Optimizing Motion-Constrained Pathfinding

High-quality motion planning can be quite expensive to perform, yet is critical for many video games. As a result, many approximations are employed to reduce costs. Common approximations include pathfinding on a grid or on a navigation mesh instead of in a real-valued world. As a result, the paths that are found are not immediately appropriate for use, and often require post-processing, such as smoothing. An alternate approach is to incorporate pathfinding constraints directly into A* search. This approach is expensive and so it hasn’t been widely applied in games. In this paper we analyze the complexity of planning with complex motion constraints and suggest optimizations which make such planning feasible for use in modern games. We propose the use of two ideas, abstract perimeter heuristics and intermediate search truncation, which can reduce the cost of search by an order of magnitude or more. Introduction and Background In this paper we are concerned with the study of pathfinding with more realistic motion models. As pathfinding is often quite expensive, especially considering the need for many different units to successively plan, the costs for planning with more realistic motion models is often considered too expensive for practical use. We analyze three motion models and propose a variety of optimizations that can be applied to make planning with more realistic motion models feasible. There are a number of approaches that are currently used for pathfinding in games. For many games that can afford the memory costs, grids are attractive, as they are easy to compute and update. But, grids can have large memory overheads, and so a variety of other data structures have been used for pathfinding such as navigation meshes (Tozour 2002) or waypoint graphs. Navigation meshes and waypoint graphs are essentially an abstract representation of the underlying state space which reduce the cost of pathfinding. When grids are used, similar abstractions are often created as well (Sturtevant 2007). In general, paths are planned in the abstract state space, and then refined into paths in the actual state space. These abstract representations do not adequately represent motion constraints which may be present with vehicular Copyright c © 2009, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. or creature movement. Thus, once an abstract path (eg one that follows obstacles constraints but not motion constraints) has been created, it must be transformed into a path which can be followed (and animated) by a character in the game. A comprehensive introduction to pathfinding with more realistic motion constraints was described by Pinter (2001). This article has many practical suggestions which are necessary for building a good pathfinding system, but also contains many ad-hoc techniques which require engineering by hand. Our goal here is not to duplicate this work, but to complement it with the suggestion of additional techniques as well as a full study of these approaches. Some of the ideas suggested by Pinter have been subsumed by the recent θ∗ (Theta*) algorithm (Nash et al. 2007). θ∗ attempts to do smoothing as part of the planning process instead of as a post-processing step. While this reduces some of the need for post-processing, it does not eliminate it completely. For instance, θ∗ does not take motion constraints into account during planning. However, it is possible that θ∗ can be combined with the ideas discussed here for even more efficient search. Researchers in robotics have also been concerned with motion-constrained pathfinding, as motion planners must generate plans that can be executed by a robot. Thus, some of the heuristic-building ideas here overlap both with work in robotics (Knepper and Kelly 2006; Likhachev and Ferguson 2009) as well as problems like road layout (Mandow and de-la Cruz 2004), which has similar constrains. This work makes the following contributions: We perform a systematic study of search with motion constraints, demonstrating that this search is not only feasible, but that it can be, given a proper heuristic, no more expensive than normal A* search. This is made possible first by breaking long paths into shorter paths using abstraction and refinement. The shorter paths can then be solved cheaply due to abstract perimeter heuristics and intermediate search truncation. These techniques will be described in more detail in the following sections.