Robots are expected to serve as intelligent assistants, helping humans with everyday household organization. A central challenge in this setting is the task of object placement, which requires reasoning about both semantic preferences (e.g., common-sense object relations) and geometric feasibility (e.g., collision avoidance). We present GOPLA, a hierarchical framework that learns generalizable object placement from augmented human demonstrations. A multi-modal large language model translates human instructions and visual inputs into structured plans that specify pairwise object relationships. These plans are then converted into 3D affordance maps with geometric common sense by a spatial mapper, while a diffusion-based planner generates placement poses guided by test-time costs, considering multi-plan distributions and collision avoidance. To overcome data scarcity, we introduce a scalable pipeline that expands human placement demonstrations into diverse synthetic training data. Extensive experiments show that our approach improves placement success rates by 30.04 percentage points over the runner-up, evaluated on positioning accuracy and physical plausibility, demonstrating strong generalization across a wide range of real-world robotic placement scenarios.

Abstract-- Advances in open-vocabulary semantic mapping and object navigation have enabled robots to perform an informed search of their environment for an arbitrary object. However, such zero-shot object navigation is typically designed for simple queries with an object name like "television" or "blue rug". Here, we consider more complex free-text queries with spatial relationships, such as "find the remote on the table" while still leveraging robustness of a semantic map. We present DIV-Nav, a real-time navigation system that efficiently addresses this problem through a series of relaxations: i) Decomposing natural language instructions with complex spatial constraints into simpler object-level queries on a semantic map, ii) computing the Intersection of individual semantic belief maps to identify regions where all objects co-exist, and iii) V alidating the discovered objects against the original, complex spatial constrains via a L VLM. We further investigate how to adapt the frontier exploration objectives of online semantic mapping to such spatial search queries to more effectively guide the search process. Robots operating in human environments must interpret natural language commands that go beyond simple object identification. While a command like "find a chair" requires handling simple object classes only, real-world search instructions often specify spatial relationships: "go to the chair next to the desk," "find the towel in the bathroom," or "get the book on the nightstand."

PySensors is a Python package for selecting and placing a sparse set of sensors for reconstruction and classification tasks. In this major update to PySensors, we introduce spatially constrained sensor placement capabilities, allowing users to enforce constraints such as maximum or exact sensor counts in specific regions, incorporate predetermined sensor locations, and maintain minimum distances between sensors. We extend functionality to support custom basis inputs, enabling integration of any data-driven or spectral basis. We also propose a thermodynamic approach that goes beyond a single "optimal" sensor configuration and maps the complete landscape of sensor interactions induced by the training data. This comprehensive view facilitates integration with external selection criteria and enables assessment of sensor replacement impacts. The new optimization technique also accounts for over- and under-sampling of sensors, utilizing a regularized least squares approach for robust reconstruction. Additionally, we incorporate noise-induced uncertainty quantification of the estimation error and provide visual uncertainty heat maps to guide deployment decisions. To highlight these additions, we provide a brief description of the mathematical algorithms and theory underlying these new capabilities. We demonstrate the usage of new features with illustrative code examples and include practical advice for implementation across various application domains. Finally, we outline a roadmap of potential extensions to further enhance the package's functionality and applicability to emerging sensing challenges.

Spatial reasoning remains a challenge for Large Language Models (LLMs), which struggle with spatial data retrieval and reasoning. We propose Spatial Retrieval-Augmented Generation (Spatial-RAG), a framework that extends RAG to spatial tasks by integrating sparse spatial retrieval (spatial databases) and dense semantic retrieval (LLM-based similarity). A multi-objective ranking strategy balances spatial constraints and semantic relevance, while an LLM-guided generator ensures coherent responses. Experiments on a real-world tourism dataset show that Spatial-RAG significantly improves spatial question answering, bridging the gap between LLMs and spatial intelligence.

The development of general robotic systems capable of manipulating in unstructured environments is a significant challenge. While Vision-Language Models(VLM) excel in high-level commonsense reasoning, they lack the fine-grained 3D spatial understanding required for precise manipulation tasks. Fine-tuning VLM on robotic datasets to create Vision-Language-Action Models(VLA) is a potential solution, but it is hindered by high data collection costs and generalization issues. To address these challenges, we propose a novel object-centric representation that bridges the gap between VLM's high-level reasoning and the low-level precision required for manipulation. Our key insight is that an object's canonical space, defined by its functional affordances, provides a structured and semantically meaningful way to describe interaction primitives, such as points and directions. These primitives act as a bridge, translating VLM's commonsense reasoning into actionable 3D spatial constraints. In this context, we introduce a dual closed-loop, open-vocabulary robotic manipulation system: one loop for high-level planning through primitive resampling, interaction rendering and VLM checking, and another for low-level execution via 6D pose tracking. This design ensures robust, real-time control without requiring VLM fine-tuning. Extensive experiments demonstrate strong zero-shot generalization across diverse robotic manipulation tasks, highlighting the potential of this approach for automating large-scale simulation data generation.

