Analytic determination of an optimal human motion

A three-rigid-links model is constructed for a gymnast performing a kip-up maneuver on a horizontal bar. Equations of motion with constrained, voluntary torques at hip and shoulder joints give a well-posed optimal control problem when boundary conditions and a performance criterion for the maneuver are specified. An approximate numerical solution for the minimum-time performance of this nonlinear process is obtained by the method of steepest descent. Results of the computations are compared with experimental results. Difficulties of solving human motion problems by existing numerical methods are pointed out.Notation element 1 arm system - element 2 head-neck-torso system - element 3 leg system - angle between element 1 and vertical - angle between elements 1 and 2 - angle between elements 2 and 3 - O ₁ hinge axis between elements 1 and 2 - O ₂ hinge axis between elements 2 and 3 - O ₃ hinge axis representing fist-horizontal-bar system - T ₁ torque between elements 1 and 2 - T ₂ torque between elements 2 and 3 - l ₁ distance betweenO ₃ andO ₁ - l ₂ distance betweenO ₁ andO ₂ - I _i moment of inertia of elementi about its CG about an axis perpendicular to the plane of motion,i = 1,2,3 - I _r moment of inertia of the horizontal bar about its longitudinal axis - m _i mass of elementi, i=1,2,3 - r ₁ distance between O₃ and CG of element 1 - r ₂ distance between O₁ and CG of element 2 - r ₃ distance between O₁ and CG of element 3 - g acceleration due to gravity This research was partially supported by the National Science Foundation through Grants Nos. GK-4944 and GK-37024x.Appreciation of Dr. Tom Bullock for discussion on numerical optimization techniques and Mr. Tom Boone for his services as an experimental test subject is gratefully acknowledged.