arXiv subjects

Haoyu Zhu

Publications and source records attributed to Haoyu Zhu.

4 recordsLinked to original sources

arXiv2026

Navigate or Relocate? Planning Among Movable Obstacles in Unknown Environments

Conventional robot planning methods seek collision-free paths to a goal but fail when all paths are blocked. In these cases, the robot must determine which objects to relocate, in what order, and where to place them to clear a path---a problem known as Navigation Among Movable Obstacles (NAMO). Most NAMO planners assume a known environment, while existing approaches for unknown environments typically reason locally about relocations and cannot plan interdependent relocation sequences. We consider NAMO in unknown environments revealed through onboard sensing, where the robot must decide whether a blocked route requires relocation or a feasible path may exist through unexplored space. We propose an online framework that addresses this ambiguity by selecting between navigation and relocation using shortest paths that treat discovered movable objects as obstacles or as removable. Navigation relies on existing motion planners, while relocation uses a sampling-based approach that, unlike existing approaches for unknown environments, searches over \textit{interdependent} relocation sequences and uses an LLM to bias sampling. Numerical experiments demonstrate scalability to cluttered environments requiring interdependent relocations and improved plan quality over existing baselines.

cs.RO↗

arXiv2026

MASS: Mesh-inellipse Aligned Deformable Surfel Splatting for Hand Reconstruction and Rendering from Egocentric Monocular Video

Reconstructing high-fidelity 3D hands from egocentric monocular videos remains a challenge due to the limitations in capturing high-resolution geometry, hand-object interactions, and complex objects on hands. Additionally, existing methods often incur high computational costs, making them impractical for real-time applications. In this work, we propose Mesh-inellipse Aligned deformable Surfel Splatting (MASS) to address these challenges by leveraging a deformable 2D Gaussian Surfel representation. We introduce the mesh-aligned Steiner Inellipse and fractal densification for mesh-to-surfel conversion that initiates high-resolution 2D Gaussian surfels from coarse parametric hand meshes, providing surface representation with photorealistic rendering potential. Second, we propose Gaussian Surfel Deformation, which enables efficient modeling of hand deformations and personalized features by predicting residual updates to surfel attributes and introducing an opacity mask to refine geometry and texture without adaptive density control. In addition, we propose a two-stage training strategy and a novel binding loss to improve the optimization robustness and reconstruction quality. Extensive experiments on the ARCTIC dataset, the Hand Appearance dataset, and the Interhand2.6M dataset demonstrate that our model achieves superior reconstruction performance compared to state-of-the-art methods.

cs.CV↗

arXiv2025

T-SKM-Net: Trainable Neural Network Framework for Linear Constraint Satisfaction via Sampling Kaczmarz-Motzkin Method

Neural network constraint satisfaction is crucial for safety-critical applications such as power system optimization, robotic path planning, and autonomous driving. However, existing constraint satisfaction methods face efficiency-applicability trade-offs, with hard constraint methods suffering from either high computational complexity or restrictive assumptions on constraint structures. The Sampling Kaczmarz-Motzkin (SKM) method is a randomized iterative algorithm for solving large-scale linear inequality systems with favorable convergence properties, but its argmax operations introduce non-differentiability, posing challenges for neural network applications. This work proposes the Trainable Sampling Kaczmarz-Motzkin Network (T-SKM-Net) framework and, for the first time, systematically integrates SKM-type methods into neural network constraint satisfaction. The framework transforms mixed constraint problems into pure inequality problems through null space transformation, employs SKM for iterative solving, and maps solutions back to the original constraint space, efficiently handling both equality and inequality constraints. We provide theoretical proof of post-processing effectiveness in expectation and end-to-end trainability guarantees based on unbiased gradient estimators, demonstrating that despite non-differentiable operations, the framework supports standard backpropagation. On the DCOPF case118 benchmark, our method achieves 4.27ms/item GPU serial forward inference with 0.0025% max optimality gap with post-processing mode and 5.25ms/item with 0.0008% max optimality gap with joint training mode, delivering over 25$\times$ speedup compared to the pandapower solver while maintaining zero constraint violations under given tolerance.

cs.LG↗

arXiv2024

On Bott--Samelson rings for Coxeter groups

We study the cohomology ring of the Bott--Samelson variety. We compute an explicit presentation of this ring via Soergel's result, which implies that it is a purely combinatorial invariant. We use the presentation to introduce the Bott--Samelson ring associated with a word in arbitrary Coxeter system by generators and relations. In general, it is a split quadratic complete intersection algebra with a triangular pattern of relations. By a result of Tate, it follows that it is a Koszul algebra and we provide a quadratic (reduced) Gr{ö}bner basis. Furthermore, we prove that it satisfies the whole Kähler package, including the Poincaré duality, the hard Lefschetz theorem, and the Hodge--Riemann bilinear relations.

math.RA↗