Daniel Harabor

Hierarchical path planning for multi-size agents in heterogeneous environments

Path planning is a central topic in games and other research areas, such as robotics. Despite this, very little research addresses problems involving agents with multiple sizes and terrain traversal capabilities. In this paper we present a new planner, Hierarchical Annotated A* (HAA*), and demonstrate how a single abstract graph can be used to plan for agents with heterogeneous sizes and terrain traversal capabilities. Through theoretical analysis and experimental evaluation we show that HAA* is able to generate near-optimal solutions to a wide range of problems while maintaining an exponential reduction in effort over low-level search. HAA* is also shown to require just a fraction of the storage space needed by the original grid map.

Optimal any-angle pathfinding in practice

Any-angle pathfinding is a fundamental problem in robotics and computer games. The goal is to find a shortest path between a pair of points on a grid map such that the path is not artificially constrained to the points of the grid. Prior research has focused on approximate online solutions. A number of exact methods exist but they all require super-linear space and pre-processing time. In this study, we describe Anya: a new and optimal any-angle pathfinding algorithm. Where other works find approximate any-angle paths by searching over individual points from the grid, Anya finds optimal paths by searching over sets of states represented as intervals. Each interval is identified on-the-fly. From each interval Anya selects a single representative point that it uses to compute an admissible cost estimate for the entire set. Anya always returns an optimal path if one exists. Moreover it does so without any offine pre-processing or the introduction of additional memory overheads. In a range of empirical comparisons we show that Anya is competitive with several recent (sub-optimal) online and pre-processing based techniques and is up to an order of magnitude faster than the most common benchmark algorithm, a grid-based implementation of A.

Fast Algorithm for Catching a Prey Quickly in Known and Partially Known Game Maps

In moving target search, the objective is to guide a hunter agent to catch a moving prey. Even though in game applications maps are always available at developing time, current approaches to moving target search do not exploit preprocessing to improve search performance. In this paper, we propose MtsCopa, an algorithm that exploits precomputed information in the form of compressed path databases (CPDs), and that is able to guide a hunter agent in both known and partially known terrain. CPDs have previously been used in standard, fixed-target pathfinding but had not been used in the context of moving target search. We evaluated MtsCopa over standard game maps. Our speed results are orders of magnitude better than current state of the art. The time per individual move is improved, which is important in real-time search scenarios, where the time available to make a move is limited. Compared to state of the art, the number of hunter moves is often better and otherwise comparable, since CPDs provide optimal moves along shortest paths. Compared to previous successful methods, such as I-ARA*, our method is simple to understand and implement. In addition, we prove MtsCopa always guides the agent to catch the prey when possible.

An integrated modelling, debugging, and visualisation environment for G12

We present G12IDE, a front-end for the G12 platform aimed at helping users create and work with constraint models in a manner independent from any underlying solver. G12IDE contains tools for writing and evaluating models using Zinc and provides a feature rich debugger for monitoring a running search process. Debugging a search, as opposed to debugging sequential code, requires concepts such as breakpoints and queries to be applied at a higher level than in standard debuggers. Our solution is to let users define special events which, once reached in a search, cause the debugger to halt and give back, possibly in a visual manner, useful information on the current state of the search. G12IDE also includes a number of visualisation tools for drawing graphs and trees, and additionally allows users to create arbitrary domain-specific visualisations, such as the drawing of a sequential plan when the constraint problem is in fact a planning problem. The inclusion of such powerful and flexible visualisation toolkit and its tight integration with the available debugging facilities is, to the best of our knowledge, completely novel.

Compressing optimal paths with run length encoding

We introduce a novel approach to Compressed Path Databases, space efficient oracles used to very quickly identify the first edge on a shortest path. Our algorithm achieves query running times on the 100 nanosecond scale, being significantly faster than state-of-the-art first-move oracles from the literature. Space consumption is competitive, due to a compression approach that rearranges rows and columns in a first-move matrix and then performs run length encoding (RLE) on the contents of the matrix. One variant of our implemented system was, by a convincing margin, the fastest entry in the 2014 Grid-Based Path Planning Competition. We give a first tractability analysis for the compression scheme used by our algorithm. We study the complexity of computing a database of minimum size for general directed and undirected graphs. We find that in both cases the problem is NP-complete. We also show that, for graphs which can be decomposed along articulation points, the problem can be decomposed into independent parts, with a corresponding reduction in its level of difficulty. In particular, this leads to simple and tractable algorithms with linear running time which yield optimal compression results for trees.

Rail Capacity Modelling with Constraint Programming

We describe a constraint programming approach to establish the coal carrying capacity of a large (2,670 km) rail network in north-eastern Australia. Computing the capacity of such a network is necessary to inform infrastructure planning and investment decisions but creating a useful model of rail operations is challenging. Analytic approaches exist but they are not very accurate. Simulation methods are common but also complex and brittle. We present an alternative where rail capacity is computed using a constraint-based optimisation model. Developed entirely in MiniZinc, our model not only captures all dynamics of interest but is also easily extended to explore a wide range of possible operational and infrastructural changes. We give results from a number of such case studies and compare against an industry-standard analytic approach.

Graph pruning and symmetry breaking on grid maps

Pathfinding systems that operate on uniform-cost grid maps are common in the AI literature and application areas such as robotics and real-time video games. Typical speed-up enhancements in such contexts include reducing the size of the search space using abstraction [Botea et al., 2004] and developing new heuristics to more accurately guide search toward the goal [Sturtevant et al., 2009]. Though effective each of these strategies has shortcomings. For example, abstraction methods usually trade optimality for speed. Meanwhile, improved heuristics usually require significant extra memory. My research proposes to speed up grid-based pathfinding by identifying and eliminating symmetric path segments from the search space. Two paths are said to be symmetric if they are identical save for the order in which the individual moves (or steps) occur. To deal with path symmetries I decompose an arbitrary grid map into a set of empty rectangles and remove from each rectangle all interior nodes and possibly some from along the perimeter. A series of macro edges are then added between selected pairs of remaining nodes in order to facilitate provably optimal traversal through each rectangle. The new algorithm, Rectangular Symmetry Reduction (RSR), can speed up A* search by up to 38 times on a range of uniform cost maps taken from the literature. In addition to being fast and optimal, RSR requires no significant extra memory and is largely orthogonal all existing speedup techniques. When compared to the state of the art, RSR often shows significant improvement across a range of benchmarks.

Compromise-free pathfinding on a navigation mesh

We want to compute geometric shortest paths in a collection of convex traversable polygons, also known as a navigation mesh. Simple to compute and easy to update, navigation meshes are widely used for pathfinding in computer games. When the mesh is static, shortest path problems can be solved exactly and very fast but only after a costly preprocessing step. When the mesh is dynamic, practitioners turn to online methods which typically compute only approximately shortest paths. In this work we present a new pathfinding algorithm which is compromise-free; i.e., it is simultaneously fast, online and optimal. Our method, Polyanya, extends and generalises Anya; a recent and related interval-based search technique developed for computing geometric shortest paths in grids. We show how that algorithm can be modified to support search over arbitrary sets of convex polygons and then evaluate its performance on a range of realistic and synthetic benchmark problems.