How would you write an AI rocket pilot? This is what I've been thinking about for the past few months in my spare time. I've been reading some books and papers about optimal control, and am still learning and collecting my thoughts, and writing code. So this is just a brief update.

A few years back I did some work in this direction. The rocket is treated as a point mass that can instantaneously accelerate in any direction, with a limit on the acceleration. One control problem is: given a starting state (position and velocity) and a desired final state (position and velocity), fly the rocket between the two states in minimum time. (No gravitational acceleration in this simple scenario.)

When I wrote that last page I conjectured that the optimal route would consist of accelerating in one direction for a duration and then (if necessary) accelerating in a second direction for an additional duration. (Flying two parabolic arcs, essentially.) I based this on an attempt to extend the one-dimensional optimal control, which is to accelerate in one direction at maximum for a duration, and then potentially reverse direction and accelerate for an additional duration.

Since reading some optimal control theory I've worked out enough to realize that this is not the optimal control. The optimal control turns out to be to thrust (with maximum acceleration) in the direction of a point that is moving along a straight line. The point is moving through a "control space" and you basically normalize the vector toward it and multiply that by the maximum acceleration to get the acceleration vector. You can see how the one-dimensional case extends to this, but in the two- or three-dimensional case the rocket potentially pivots through a range of directions as it accelerates. The trick, then, is to come up with the equation of motion for the control point that results in the rocket getting from the initial state to the final state.

That's all I have for now; hopefully more to follow.

## Sunday, May 13, 2012

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