GAME STATE MANAGEMENT OF MMOGS OVER GRID/CLOUD TECHNOLOGIES

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Influence-based motion planning algorithms for games

Publication . Amador, Gonçalo Nuno Paiva; Gomes, Abel João Padrão

In games, motion planning has to do with the motion of non-player characters (NPCs) from one place to another in the game world. In today’s video games there are two major approaches for motion planning, namely, path-finding and influence fields. Path-finding algorithms deal with the problem of finding a path in a weighted search graph, whose nodes represent locations of a game world, and in which the connections among nodes (edges) have an associated cost/weight. In video games, the most employed pathfinders are A* and its variants, namely, Dijkstra’s algorithm and best-first search. As further will be addressed in detail, the former pathfinders cannot simulate or mimic the natural movement of humans, which is usually without discontinuities, i.e., smooth, even when there are sudden changes in direction. Additionally, there is another problem with the former pathfinders, namely, their lack of adaptivity when changes to the environment occur. Therefore, such pathfinders are not adaptive, i.e., they cannot handle with search graph modifications during path search as a consequence of an event that happened in the game (e.g., when a bridge connecting two graph nodes is destroyed by a missile). On the other hand, influence fields are a motion planning technique that does not suffer from the two problems above, i.e., they can provide smooth human-like movement and are adaptive. As seen further ahead, we will resort to a differentiable real function to represent the influence field associated with a game map as a summation of functions equally differentiable, each associated to a repeller or an attractor. The differentiability ensures that there are no abrupt changes in the influence field, consequently, the movement of any NPC will be smooth, regardless if the NPC walks in the game world in the growing sense of the function or not. Thus, it is enough to have a spline curve that interpolates the path nodes to mimic the smooth human-like movement. Moreover, given the nature of the differentiable real functions that represent an influence field, the removal or addition of a repeller/attractor (as the result of the destruction or the construction of a bridge) does not alter the differentiability of the global function associated with the map of a game. That is to say that, an influence field is adaptive, in that it adapts to changes in the virtual world during the gameplay. In spite of being able to solve the two problems of pathfinders, an influence field may still have local extrema, which, if reached, will prevent an NPC from fleeing from that location. The local extremum problem never occurs in pathfinders because the goal node is the sole global minimum of the cost function. Therefore, by conjugating the cost function with the influence function, the NPC will never be detained at any local extremum of the influence function, because the minimization of the cost function ensures that it will always walk in the direction of the goal node. That is, the conjugation between pathfinders and influence fields results in movement planning algorithms which, simultaneously, solve the problems of pathfinders and influence fields. As will be demonstrated throughout this thesis, it is possible to combine influence fields and A*, Dijkstra’s, and best-first search algorithms, so that we get hybrid algorithms that are adaptive. Besides, these algorithms can generate smooth paths that resemble the ones traveled by human beings, though path smoothness is not the main focus of this thesis. Nevertheless, it is not always possible to perform this conjugation between influence fields and pathfinders; an example of such a pathfinder is the fringe search algorithm, as well as the new pathfinder which is proposed in this thesis, designated as best neighbor first search.

2017-06Doctoral thesis

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