Links For Further Research

There's been further research since this paper was originally written in 1987, most of which I haven't kept up with. My thanks to Reid Sweatman for providing the following comments and links. (Reid Sweatman currently works for Multi-Edit Software. He may be contacted at

Curious side note: this problem is susceptible to fairly easy solution by neural net, and as such, is an example problem in several texts, sometimes slightly modified to balance the stick upright, rather than oscillate it. Of course, this removes a number of exponential terms from the differential solution, but, strangely enough, that doesn't make much difference to the neural net solution, beyond requiring extra feed-forward layers.

I believe a genetic algorithm might also be capable of handling the problem, so long as it was updated often enough to keep the stick reasonably within the solution space. However, I've never seen that done, or tried it myself. I do neural nets more frequently than genetic algorithms, but have a friend who has done several exceedingly complex game AIs (essentially very complex routing schedulers) who maintains it's possible. I suppose of equal interest is the frequency with which AIs are simulated by physical systems, like constrained springs.

I've got two favorite books on neural nets:

For a web site, you can't do much better for a launch point than Steve Woodcock’s site,. Lots of good stuff there. Lots of really funny things (check the "You know your game is in trouble when..." page), and links to just about everything in AI. Although the site is dedicated to AI in computer games, Steve works for Raytheon doing, last I talked to him, missle guidance systems. Before his brief sojourn into gaming, he wrote AI code for Star Wars (not the movie one). I think he still co-chairs the AI roundtable discussions at the annual Computer Game Developers' conference in San Jose, as well as a more academic one just up the road about two weeks later. Those roundtables are the thing I always like best about the GDC, although I haven't been since 2000. Hey, where else can you get a few hours of what's essentially free consulting with guys like Steve and Neil Kirby from Lucent on your game AI? Hashed out a messy flocking/steering infantry AI with Steve, then the same for training a neural net flight simulation pilot later that night with Neil. Keeps the old brain cells in motion.

—Reid Sweatman (

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