Subject: ScienceDirect - Journal of Biomechanics : An optimal control model for maximum-height human jumping
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Volume 23, Issue 12, 1990, Pages 1185-1198 |
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doi:10.1016/0021-9290(90)90376-E
Copyright © 1990 Published by Elsevier Science Ltd.
An optimal control model for maximum-height human jumping
Marcus G. Pandy b, a, †, Felix E. Zajac b, a, Eunsup Sim c and William S. Levine c
a Mechanical Engineering Department, Design Division, Stanford University, Stanford, CA 94305-4201, U.S.A.
b Rehabilitation Research and Development Center (153), Veterans' Affairs Medical Center, Palo Alto, CA 94304-1200, U.S.A.
c Electrical Engineering Department, University of Maryland, College Park, MD 20742, U.S.A.
Received 14 May 1990. Available online 9 April 2004.
Abstract
To understand how intermuscular control, inertial interactions among body segments, and musculotendon dynamics coordinate human movement, we have chosen to study maximum-height jumping. Because this activity presents a relatively unambiguous performance criterion, it fits well into the framework of optimal control theory. The human body is modeled as a four-segment, planar, articulated linkage, with adjacent links joined together by frictionless revolutes. Driving the skeletal system are eight musculotendon actuators, each muscle modeled as a three-element, lumped-parameter entity, in series with tendon. Tendon is assumed to be elastic, and its properties are defined by a stress-strain curve. The mechanical behavior of muscle is described by a Hill-type contractile element, including both series and parallel elasticity. Driving the musculotendon model is a first-order representation of excitation-contraction (activation) dynamics. The optimal control problem is to maximize the height reached by the center of mass of the body subject to body-segmental, musculotendon, and activation dynamics, a zero vertical ground reaction force at lift-off, and constraints which limit the magnitude of the incoming neural control signals to lie between zero (no excitation) and one (full excitation). A computational solution to this problem was found on the basis of a Mayne-Polak dynamic optimization algorithm. Qualitative comparisons between the predictions of the model and previously reported experimental findings indicate that the model reproduces the major features of a maximum-height squat jump (i.e. limb-segmental angular displacements, vertical and horizontal ground reaction forces, sequence of muscular activity, overall jump height, and final lift-off time).
† Present address: Dept. of Kinesiology and Health Education, The University of Texas at Austin, Austin, TX 78712, U.S.A.
Volume 23, Issue 12, 1990, Pages 1185-1198 |
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