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Donghang Zhang

Publications and source records attributed to Donghang Zhang.

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Bench2Dex: Benchmarking Visuo-Tactile Bimanual Dexterous Manipulation Across Dexterous Hands

Tactile sensing provides contact information that can be difficult to infer from vision alone, but tactile hardware for dexterous hands has not converged to a common design. Dexterous hands differ in finger structure, contact surfaces, and sensor layouts, while simulated tactile signals still differ from measurements produced by physical sensors. These factors make it difficult to study visuo-tactile manipulation across diverse dexterous hands within a consistent experimental setting. We present Bench2Dex, a simulation benchmark for visuo-tactile bimanual manipulation across 12 dexterous hands. We adapt existing robot models with a shared simulated tactile interface that converts local contact geometry into image-like tactile observations. The interface provides a consistent observation format across different hand morphologies without attempting to reproduce the output of a specific physical tactile sensor. Bench2Dex includes 26 bimanual manipulation tasks that involve tool use, articulated-object interaction, and multi-stage manipulation, together with about 1.3K human-teleoperated demonstrations. The benchmark provides synchronized visual, tactile, proprioceptive, action, and object-state observations, together with executable task metrics. For robustness, we group seven perturbation types into invariance axis, where the correct action does not change, and equivariance axis, where the correct action changes together with the perturbation. We evaluate ACT, Diffusion Policy, pi0.5, and GR00T N1.5 on Bench2Dex and report their performance and failure modes. Bench2Dex is meant as a platform for studying visuo-tactile learning across dexterous hands. It does not assume that simulated tactile observations can replace real tactile sensing; it offers a shared setting for algorithm development while tactile hardware and simulation models are still evolving.

cs.RO

HandEdit: A Unified Benchmark for Egocentric Human-to-Robot Dexterous Hand Image Editing

Robotic manipulation with dexterous hands is a cornerstone of Embodied AI, yet its progress is stifled by the high cost of collecting embodiment-aware teleoperation data. While abundant egocentric videos of human hands offer a scalable alternative, the profound discrepancies in appearance, articulation, and camera viewpoints between human and robotic data raise significant challenges for co-training. Though existing general image-editing models demonstrate strong capabilities, they lack necessary embodiment-specific priors to fully bridge this gap. In this work, we present HandEdit, a unified large-scale embodiment-aware image-editing dataset and benchmark specifically designed to transform human hands and arms into various dexterous robotic embodiments within egocentric frames. HandEdit comprises over 200M editing instances derived from five diverse source datasets, covering 26 distinct URDFs, including 13 hand-only and 13 hand-arm configurations. Alongside the dataset, we establish a unified benchmark protocol with two tracks: Hand-only and Hand-Arm, supporting URDF-conditioned evaluation. We conduct extensive evaluations of 11 representative image-editing baselines using a multi-dimensional metric suite, including generic similarity metrics, VLM-based judgment, and embodiment-aware metrics. HandEdit serves as a critical resource at the intersection of image editing and robotics: it advances embodiment-aware editing models while enabling scalable dexterous robotic learning from abundant human video data, paving the way for more generalizable Embodied AI.

cs.RO

p-multigrid method for the discontinuous Galerkin discretization of elliptic problems

In this paper, we propose a $W$-cycle $p$-multigrid method for solving the $p$-version symmetric interior penalty discontinuous Galerkin (SIPDG) discretization of elliptic problems. This SIPDG discretization employs hierarchical Legendre polynomial basis functions. Inspired by the uniform convergence theory of the $W$-cycle $hp$-multigrid method in [P. F. Antonietti, et al., SIAM J. Numer. Anal., 53 (2015)], we provide a rigorous convergence analysis for the proposed $p$-multigrid method, considering both inherited and non-inherited bilinear forms of SIPDG discretization. Our theoretical results show significant improvement over [P. F. Antonietti, et al., SIAM J. Numer. Anal., 53 (2015)], reducing the required number of smoothing steps from $O(p^2)$ to $O(p)$, where $p$ is the polynomial degree of the discrete broken polynomial space. Moreover, the convergence rate remains independent of the mesh size. Several numerical experiments are presented to verify our theoretical findings. Finally, we numerically verify the effectiveness of the $p$-multigrid method for unfitted finite element discretization in solving elliptic interface problems on general $C^{2} $-smooth interfaces.

math.NA

Spectral Deferred Correction Method for Landau-Brazovskii Model with Convex Splitting Technique

The Landau-Brazovskii model is a well-known Landau model for finding the complex phase structures in microphase-separating systems ranging from block copolymers to liquid crystals. It is critical to design efficient numerical schemes for the Landau-Brazovskii model with energy dissipation and mass conservation properties. Here, we propose a mass conservative and energy stable scheme by combining the spectral deferred correction (SDC) method with the convex splitting technique to solve the Landau-Brazovskii model efficiently. An adaptive correction strategy for the SDC method is implemented to reduce the cost time and preserve energy stability. Numerical experiments, including two- and three-dimensional periodic crystals in the Landau-Brazovskii model, are presented to show the efficiency of the proposed numerical method.

math.NA

A constrained transport divergence-free finite element method for Incompressible MHD equations

In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the discrete solutions should also satisfy divergence-free conditions exactly especially for the momentum equations. Inspired by constrained transport method,we devise a new stable mixed finite element method that can achieve the goal. We also prove the well-posedness of the discrete solutions. To solve the resulting linear algebraic equations, we propose a GMRES solver with an augmented Lagrangian block preconditioner. By numerical experiments, we verify the theoretical results and demonstrate the quasi-optimality of the discrete solver with respect to the number of degrees of freedom

math.NA