Monocular Depth Estimation via Neural Network with Learnable Algebraic Group and Ring Structures

Monocular depth estimation (MDE) has witnessed remarkable progress driven by Convolutional Neural Networks and transformer-based architectures. However, these approaches typically treat the problem as a generic image-to-image regression on Euclidean grids, thereby overlooking the intrinsic algebraic and geometric structures induced by perspective projection. To address this limitation, we propose LAGRNet, a novel framework that fundamentally grounds MDE in algebraic geometry by explicitly embedding learnable group, ring, and sheaf structures into the deep learning pipeline. Modeling feature maps as sections of a sheaf over an approximated image manifold, our method first establishes a Group-defined Feature Manifold (GFM) parameterized by a learned algebraic group action to enforce projective equivariance and robustness against view changes. To facilitate algebraically consistent cross-scale interactions, we subsequently introduce a Ring Convolution Layer (RCL) that formulates feature fusion as a graded ring homomorphism. Furthermore, to ensure global topological consistency, a Sheaf-based Module (SM) aggregates local depth cues via Čech nerve on the image topology. Extensive zero-shot evaluations across the KITTI, NYU-Depth V2, and ETH3D benchmarks demonstrate that LAGRNet significantly outperforms state-of-the-art methods in both accuracy and generalization capabilities.

Bootstrapping Imitation Learning for Long-horizon Manipulation via Hierarchical Data Collection Space

Imitation learning (IL) with human demonstrations is a promising method for robotic manipulation tasks. While minimal demonstrations enable robotic action execution, achieving high success rates and generalization requires high cost, e.g., continuously adding data or incrementally conducting human-in-loop processes with complex hardware/software systems. In this paper, we rethink the state/action space of the data collection pipeline as well as the underlying factors responsible for the prediction of non-robust actions. To this end, we introduce a Hierarchical Data Collection Space (HD-Space) for robotic imitation learning, a simple data collection scheme, endowing the model to train with proactive and high-quality data. Specifically, We segment the fine manipulation task into multiple key atomic tasks from a high-level perspective and design atomic state/action spaces for human demonstrations, aiming to generate robust IL data. We conduct empirical evaluations across two simulated and five real-world long-horizon manipulation tasks and demonstrate that IL policy training with HD-Space-based data can achieve significantly enhanced policy performance. HD-Space allows the use of a small amount of demonstration data to train a more powerful policy, particularly for long-horizon manipulation tasks. We aim for HD-Space to offer insights into optimizing data quality and guiding data scaling. project page: https://hd-space-robotics.github.io.

Enhancing Multi-Robot Semantic Navigation Through Multimodal Chain-of-Thought Score Collaboration

Understanding how humans cooperatively utilize semantic knowledge to explore unfamiliar environments and decide on navigation directions is critical for house service multi-robot systems. Previous methods primarily focused on single-robot centralized planning strategies, which severely limited exploration efficiency. Recent research has considered decentralized planning strategies for multiple robots, assigning separate planning models to each robot, but these approaches often overlook communication costs. In this work, we propose Multimodal Chain-of-Thought Co-Navigation (MCoCoNav), a modular approach that utilizes multimodal Chain-of-Thought to plan collaborative semantic navigation for multiple robots. MCoCoNav combines visual perception with Vision Language Models (VLMs) to evaluate exploration value through probabilistic scoring, thus reducing time costs and achieving stable outputs. Additionally, a global semantic map is used as a communication bridge, minimizing communication overhead while integrating observational results. Guided by scores that reflect exploration trends, robots utilize this map to assess whether to explore new frontier points or revisit history nodes. Experiments on HM3D_v0.2 and MP3D demonstrate the effectiveness of our approach. Our code is available at https://github.com/FrankZxShen/MCoCoNav.git.