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arXiv · 2503.06802

A Physically Consistent Stiffness Formulation for Contact-Rich Manipulation

Johannes Lachner·Moses C. Nah·Neville Hogan
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Abstract

Ensuring symmetric stiffness in impedance-controlled robots is crucial for physically meaningful and stable interaction in contact-rich manipulation. Conventional approaches neglect the change of basis vectors in curved spaces, leading to an asymmetric joint-space stiffness matrix that violates passivity and conservation principles. In this work, we derive a physically consistent, symmetric joint-space stiffness formulation directly from the task-space stiffness matrix by explicitly incorporating Christoffel symbols. This correction resolves long-standing inconsistencies in stiffness modeling, ensuring energy conservation and stability. We validate our approach experimentally on a robotic system, demonstrating that omitting these correction terms results in significant asymmetric stiffness errors. Our findings bridge theoretical insights with practical control applications, offering a robust framework for stable and interpretable robotic interactions.

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Johannes Lachner, Moses C. Nah, Neville Hogan. 2025-03-09. A Physically Consistent Stiffness Formulation for Contact-Rich Manipulation. https://arxiv.org/abs/2503.06802

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