This paper addresses the movement and placement of mobile agents to establish a communication network in initially unknown environments. We cast the problem in a computational-geometric framework by relating the coverage problem and line-of-sight constraints to the Cooperative Guard Art Gallery Problem, and introduce its partially observable variant, the Partially Observable Cooperative Guard Art Gallery Problem (POCGAGP). We then present two algorithms that solve POCGAGP: CADENCE, a centralized planner that incrementally selects 270 degree corners at which to deploy agents, and DADENCE, a decentralized scheme that coordinates agents using local information and lightweight messaging. Both approaches operate under partial observability and target simultaneous coverage and connectivity. We evaluate the methods in simulation across 1,500 test cases of varied size and structure, demonstrating consistent success in forming connected networks while covering and exploring unknown space. These results highlight the value of geometric abstractions for communication-driven exploration and show that decentralized policies are competitive with centralized performance while retaining scalability.

Passive deformation due to compliance is a commonly used benefit of soft robots, providing opportunities to achieve robust actuation with few active degrees of freedom. Soft growing robots in particular have shown promise in navigation of unstructured environments due to their passive deformation. If their collisions and subsequent deformations can be better understood, soft robots could be used to understand the structure of the environment from direct tactile measurements. In this work, we propose the use of soft growing robots as mapping and exploration tools. We do this by first characterizing collision behavior during discrete turns, then leveraging this model to develop a geometry-based simulator that models robot trajectories in 2D environments. Finally, we demonstrate the model and simulator validity by mapping unknown environments using Monte Carlo sampling to estimate the optimal next deployment given current knowledge. Over both uniform and non-uniform environments, this selection method rapidly approaches ideal actions, showing the potential for soft growing robots in unstructured environment exploration and mapping.

T o overcome the limitations of traditional approaches, we introduce Navigable Exemplar-Based Dispatch Coverage (NavEX), a novel dispatch coverage framework that combines exemplar-clustering with obstacle-aware and traversability-aware shortest distances, offering a deployment framework based on submodular optimization. NavEX provides a unified approach to solve two critical coverage tasks: (a) fair-access deployment, aiming to provide equitable service by minimizing agent-target distances, and (b) hotspot deployment, prioritizing high-density target regions. A key feature of NavEX is the use of exemplar-clustering for the coverage utility measure, which provides the flexibility to employ non-Euclidean distance metrics that do not necessarily conform to the triangle inequality. This allows NavEX to incorporate visibility graphs for shortest-path computation in environments with planar obstacles, and traversability-aware RRT for complex, rugged terrains. By leveraging submodular optimization, the NavEX framework enables efficient, near-optimal solutions with provable performance guarantees for multi-agent deployment in realistic and complex settings, as demonstrated by our simulations.

-- Navigation Among Movable Obstacles (NAMO) poses a challenge for traditional path-planning methods when obstacles block the path, requiring push actions to reach the goal. We propose a framework that enables movability-aware planning to overcome this challenge without relying on explicit obstacle placement. A physics engine is adopted to simulate the interaction result of the rollouts with the environment, and generate trajectories that minimize contact force. In qualitative and quantitative experiments, SVG-MPPI outperforms the existing paradigm that uses only binary movability for planning, achieving higher success rates with reduced cumulative contact forces. Our code is available at: https://github.com/tud-amr/SVG-MPPI I. INTRODUCTION A fundamental ability of autonomous robots is to navigate towards a goal while avoiding collisions along the way [1]. However, in complex and cluttered environments, such as domestic settings where obstacles like chairs and boxes may obstruct the path to the goal, finding collision-free paths often becomes impractical. In such cases, traditional navigation methods often fail and Navigation Amongst Movable Obstacles (NAMO) becomes essential.

Time series analysis has become crucial in various fields, from engineering and finance to healthcare and social sciences. In this paper, we present a comprehensive review and evaluation of time series embedding methods for effective representations in machine learning and deep learning models. We introduce a taxonomy of embedding techniques, categorizing them based on their theoretical foundations and application contexts. Unlike previous surveys, our work provides a quantitative evaluation of representative methods from each category by assessing their performance on downstream classification tasks across diverse real-world datasets. Our experimental results demonstrate that the performance of embedding methods varies significantly depending on the dataset and classification algorithm used, highlighting the importance of careful model selection and extensive experimentation for specific applications, including engineering systems. To facilitate further research and practical applications, we provide an open-source code repository implementing these embedding methods. This study contributes to the field by offering a systematic comparison of time series embedding techniques, guiding practitioners in selecting appropriate methods for their specific applications, and providing a foundation for future advancements in time series analysis.

