CATCH-FORM-3D: Compliance-Aware Tactile Control and Hybrid Deformation Regulation for 3D Viscoelastic Object Manipulation
Hongjun Ma, Weichang Li
TL;DR
This work tackles precise manipulation of viscoelastic objects by introducing CATCH-FORM-3D, which unifies Kelvin–Voigt and Maxwell dynamics into a 3D viscoelastic continuum PDE. An adaptive observer estimates real-time material parameters from visual-tactile data, enabling a physics-guided deformation plan and a dual-loop controller that couples admittance-based force regulation with boundary control enforcing Dirichlet conditions via geometric templates. Key contributions include an interpretable PDE-based parameter identification scheme, a boundary-control strategy to ensure globally convergent strain fields, and an inner-outer control framework that achieves low-force-error and high-deformation-precision in dynamic tasks. Experimental validation on a PaXini hand across diverse materials demonstrates sub-millimeter deformation accuracy and force-tracking errors below 5%, indicating strong potential for industrial shaping, surgical assistance, and domestic automation. The combination of real-time PDE-based estimation with physics-guided planning and boundary-constrained deformation offers a computationally efficient, physically faithful route to compliant, high-precision robotic manipulation of viscoelastic media.
Abstract
This paper investigates a framework (CATCH-FORM-3D) for the precise contact force control and surface deformation regulation in viscoelastic material manipulation. A partial differential equation (PDE) is proposed to model the spatiotemporal stress-strain dynamics, integrating 3D Kelvin-Voigt (stiffness-damping) and Maxwell (diffusion) effects to capture the material's viscoelastic behavior. Key mechanical parameters (stiffness, damping, diffusion coefficients) are estimated in real time via a PDE-driven observer. This observer fuses visual-tactile sensor data and experimentally validated forces to generate rich regressor signals. Then, an inner-outer loop control structure is built up. In the outer loop, the reference deformation is updated by a novel admittance control law, a proportional-derivative (PD) feedback law with contact force measurements, ensuring that the system responds adaptively to external interactions. In the inner loop, a reaction-diffusion PDE for the deformation tracking error is formulated and then exponentially stabilized by conforming the contact surface to analytical geometric configurations (i.e., defining Dirichlet boundary conditions). This dual-loop architecture enables the effective deformation regulation in dynamic contact environments. Experiments using a PaXini robotic hand demonstrate sub-millimeter deformation accuracy and stable force tracking. The framework advances compliant robotic interactions in applications like industrial assembly, polymer shaping, surgical treatment, and household service.