Constraint-Aware Physics-Informed Neural Networks for Static Shape Estimation of Co-Manipulative Continuum Robots
arXiv:2608.26273v1 Announce Type: new Abstract: Static shape estimation of co-manipulative continuum robots (CCRs) is challenging because the continuum arms and manipulated flexible object form a closed chain that must satisfy both static equilibrium and geometric loop-closure constraints. This paper presents a constraint-aware physics-informed neural network (PINN) for static shape estimation of a tendon-driven CCR modeled using the geometric variable strain formulation. The proposed method incorporates a projected static equilibrium residual and a configuration-level geometric residual to enforce the governing mechanics and closed-chain geometry. In simulation, the PINN is compared with a purely data-driven artificial neural network (ANN) under limited and noisy training data. With 140 samples and 50% label noise, the PINN reduces the relative configuration error, equilibrium residual, and closed-chain residual by 67.88%, 67.35%, and 88.06%, respectively. Using the full dataset, the PINN achieves 0.1597% relative configuration error with an inference time of 0.1773 ms, compared with 17.97 s for an iterative nonlinear solver. Experimental fine-tuning reduces the marker RMSE from 2.657 mm to 0.497 mm and increases R2 from -0.788 to 0.937. These results demonstrate accurate, physically consistent, and computationally efficient static shape estimation of closed-chain CCRs.
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[Submitted on 26 Aug 2026]
Title:Constraint-Aware Physics-Informed Neural Networks for Static Shape Estimation of Co-Manipulative Continuum Robots
View a PDF of the paper titled Constraint-Aware Physics-Informed Neural Networks for Static Shape Estimation of Co-Manipulative Continuum Robots, by Rana Danesh and 2 other authors
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Abstract:Static shape estimation of co-manipulative continuum robots (CCRs) is challenging because the continuum arms and manipulated flexible object form a closed chain that must satisfy both static equilibrium and geometric loop-closure constraints. This paper presents a constraint-aware physics-informed neural network (PINN) for static shape estimation of a tendon-driven CCR modeled using the geometric variable strain formulation. The proposed method incorporates a projected static equilibrium residual and a configuration-level geometric residual to enforce the governing mechanics and closed-chain geometry. In simulation, the PINN is compared with a purely data-driven artificial neural network (ANN) under limited and noisy training data. With 140 samples and 50% label noise, the PINN reduces the relative configuration error, equilibrium residual, and closed-chain residual by 67.88%, 67.35%, and 88.06%, respectively. Using the full dataset, the PINN achieves 0.1597% relative configuration error with an inference time of 0.1773 ms, compared with 17.97 s for an iterative nonlinear solver. Experimental fine-tuning reduces the marker RMSE from 2.657 mm to 0.497 mm and increases R2 from -0.788 to 0.937. These results demonstrate accurate, physically consistent, and computationally efficient static shape estimation of closed-chain CCRs.
Subjects:
Robotics (cs.RO); Machine Learning (cs.LG)
Cite as: arXiv:2608.26273 [cs.RO]
(or arXiv:2608.26273v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2608.26273
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Rana Danesh [view email] [v1] Wed, 26 Aug 2026 18:00:39 UTC (557 KB)
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