optimizing actuator gain for minimal shape error
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IIT Madras
V
Vishnu Deo Mishra
Department of Applied Mechanics & Biomedical Engineering, IIT Madras, Chennai, TN 600036
S Ganga Prasath
S Ganga Prasath
Indian Institute of Technology Madras
Soft-mechanicsRoboticsBehavior