Hierarchical path-finding for Navigation Meshes (HNA*)

Path-finding can become an important bottleneck as both the size of the virtual environments and the number of agents navigating them increase. It is important to develop techniques that can be efficiently applied to any environment independently of its abstract representation. In this paper we present a hierarchical NavMesh representation to speed up path-finding. Hierarchical path-finding (HPA*) has been successfully applied to regular grids, but there is a need to extend the benefits of this method to polygonal navigation meshes. As opposed to regular grids, navigation meshes offer representations with higher accuracy regarding the underlying geometry, while containing a smaller number of cells. Therefore, we present a bottom-up method to create a hierarchical representation based on a multilevel k-way partitioning algorithm (MLkP), annotated with sub-paths that can be accessed online by our Hierarchical NavMesh Path-finding algorithm (HNA*). The algorithm benefits from searching in graphs with a much smaller number of cells, thus performing up to 7.7 times faster than traditional A¿ over the initial NavMesh. We present results of HNA* over a variety of scenarios and discuss the benefits of the algorithm together with areas for improvement.Peer ReviewedPostprint (author's final draft

Dynamic real-time hierarchical heuristic search for pathfinding.

Movement of Units in Real-Time Strategy (RTS) Games is a non-trivial and challenging task mainly due to three factors which are constraints on CPU and memory usage, dynamicity of the game world, and concurrency. In this paper, we are focusing on finding a novel solution for solving the pathfinding problem in RTS Games for the units which are controlled by the computer. The novel solution combines two AI Planning approaches: Hierarchical Task Network (HTN) and Real-Time Heuristic Search (RHS). In the proposed solution, HTNs are used as a dynamic abstraction of the game map while RHS works as planning engine with interleaving of plan making and action executions. The article provides algorithmic details of the model while the empirical details of the model are obtained by using a real-time strategy game engine called ORTS (Open Real-time Strategy). The implementation of the model and its evaluation methods are in progress however the results of the automatic HTN creation are obtained for a small scale game map

Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces.Comment: 86 pages, 15 figure

A survey of behavioral-level partitioning systems

Many approaches have been developed to partition a system's behavioral description before a structural implementation is synthesized. We highlight the foundations and motivations for behavioral partitioning. We survey behavioral partitioning approaches, discussing abstraction levels, goals, major steps, and key assumptions in each

Depicting urban boundaries from a mobility network of spatial interactions: A case study of Great Britain with geo-located Twitter data

Existing urban boundaries are usually defined by government agencies for administrative, economic, and political purposes. Defining urban boundaries that consider socio-economic relationships and citizen commute patterns is important for many aspects of urban and regional planning. In this paper, we describe a method to delineate urban boundaries based upon human interactions with physical space inferred from social media. Specifically, we depicted the urban boundaries of Great Britain using a mobility network of Twitter user spatial interactions, which was inferred from over 69 million geo-located tweets. We define the non-administrative anthropographic boundaries in a hierarchical fashion based on different physical movement ranges of users derived from the collective mobility patterns of Twitter users in Great Britain. The results of strongly connected urban regions in the form of communities in the network space yield geographically cohesive, non-overlapping urban areas, which provide a clear delineation of the non-administrative anthropographic urban boundaries of Great Britain. The method was applied to both national (Great Britain) and municipal scales (the London metropolis). While our results corresponded well with the administrative boundaries, many unexpected and interesting boundaries were identified. Importantly, as the depicted urban boundaries exhibited a strong instance of spatial proximity, we employed a gravity model to understand the distance decay effects in shaping the delineated urban boundaries. The model explains how geographical distances found in the mobility patterns affect the interaction intensity among different non-administrative anthropographic urban areas, which provides new insights into human spatial interactions with urban space.Comment: 32 pages, 7 figures, International Journal of Geographic Information Scienc

Topomap: Topological Mapping and Navigation Based on Visual SLAM Maps

Visual robot navigation within large-scale, semi-structured environments deals with various challenges such as computation intensive path planning algorithms or insufficient knowledge about traversable spaces. Moreover, many state-of-the-art navigation approaches only operate locally instead of gaining a more conceptual understanding of the planning objective. This limits the complexity of tasks a robot can accomplish and makes it harder to deal with uncertainties that are present in the context of real-time robotics applications. In this work, we present Topomap, a framework which simplifies the navigation task by providing a map to the robot which is tailored for path planning use. This novel approach transforms a sparse feature-based map from a visual Simultaneous Localization And Mapping (SLAM) system into a three-dimensional topological map. This is done in two steps. First, we extract occupancy information directly from the noisy sparse point cloud. Then, we create a set of convex free-space clusters, which are the vertices of the topological map. We show that this representation improves the efficiency of global planning, and we provide a complete derivation of our algorithm. Planning experiments on real world datasets demonstrate that we achieve similar performance as RRT* with significantly lower computation times and storage requirements. Finally, we test our algorithm on a mobile robotic platform to prove its advantages.Comment: 8 page