5.1 How Can You Use Potential Functions for Game AI?

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5.1 How Can You Use Potential Functions for Game AI? Let's revisit the chasing and evading problem we discussed at length in Chapter 2. If you recall, we considered a few different techniques for having a computer-controlled unit chase down or evade a player-controlled unit. Those techniques included the basic chase algorithm, in which the computer-controlled unit always moved directly toward the player, and an intercept algorithm. We can use potential functions to achieve behavior similar to what we can achieve using both of those techniques. The benefit to using potential functions here is that a single function handles both chasing and evading, and we don't need all the other conditionals and control logic associated with the algorithms we presented earlier. Further, this same potential function also can handle obstacle avoidance for us. Although this is convenient, there is a price to be paid. As we'll discuss later, the potential function algorithms can be quite CPU-intensive for large numbers of interacting game units and objects. Another benefit to the potential function algorithm is that it is very simple to implement. All you have to do is calculate the force between the two units�the computer-controlled unit and the player in this case�and then apply that force to the front end of the computer-controlled unit, where it essentially acts as a steering force. The steering model here is similar to those we discussed in Chapters 2 and 4; however, in this case the force will always point along a line of action connecting the two units under consideration. This means the force can point in any direction relative to the computer-controlled unit, and not just to its left or right. By applying this force to the front end of the unit, we can get it to turn and head in the direction in which the force is pointing. By reversing the direction of this force, we can get a unit to either chase or evade as desired. Note that this steering force contributes to the propulsive force, or the thrust, of the unit, so you might see it speed up or slow down as it moves around. As you've probably guessed, the examples we'll consider throughout the remainder of this chapter use the physically simulated model that you saw in earlier chapters. In fact, we use the examples from Chapters 2, 3, and 4 with some minor modifications. As before, you can find the example programs on this book's web site (http://www.oreilly.com/catalog/ai). 5.2.1 So, What Is a Potential Function? Entire books have been written concerning potential theory as applied to all sorts of physical phenomena, and in the world of physics well-established relationships exist between potentials (as in potential energy, for example), forces, and work. However, we need not concern ourselves with too much theory to adapt the so-called Lenard-Jones potential function to game AI. What's important to us is how this function behaves and how we can take advantage of that behavior in our games. This equation is the Lenard-Jones potential function. Figure 5-1 shows three graphs of this function for different values of the exponents, n and m. Figure 5-1. Lenard-Jones potential function In physics, the Lenard-Jones potential represents the potential energy of attraction and repulsion between molecules. Here, U represents the interatomic potential energy, which is inversely proportional to the separation distance, r, between molecules. A and B are parameters, as are the exponents m and n. If we take the derivative of this potential function, we get a function representing a force. The force function produces both attractive and repulsive forces depending on the proximity of two molecules, or in our case game units, being acted upon. It's this ability to represent both attractive and repulsive forces that will benefit us; however, instead of molecules, we're going to deal with computer-controlled units. So, what can we do with this ability to attract or repel computer-controlled units? Well, first off we can use the Lenard-Jones function to cause our computer-controlled unit to be attracted to the player unit so that the computer-controlled unit will chase the player. We also can tweak the parameters of the potential function to cause the computer-controlled unit to be repelled by the player, thus causing it to evade the player. Further, we can give any number of player units various weights to cause some of them to be more attractive or repulsive to the computer-controlled units than others. This will give us a means of prioritizing targets and threats. In addition to chasing and evading, we can apply the same potential function to cause the computer-controlled units to avoid obstacles. Basically, the obstacles will repel the computer-controlled units when in close proximity, causing them to essentially steer away from them. We even can have many computer-controlled units attract one another to form a swarm. We then can apply other influences to induce the swarm to move either toward or away from a player or some other object and to avoid obstacles along the way. The cool thing about using the Lenard-Jones potential function for these tasks is that this one simple function enables us to create all sorts of seemingly intelligent behavior.

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