REST: Receding Horizon Explorative Steiner Tree for Zero-Shot Object-Goal Navigation

Zero-shot object-goal navigation (ZSON) requires navigating unknown environments to find a target object without task-specific training. Prior hierarchical training-free solutions invest in scene understanding (\textit{belief}) and high-level decision-making (\textit{policy}), yet overlook the design of \textit{option}, i.e., a subgoal candidate proposed from evolving belief and presented to policy for selection. In practice, options are reduced to isolated waypoints scored independently: single destinations hide the value gathered along the journey; an unstructured collection obscures the relationships among candidates. Our insight is that the option space should be a \textit{tree of paths}. Full paths expose en-route information gain that destination-only scoring systematically neglects; a tree of shared segments enables coarse-to-fine LLM reasoning that dismisses or pursues entire branches before examining individual leaves, compressing the combinatorial path space into an efficient hierarchy. We instantiate this insight in \textbf{REST} (Receding Horizon Explorative Steiner Tree), a training-free framework that (1) builds an explicit open-vocabulary 3D map from online RGB-D streams; (2) grows an agent-centric tree of safe and informative paths as the option space via sampling-based planning; and (3) textualizes each branch into a spatial narrative and selects the next-best path through chain-of-thought LLM reasoning. Across the Gibson, HM3D, and HSSD benchmarks, REST consistently ranks among the top methods in success rate while achieving the best or second-best path efficiency, demonstrating a favorable efficiency-success balance.

SignNav: Leveraging Signage for Semantic Visual Navigation in Large-Scale Indoor Environments

Humans routinely leverage semantic hints provided by signage to navigate to destinations within novel Large-Scale Indoor (LSI) environments, such as hospitals and airport terminals. However, this capability remains underexplored within the field of embodied navigation. This paper introduces a novel embodied navigation task, SignNav, which requires the agent to interpret semantic hint from signage and reason about the subsequent action based on current observation. To facilitate research in this domain, we construct the LSI-Dataset for the training and evaluation of various SignNav agents. Dynamically changing semantic hints and sparse placement of signage in LSI environments present significant challenges to the SignNav task. To address these challenges, we propose the Spatial-Temporal Aware Transformer (START) model for end-to-end decision-making. The spatial-aware module grounds the semantic hint of signage into physical world, while the temporal-aware module captures long-range dependencies between historical states and current observation. Leveraging a two-stage training strategy with Dataset Aggregation (DAgger), our approach achieves state-of-the-art performance, recording an 80% Success Rate (SR) and 0.74 NDTW on val-unseen split. Real-world deployment further demonstrates the practicality of our method in physical environment without pre-built map.

Tensegrity Robot Endcap-Ground Contact Estimation with Symmetry-aware Heterogeneous Graph Neural Network

Tensegrity robots possess lightweight and resilient structures but present significant challenges for state estimation due to compliant and distributed ground contacts. This paper introduces a symmetry-aware heterogeneous graph neural network (Sym-HGNN) that infers contact states directly from proprioceptive measurements, including IMU and cable-length histories, without dedicated contact sensors. The network incorporates the robot's dihedral symmetry $D_3$ into the message-passing process to enhance sample efficiency and generalization. The predicted contacts are integrated into a state-of-the-art contact-aided invariant extended Kalman filter (InEKF) for improved pose estimation. Simulation results demonstrate that the proposed method achieves up to 15% higher accuracy and 5% higher F1-score using only 20% of the training data compared to the CNN and MI-HGNN baselines, while maintaining low-drift and physically consistent state estimation results comparable to ground truth contacts. This work highlights the potential of fully proprioceptive sensing for accurate and robust state estimation in tensegrity robots. Code available at: https://github.com/Jonathan-Twz/Tensegrity-Sym-HGNN

