An optimal control model for maximum-height human jumping

• Published in: Journal of biomechanics Vol. 23; no. 12; pp. 1185 - 1198
• Main Authors: Pandy, Marcus G., Zajac, Felix E., Sim, Eunsup, Levine, William S.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1990; Elsevier Science
• Subjects: Biological and medical sciences; Biomechanical Phenomena; Fundamental and applied biological sciences. Psychology; Humans; Medical sciences; Models, Biological; Movement - physiology; Muscle Contraction - physiology; Musculoskeletal Physiological Phenomena; Radiotherapy. Instrumental treatment. Physiotherapy. Reeducation. Rehabilitation, orthophony, crenotherapy. Diet therapy and various other treatments (general aspects); Sports; Vertebrates: body movement. Posture. Locomotion. Flight. Swimming. Physical exercise. Rest. Sports; Biomechanics; Human; Dynamic system; Excitation contraction coupling; Body movement; Skeleton; Mathematical model; Striated muscle; Jumping; Modeling; Muscular coordination; Tendon; Lower limb
• ISSN: 0021-9290; 1873-2380
• DOI: 10.1016/0021-9290(90)90376-E

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).