Computer Optimization of a Minimal Biped Model Discovers Walking and Running (PDF preprint)

Manoj Srinivasan and Andy Ruina, Nature Magazine,
(online version dated Sept 11, 2005), 5 January 2006, Vol 439, Pages 72-75 doi:10.1038/nature04113
Get the idea in this nice news story
Also glance at a talk given at Cornell (Feb 06) and Michigan (May 06) on related topics (PDF)

Here is the same idea, partially derived numerically.

"Idealized walking and running gaits minimize work." pdf
Srinivasan, Manoj, and Andy Ruina.  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 463.2086 (2007): 2429-2446.

See also these more expansive papers on related topics

Why walk and run: energetic costs and energetic optimality in simple mechanics-based models of a bipedal animal (PDF)

Manoj Srinivasan's 2006 Cornell PhD thesis

Collisional model of the energetic cost Between Leg Sequencing in Walking and Galloping (PDF)

Ruina, A., Bertram, J.E.A., Srinivasan, M., Journal of Theoretical Biology,
Volume 237, Issue 2, Pages 170-192, November 21, 2005.
A collisional model of the energetic cost of support work qualitatively explains leg sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition.

For More Information on Related See the Author's Web Sites

YouTube: Pendular Running
VIDEO: Pendular Running (MOV) (16MB)
Screen Shot of Video
This video shows walking, running, pendular running, and level walking.
View in slow motion to see better. These were made by Deborah King of Ithaca college.