LongNav-R1: Horizon-Adaptive Multi-Turn RL for Long-Horizon VLA Navigation

This paper develops LongNav-R1, an end-to-end multi-turn reinforcement learning (RL) framework designed to optimize Visual-Language-Action (VLA) models for long-horizon navigation. Unlike existing single-turn paradigm, LongNav-R1 reformulates the navigation decision process as a continuous multi-turn conversation between the VLA policy and the embodied environment. This multi-turn RL framework offers two distinct advantages: i) it enables the agent to reason about the causal effects of historical interactions and sequential future outcomes; and ii) it allows the model to learn directly from online interactions, fostering diverse trajectory generation and avoiding the behavioral rigidity often imposed by human demonstrations. Furthermore, we introduce Horizon-Adaptive Policy Optimization. This mechanism explicitly accounts for varying horizon lengths during advantage estimation, facilitating accurate temporal credit assignment over extended sequences. Consequently, the agent develops diverse navigation behaviors and resists collapse during long-horizon tasks. Experiments on object navigation benchmarks validate the framework's efficacy: With 4,000 rollout trajectories, LongNav-R1 boosts the Qwen3-VL-2B success rate from 64.3% to 73.0%. These results demonstrate superior sample efficiency and significantly outperform state-of-the-art methods. The model's generalizability and robustness are further validated by its zero-shot performance in long-horizon real-world navigation settings. All source code will be open-sourced upon publication.

Lies We Can Trust: Quantifying Action Uncertainty with Inaccurate Stochastic Dynamics through Conformalized Nonholonomic Lie Groups

We propose Conformal Lie-group Action Prediction Sets (CLAPS), a symmetry-aware conformal prediction-based algorithm that constructs, for a given action, a set guaranteed to contain the resulting system configuration at a user-defined probability. Our assurance holds under both aleatoric and epistemic uncertainty, non-asymptotically, and does not require strong assumptions about the true system dynamics, the uncertainty sources, or the quality of the approximate dynamics model. Typically, uncertainty quantification is tackled by making strong assumptions about the error distribution or magnitude, or by relying on uncalibrated uncertainty estimates - i.e., with no link to frequentist probabilities - which are insufficient for safe control. Recently, conformal prediction has emerged as a statistical framework capable of providing distribution-free probabilistic guarantees on test-time prediction accuracy. While current conformal methods treat robots as Euclidean points, many systems have non-Euclidean configurations, e.g., some mobile robots have SE(2). In this work, we rigorously analyze configuration errors using Lie groups, extending previous Euclidean Space theoretical guarantees to SE(2). Our experiments on a simulated JetBot, and on a real MBot, suggest that by considering the configuration space's structure, our symmetry-informed nonconformity score leads to more volume-efficient prediction regions which represent the underlying uncertainty better than existing approaches.

Equivariant Neural Networks for General Linear Symmetries on Lie Algebras

Encoding symmetries is a powerful inductive bias for improving the generalization of deep neural networks. However, most existing equivariant models are limited to simple symmetries like rotations, failing to address the broader class of general linear transformations, GL(n), that appear in many scientific domains. We introduce Reductive Lie Neurons (ReLNs), a novel neural network architecture exactly equivariant to these general linear symmetries. ReLNs are designed to operate directly on a wide range of structured inputs, including general n-by-n matrices. ReLNs introduce a novel adjoint-invariant bilinear layer to achieve stable equivariance for both Lie-algebraic features and matrix-valued inputs, without requiring redesign for each subgroup. This architecture overcomes the limitations of prior equivariant networks that only apply to compact groups or simple vector data. We validate ReLNs' versatility across a spectrum of tasks: they outperform existing methods on algebraic benchmarks with sl(3) and sp(4) symmetries and achieve competitive results on a Lorentz-equivariant particle physics task. In 3D drone state estimation with geometric uncertainty, ReLNs jointly process velocities and covariances, yielding significant improvements in trajectory accuracy. ReLNs provide a practical and general framework for learning with broad linear group symmetries on Lie algebras and matrix-valued data. Project page: https://reductive-lie-neuron.github.io/

