Approximating the Stance Map of a 2 DOF Monoped Runner
Postprint version. Published in Journal of Nonlinear Science, Volume 10, Issue 5, December 2000, pages 533-568.
Publisher URL: http://dx.doi.org/10.1007/s004530010001
NOTE: At the time of publication, author Daniel Koditschek was affiliated with the University of Michigan. Currently, he is a faculty member in the Department of Electrical and Systems Engineering at the University of Pennsylvania.
We report in this paper a relatively simple means of generating closed-form approximants to the return map associated with a family of nonintegrable Hamiltonian systems. These systems arise in consideration of legged locomotion by animals and robots. The approximations proceed through the iterated application of the mean value theorem for integral operators applied to a nonintegrable perturbation of the system of interest. Both the accuracy of these approximants and their algebraic intractability grow in a relatively controlled manner.
William J. Schwind and Daniel E. Koditschek. "Approximating the Stance Map of a 2 DOF Monoped Runner" Departmental Papers (ESE) (2000).
Available at: http://works.bepress.com/daniel_koditschek/45