arXiv subjects

Jan Mikula

Publications and source records attributed to Jan Mikula.

4 recordsLinked to original sources

arXiv2025

Anytime Metaheuristic Framework for Global Route Optimization in Expected-Time Mobile Search

Expected-time mobile search (ETS) is a fundamental robotics task where a mobile sensor navigates an environment to minimize the expected time required to locate a hidden object. Global route optimization for ETS in static 2D continuous environments remains largely underexplored due to the intractability of objective evaluation, stemming from the continuous nature of the environment and the interplay of motion and visibility constraints. Prior work has addressed this through partial discretization, leading to discrete-sensing formulations tackled via utility-greedy heuristics. Others have taken an indirect approach by heuristically approximating the objective using minimum latency problems on fixed graphs, enabling global route optimization via efficient metaheuristics. This paper builds on and significantly extends the latter by introducing Milaps (Minimum latency problems), a model-based solution framework for ETS. Milaps integrates novel auxiliary objectives and adapts a recent anytime metaheuristic for the traveling deliveryman problem, chosen for its strong performance under tight runtime constraints. Evaluations on a novel large-scale dataset demonstrate superior trade-offs between solution quality and runtime compared to state-of-the-art baselines. The best-performing strategy rapidly generates a preliminary solution, assigns static weights to sensing configurations, and optimizes global costs metaheuristically. Additionally, a qualitative study highlights the framework's flexibility across diverse scenarios.

cs.RO↗

arXiv2025

Optimizing Mesh to Improve the Triangular Expansion Algorithm for Computing Visibility Regions

This paper addresses the problem of improving the query performance of the triangular expansion algorithm (TEA) for computing visibility regions by finding the most advantageous instance of the triangular mesh, the preprocessing structure. The TEA recursively traverses the mesh while keeping track of the visible region, the set of all points visible from a query point in a polygonal world. We show that the measured query time is approximately proportional to the number of triangle edge expansions during the mesh traversal. We propose a new type of triangular mesh that minimizes the expected number of expansions assuming the query points are drawn from a known probability distribution. We design a heuristic method to approximate the mesh and evaluate the approach on many challenging instances that resemble real-world environments. The proposed mesh improves the mean query times by 12-16% compared to the reference constrained Delaunay triangulation. The approach is suitable to boost offline applications that require computing millions of queries without addressing the preprocessing time. The implementation is publicly available to replicate our experiments and serve the community.

cs.CG↗

arXiv2024

Omnidirectional Sensor Placement: A Large-Scale Computational Study and Novel Hybrid Accelerated-Refinement Heuristics

This paper studies the omnidirectional sensor-placement problem (OSPP), which involves placing static sensors in a continuous 2D environment to achieve a user-defined coverage requirement while minimizing sensor count. The problem is motivated by applications in mobile robotics, particularly for optimizing visibility-based route planning tasks such as environment inspection, target search, and region patrolling. We focus on omnidirectional visibility models, which eliminate sensor orientation constraints while remaining relevant to real-world sensing technologies like LiDAR, 360-degree cameras, and multi-sensor arrays. Three key models are considered: unlimited visibility, limited-range visibility to reflect physical or application-specific constraints, and localization-uncertainty visibility to account for sensor placement uncertainty in robotics. Our first contribution is a large-scale computational study comparing classical convex-partitioning and sampling-based heuristics for the OSPP, analyzing their trade-off between runtime efficiency and solution quality. Our second contribution is a new class of hybrid accelerated-refinement (HAR) heuristics, which combine and refine outputs from multiple sensor-placement methods while incorporating preprocessing techniques to accelerate refinement. Results demonstrate that HAR heuristics significantly outperform traditional methods, achieving the lowest sensor counts and improving the runtime of sampling-based approaches. Additionally, we adapt a specific HAR heuristic to the localization-uncertainty visibility model, showing that it achieves the required coverage for small to moderate localization uncertainty. Future work may apply HAR to visibility-based route planning tasks or explore novel sensor-placement approaches to achieve formal coverage guarantees under uncertainty.

cs.RO↗

arXiv2024

T\v{r}iVis: Versatile, Reliable, and High-Performance Tool for Computing Visibility in Polygonal Environments

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.

cs.RO↗