Memory-Efficient Abstractions for Pathfinding

From an academic perspective there has been a lot of work on using state abstraction to speed path planning. But, this work often does not directly address the needs of the game development community, specifically for mechanisms that will fit the limited memory budget of most commercial games. In this paper we bring together several related pieces of work on using abstraction for pathfinding, showing how the ideas can be implemented using a minimal amount of memory. Our techniques use about 3% additional storage to compute complete paths up to 100 times faster than A*. Introduction and Overview Pathfinding is a key task in many domains, including video games. In games in particular, computers must compute a path between two points as efficiently as possible, as there many are many other demands on the CPU, such as physics, graphics, and even additional pathfinding tasks from other units (agents). We present a new method to build automated, minimal-memory state abstractions to speed pathfinding. With just 3% additional storage, we show large reductions in computational costs. State abstractions for pathfinding have been explored by in a variety of different settings using a variety of methods for abstraction (Holte et al. 1996a; 1996b; Tozour 2003; Sturtevant & Buro 2005; Botea, Müller, & Schaeffer 2004). This paper describes in detail how state abstraction techniques can be optimized for use in games which have tight memory constraints. Specifically, this work is the product of a successful collaboration between BioWare Corp R © and our university. According to Mark Brockington, Programming Fellow for BioWare Corp R ©, “Our collaboration with the University of Alberta on this project has been successful, and we are pleased with the performance and implementation of their pathfinding research within Dragon AgeTM.” Abstraction For Pathfindingion For Pathfinding Automatic state abstractions are able to take a highresolution map of the world and automatically transform it into a smaller, more abstract map, which can be used to speed pathfinding in the actual world environment. Copyright c © 2007, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. The concept of using some sort of abstraction for pathfinding is a natural one, as humans often use abstractions to reason about the world. A long car trip does not being with minute-by-minute planning of the expected route. Instead, a general plan is composed which includes the start and goal cities and a high-level route between these cities. One may, for instance, decide whether to travel from Los Angeles to San Francisco by taking the faster but less scenic interstate or to take the scenic drive up the coast at the cost of additional time. Once this high-level decision has been made, it is up to the driver of the car to make low-level decisions such as which lane to drive in and how and when to pass other cars on the road. Once a high-level route is known, pathfinding becomes a local operation. It is sufficient to plan the next few steps leading along the high-level abstract route as they guarantee that the goal will be reached. This is an ideal feature when running in environments which tightly limit computation costs. The approach of first planning an abstract path before refining it has been considered in a variety of forms (Holte et al. 1996b; Sturtevant & Buro 2005; Botea, Müller, & Schaeffer 2004) and in a variety of domains (G.R. Jagadeesh 2002; Yang, Tenenberg, & Woods 1996). In this paper we address the issue of automatically building a state abstraction from an underlying map representation in a memory efficient manner. We then demonstrate the performance of our implementation in terms of memory used, pathfinding speed, and resulting path optimality. Efficient Abstraction Implementation We first describe how we can represent a map in a memory efficient manner, and then demonstrate how the representation can be used for pathfinding. Computing Abstract Map One common representation of a map is a simple grid, where a grid cell is the smallest unit of space that can be occupied by a single unit within the world. This is the underlying representation that BioWare Corp R © decided to use for their maps in Dragon AgeTM. In one respect this representation is efficient, as there is a simple mapping between x/y coordinates and grid cells, avoiding the memory cost of using pointers. But for large maps, the total memory usage and