The complete optimization of a human motion

Abstract

The dynamical behavior of a musculo-skeletal link system, consisting of the right leg of a human subject, is simulated by a mathematical model which contains two control parameters for each of the five muscle groups involved. A time-optimal problem in which the right-hand end point of the state trajectory is variable is formulated and an optimization performed. The computational procedure is based on an algorithm of differential dynamic programming. The optimal model solution is then compared with the performance of the living system. It is found that any motion of the biosystem which deviates from the predicted optimal one takes a longer time to complete and is thus not optimal. Moreover, the trajectories and control functions of near-optimal motions as measured on the living system were indeed found to be very close to the theoretical optimal process thus again confirming the optimality of the model solution. In addition, the model predicts biologically highly significant phenomena such as the occurence of a stretch reflex, the incompatibility of speed and accuracy in a genetically non-determined biomotion, etc. Certain characteristic changes in the motion pattern occuring when the subject became fatigued are analyzed, and a possible explanation for this phenomenon is suggested. It is believed that this is the first time that an optimization of this kind has been performed successfully. Possible practical applications of the findings of this study are discussed.