A physically consistent stiffness formulation for contact-rich manipulation
Year: 2025
Type: article
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.
Authors: Johannes Lachner, Moses C. Nah, Neville Hogan
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,400
Funder: MathWorks
OpenAlex ID: W4416077268