Visibility is a fundamental concept in computational geometry, with numerous applications in surveillance, robotics, and games. This software paper presents T\v{r}iVis, a C++ library developed by the authors for computing numerous visibility-related queries in highly complex polygonal environments. Adapting the triangular expansion algorithm, T\v{r}iVis stands out as a versatile, high-performance, more reliable and easy-to-use alternative to current solutions that is also free of heavy dependencies. Through evaluation on a challenging dataset, T\v{r}iVis has been benchmarked against existing visibility libraries. The results demonstrate that T\v{r}iVis outperforms the competing solutions by at least an order of magnitude in query times, while exhibiting more reliable runtime behavior. T\v{r}iVis is freely available for private, research, and institutional use at https://github.com/janmikulacz/trivis.

This paper introduces a novel Graph Neural Network (GNN) architecture for time series classification, based on visibility graph representations. Traditional time series classification methods often struggle with high computational complexity and inadequate capture of spatio-temporal dynamics. By representing time series as visibility graphs, it is possible to encode both spatial and temporal dependencies inherent to time series data, while being computationally efficient. Our architecture is fully modular, enabling flexible experimentation with different models and representations. We employ directed visibility graphs encoded with in-degree and PageRank features to improve the representation of time series, ensuring efficient computation while enhancing the model's ability to capture long-range dependencies in the data. We show the robustness and generalization capability of the proposed architecture across a diverse set of classification tasks and against a traditional model. Our work represents a significant advancement in the application of GNNs for time series analysis, offering a powerful and flexible framework for future research and practical implementations.

The capability to learn latent representations plays a key role in the effectiveness of recent machine learning methods. An active frontier in representation learning is understanding representations for combinatorial structures which may not admit well-behaved local neighborhoods or distance functions. For example, for polygons, slightly perturbing vertex locations might lead to significant changes in their combinatorial structure (expressed as their triangulation or visibility graph) and may even lead to invalid polygons. In this paper, we investigate representations to capture the underlying combinatorial structures of polygons. Specifically, we study the open problem of Visibility Reconstruction: Given a visibility graph G, construct a polygon P whose visibility graph is G. Visibility Reconstruction belongs to the Existential Theory of Reals ( R) complexity class (which lies between NP and P-SPACE). Currently, reconstruction algorithms are available only for specific polygon classes. Establishing the hardness of the general problem is open. We introduce VisDiff, a novel diffusion-based approach to reconstruct a polygon from its given visibility graph G. Our method first estimates the signed distance function (SDF) of P from G. Afterwards, it extracts ordered vertex locations that have the pairwise visibility relationship given by the edges of G. Our main insight is that going through the SDF significantly improves learning for reconstruction. In order to train VisDiff, we make two main contributions: (1) We design novel loss components for computing the visibility in a differentiable manner and (2) create a carefully curated dataset. We use this dataset to benchmark our method and achieve 21% improvement in F1-Score over standard methods. We also demonstrate effective generalization to out-of-distribution polygon types and show that learning a generative model allows us to sample the set of polygons with a given visibility graph. Finally, we extend our method to the related combinatorial problem of reconstruction from a triangulation.

This paper presents a novel method for real-time 3D navigation in large-scale, complex environments using a hierarchical 3D visibility graph (V-graph). The proposed algorithm addresses the computational challenges of V-graph construction and shortest path search on the graph simultaneously. By introducing hierarchical 3D V-graph construction with heuristic visibility update, the 3D V-graph is constructed in O(K*n^2logn) time, which guarantees real-time performance. The proposed iterative divide-and-conquer path search method can achieve near-optimal path solutions within the constraints of real-time operations. The algorithm ensures efficient 3D V-graph construction and path search. Extensive simulated and real-world environments validated that our algorithm reduces the travel time by 42%, achieves up to 24.8% higher trajectory efficiency, and runs faster than most benchmarks by orders of magnitude in complex environments. The code and developed simulator have been open-sourced to facilitate future research.

The moving target traveling salesman problem with obstacles (MT-TSP-O) is a generalization of the traveling salesman problem (TSP) where, as its name suggests, the targets are moving. A solution to the MT-TSP-O is a trajectory that visits each moving target during a certain time window(s), and this trajectory avoids stationary obstacles. We assume each target moves at a constant velocity during each of its time windows. The agent has a speed limit, and this speed limit is no smaller than any target's speed. This paper presents the first complete algorithm for finding feasible solutions to the MT-TSP-O. Our algorithm builds a tree where the nodes are agent trajectories intercepting a unique sequence of targets within a unique sequence of time windows. We generate each of a parent node's children by extending the parent's trajectory to intercept one additional target, each child corresponding to a different choice of target and time window. This extension consists of planning a trajectory from the parent trajectory's final point in space-time to a moving target. To solve this point-to-moving-target subproblem, we define a novel generalization of a visibility graph called a moving target visibility graph (MTVG). Our overall algorithm is called MTVG-TSP. To validate MTVG-TSP, we test it on 570 instances with up to 30 targets. We implement a baseline method that samples trajectories of targets into points, based on prior work on special cases of the MT-TSP-O. MTVG-TSP finds feasible solutions in all cases where the baseline does, and when the sum of the targets' time window lengths enters a critical range, MTVG-TSP finds a feasible solution with up to 38 times less computation time.