Some results on constrained maximal height jumps

Recently, there have been a number of attempts to apply optimal control theory to the analysis of animal and human locomotion[1,2,3]. These attempts have been Motivated by problems in prosthesis design, rehabilitation engineering, and sports and by the belief that optimal control theory is a useful technique for the elucidation of complex control problems. There is also interest, at present, in legged vehicles [4] and other anthropomorphic devices [5]. All these problems involve the dynamics of multi-segment pendula. The problems are thus nonlinear, have unusual state constraints and often involve controls that are not bang-bang. Because of this, it has generally been impossible to solve these optimization problems analytically. The exception to this has been a recent paper [6] in which the simplest case, that of making a baton "jump" as high as possible, was solved analytically.