In this paper, we present a novel approach for learning bimanual manipulation actions from human demonstration by extracting spatial constraints between affordance regions, termed affordance constraints, of the objects involved. Affordance regions are defined as object parts that provide interaction possibilities to an agent. For example, the bottom of a bottle affords the object to be placed on a surface, while its spout affords the contained liquid to be poured. We propose a novel approach to learn changes of affordance constraints in human demonstration to construct spatial bimanual action models representing object interactions. To exploit the information encoded in these spatial bimanual action models, we formulate an optimization problem to determine optimal object configurations across multiple execution keypoints while taking into account the initial scene, the learned affordance constraints, and the robot's kinematics. We evaluate the approach in simulation with two example tasks (pouring drinks and rolling dough) and compare three different definitions of affordance constraints: (i) component-wise distances between affordance regions in Cartesian space, (ii) component-wise distances between affordance regions in cylindrical space, and (iii) degrees of satisfaction of manually defined symbolic spatial affordance constraints.

This study investigates the potential of Large Language Models (LLMs) for reconstructing and constructing the physical world solely based on textual knowledge. It explores the impact of model performance on spatial understanding abilities. To enhance the comprehension of geometric and spatial relationships in the complex physical world, the study introduces a set of geometric conventions and develops a workflow based on multi-layer graphs and multi-agent system frameworks. It examines how LLMs achieve multi-step and multi-objective geometric inference in a spatial environment using multi-layer graphs under unified geometric conventions. Additionally, the study employs a genetic algorithm, inspired by large-scale model knowledge, to solve geometric constraint problems. In summary, this work innovatively explores the feasibility of using text-based LLMs as physical world builders and designs a workflow to enhance their capabilities.

This article presents a three-dimensional nonlinear trajectory tracking control strategy for unmanned aerial vehicles (UAVs) in the presence of spatial constraints. As opposed to many existing control strategies, which do not consider spatial constraints, the proposed strategy considers spatial constraints on each degree of freedom movement of the UAV. Such consideration makes the design appealing for many practical applications, such as pipeline inspection, boundary tracking, etc. The proposed design accounts for the limited information about the inertia matrix, thereby affirming its inherent robustness against unmodeled dynamics and other imperfections. We rigorously show that the UAV will converge to its desired path by maintaining bounded position, orientation, and linear and angular speeds. Finally, we demonstrate the effectiveness of the proposed strategy through various numerical simulations.

Close and precise placement of irregularly shaped objects requires a skilled robotic system. Particularly challenging is the manipulation of objects that have sensitive top surfaces and a fixed set of neighbors. To avoid damaging the surface, they have to be grasped from the side, and during placement, their neighbor relations have to be maintained. In this work, we train a reinforcement learning agent that generates smooth end-effector motions to place objects as close as possible next to each other. During the placement, our agent considers neighbor constraints defined in a given layout of the objects while trying to avoid collisions. Our approach learns to place compact object assemblies without the need for predefined spacing between objects as required by traditional methods. We thoroughly evaluated our approach using a two-finger gripper mounted to a robotic arm with six degrees of freedom. The results show that our agent outperforms two baseline approaches in terms of object assembly compactness, thereby reducing the needed space to place the objects according to the given neighbor constraints. On average, our approach reduces the distances between all placed objects by at least 60%, with fewer collisions at the same compactness compared to both baselines.

Despite an emerging interest in MIMO radar, the utilization of its complementary strengths in combination with optical sensors has so far been limited to far-field applications, due to the challenges that arise from mutual sensor calibration in the near field. In fact, most related approaches in the autonomous industry propose target-based calibration methods using corner reflectors that have proven to be unsuitable for the near field. In contrast, we propose a novel, joint calibration approach for optical RGB-D sensors and MIMO radars that is designed to operate in the radar's near-field range, within decimeters from the sensors. Our pipeline consists of a bespoke calibration target, allowing for automatic target detection and localization, followed by the spatial calibration of the two sensor coordinate systems through target registration. We validate our approach using two different depth sensing technologies from the optical domain. The experiments show the efficiency and accuracy of our calibration for various target displacements, as well as its robustness of our localization in terms of signal ambiguities.