# chaotic control

Chaotic control is a relatively new spaceflight technique which, like gravity assist, enables interplanetary missions to be flown with much smaller amounts of propellant and therefore at lower cost. First used by NASA in the 1980s to maneuver ICE (International Cometary Explorer), it involves exploiting the gravitational properties of the unstable Lagrangian points, L1, L2, and L3, for navigational purposes.

The basic idea of chaotic control is that a tiny nudge to a spacecraft at one of the unstable Lagrangian points, involving the expenditure of very little fuel, can result in a significant change in the spacecraft's trajectory. Following NASA's initial trial-and-error approach with ICE, the mathematics of chaotic control began to be developed properly in 1990, starting with some work of Edward Ott, Celso Gregobi, and Jim Yorke of the University of Maryland. Their method, known after their initials as the OGY technique, involves calculating a sequence of small maneuvers that will produce the desired overall effect. NASA exploited this more refined version of chaotic control on the Genesis mission to catch specimens of the solar wind. At the end of its two-and-a-half-year sample collection, Genesis did not have enough fuel for a direct return to Earth. Instead, it was first sent on a long detour to the L2 point, outside Earth's orbit around the Sun, from which it was brought back very economically to the Earth-Moon L1 point and from there, by way of a few, cheap chaotic orbits of the Moon, into a stable Earth orbit. Finally, its cargo capsule will be released, to parachute down onto the salt flats of Utah in August 2003.

### Reference

1. Taubes, G. "The Art of the Orbit." *Science* 283 (1999): 620-22.