Super LiDAR Reflectance for Robotic Perception

Conventionally, human intuition often defines vision as a modality of passive optical sensing, while active optical sensing is typically regarded as measuring rather than the default modality of vision. However, the situation now changes: sensor technologies and data-driven paradigms empower active optical sensing to redefine the boundaries of vision, ushering in a new era of active vision. Light Detection and Ranging (LiDAR) sensors capture reflectance from object surfaces, which remains invariant under varying illumination conditions, showcasing significant potential in robotic perception tasks such as detection, recognition, segmentation, and Simultaneous Localization and Mapping (SLAM). These applications often rely on dense sensing capabilities, typically achieved by high-resolution, expensive LiDAR sensors. A key challenge with low-cost LiDARs lies in the sparsity of scan data, which limits their broader application. To address this limitation, this work introduces an innovative framework for generating dense LiDAR reflectance images from sparse data, leveraging the unique attributes of non-repeating scanning LiDAR (NRS-LiDAR). We tackle critical challenges, including reflectance calibration and the transition from static to dynamic scene domains, facilitating the reconstruction of dense reflectance images in real-world settings. The key contributions of this work include a comprehensive dataset for LiDAR reflectance image densification, a densification network tailored for NRS-LiDAR, and diverse applications such as loop closure and traffic lane detection using the generated dense reflectance images.

Imaginative World Modeling with Scene Graphs for Embodied Agent Navigation

Semantic navigation requires an agent to navigate toward a specified target in an unseen environment. Employing an imaginative navigation strategy that predicts future scenes before taking action, can empower the agent to find target faster. Inspired by this idea, we propose SGImagineNav, a novel imaginative navigation framework that leverages symbolic world modeling to proactively build a global environmental representation. SGImagineNav maintains an evolving hierarchical scene graphs and uses large language models to predict and explore unseen parts of the environment. While existing methods solely relying on past observations, this imaginative scene graph provides richer semantic context, enabling the agent to proactively estimate target locations. Building upon this, SGImagineNav adopts an adaptive navigation strategy that exploits semantic shortcuts when promising and explores unknown areas otherwise to gather additional context. This strategy continuously expands the known environment and accumulates valuable semantic contexts, ultimately guiding the agent toward the target. SGImagineNav is evaluated in both real-world scenarios and simulation benchmarks. SGImagineNav consistently outperforms previous methods, improving success rate to 65.4 and 66.8 on HM3D and HSSD, and demonstrating cross-floor and cross-room navigation in real-world environments, underscoring its effectiveness and generalizability.

Registration beyond Points: General Affine Subspace Alignment via Geodesic Distance on Grassmann Manifold

Affine Grassmannian has been favored for expressing proximity between lines and planes due to its theoretical exactness in measuring distances among features. Despite this advantage, the existing method can only measure the proximity without yielding the distance as an explicit function of rigid body transformation. Thus, an optimizable distance function on the manifold has remained underdeveloped, stifling its application in registration problems. This paper is the first to explicitly derive an optimizable cost function between two Grassmannian features with respect to rigid body transformation ($\mathbf{R}$ and $\mathbf{t}$). Specifically, we present a rigorous mathematical proof demonstrating that the bases of high-dimensional linear subspaces can serve as an explicit representation of the cost. Finally, we propose an optimizable cost function based on the transformed bases that can be applied to the registration problem of any affine subspace. Compared to vector parameter-based approaches, our method is able to find a globally optimal solution by directly minimizing the geodesic distance which is agnostic to representation ambiguity. The resulting cost function and its extension to the inlier-set maximizing \ac{BnB} solver have been demonstrated to improve the convergence of existing solutions or outperform them in various computer vision tasks. The code is available on https://github.com/joomeok/GrassmannRegistration.

GPS-DRIFT: Marine Surface Robot Localization using IMU-GPS Fusion and Invariant Filtering

This paper presents an extension of the DRIFT invariant state estimation framework, enabling robust fusion of GPS and IMU data for accurate pose and heading estimation. Originally developed for testing and usage on a marine autonomous surface vehicle (ASV), this approach can also be utilized on other mobile systems. Building upon the original proprioceptive only DRIFT algorithm, we develop a symmetry-preserving sensor fusion pipeline utilizing the invariant extended Kalman filter (InEKF) to integrate global position updates from GPS directly into the correction step. Crucially, we introduce a novel heading correction mechanism that leverages GPS course-over-ground information in conjunction with IMU orientation, overcoming the inherent unobservability of yaw in dead-reckoning. The system was deployed and validated on a customized Blue Robotics BlueBoat, but the methodological focus is on the algorithmic approach to fusing exteroceptive and proprioceptive sensors for drift-free localization and reliable orientation estimation. This work provides an open source solution for accurate yaw observation and localization in challenging or GPS-degraded conditions, and lays the groundwork for future experimental and comparative studies.