Action-Based Discretization for AI Search
Action-Based Discretization for AI Search
Dr. Todd W. Neller*
Department of Computer Science Gettysburg College Campus Box 402 Gettysburg, PA 17325-1486 Introduction As computer gaming reaches ever-greater heights in realism, we can expect the complexity of simulated dynamics to reach further as well. To populate such gaming environments with agents that behave intelligently, there must be some means of reasoning about the consequences of agent actions. Such ability to seek out the ramifications of various possible action sequences, commonly called “lookahead”, is found in programs that play chess, but there are special challenges that face game programmers who wish to apply AI search techniques to complex continuous dynamical systems. In particular, the game programmer must “discretize” the problem, that is, approximate the continuous problem as a discrete problem suitable for an AI search algorithm. As a concrete example, consider the problem of navigating a simulated submarine through a set of static obstacles. This continuous problem has infinite possible states (e.g. submarine position and velocity) and infinite possible trajectories. The standard approach to discretize the problem is to define a graph of “waypoints” between which the submarine can easily travel. A simple waypoint graph can be searched, but this approach is not without significant disadvantages. First, the dynamics of such approximate navigation are not realistic. It’s still common to see massive vehicles in computer games turn about instantly and maintain constant velocity at all times. When considering acceleration in agent behavior, there’s a quick realization that the notion of a “waypoint” becomes far more complex. For example, a vehicle with realistic physical limitations cannot ignore momentum and turn a tight corner at any velocity. A generalized waypoint for such a system would contain not only a position vector, but a velocity vector as well, doubling the dimensions of the
Dr. Todd W. Neller*
Department of Computer Science Gettysburg College Campus Box 402 Gettysburg, PA 17325-1486 Introduction As computer gaming reaches ever-greater heights in realism, we can expect the complexity of simulated dynamics to reach further as well. To populate such gaming environments with agents that behave intelligently, there must be some means of reasoning about the consequences of agent actions. Such ability to seek out the ramifications of various possible action sequences, commonly called “lookahead”, is found in programs that play chess, but there are special challenges that face game programmers who wish to apply AI search techniques to complex continuous dynamical systems. In particular, the game programmer must “discretize” the problem, that is, approximate the continuous problem as a discrete problem suitable for an AI search algorithm. As a concrete example, consider the problem of navigating a simulated submarine through a set of static obstacles. This continuous problem has infinite possible states (e.g. submarine position and velocity) and infinite possible trajectories. The standard approach to discretize the problem is to define a graph of “waypoints” between which the submarine can easily travel. A simple waypoint graph can be searched, but this approach is not without significant disadvantages. First, the dynamics of such approximate navigation are not realistic. It’s still common to see massive vehicles in computer games turn about instantly and maintain constant velocity at all times. When considering acceleration in agent behavior, there’s a quick realization that the notion of a “waypoint” becomes far more complex. For example, a vehicle with realistic physical limitations cannot ignore momentum and turn a tight corner at any velocity. A generalized waypoint for such a system would contain not only a position vector, but a velocity vector as well, doubling the dimensions of the
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