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|Title:||Application of Optimal Control Theory to Human Movement Problems: The Golf Swing|
|Author(s):||Campbell, Kevin Robert|
|Department / Program:||Physical Education|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||The purpose of this study was to investigate the applicability of optimal control theory to complex human motion problems using simplified models. A three link model of the golf swing was developed identifying the upper torso, the left arm, and the club as the segments. The torques acting on the torso, left shoulder and wrist were identified as the system controls. An inverse dynamic analysis using two dimensional cinematographic techniques was employed to examine the validity of the model. The results suggested that the model was useful and provided added insight into the mechanics of the golf swing.
To completely formulate the optimization problems it was necessary to determine the constraints on the system and derive the performance indicies. An isokinetic strength testing device was used to obtain position, velocity, and torque data for the shoulder and wrist. This data was subsequently input to a stepwise multiple regression analysis which produced predictor equations for maximum torques as functions of the states of the system. It was hypothesized that the magnitude of the upper torso torque would be limited through the system kinematics, therefore, no constraints were directly imposed on the upper torso torque. To study the application of the optimal control theory to human motion it was desired to examine both minimization and maximization problems. For the maximization problem the clubhead velocity at impact was identified as the performance measure to be optimized. The mechanical work done by the system in driving the ball 250 yards was selected as the performance index to be minimized. State variable constraints were imposed on: the final position of the system, the angles between adjacent segments, the height of the clubhead, and the final velocity (for the minimization only).
The variational formulation of the optimal control theory was employed to establish the necessary conditions for optimality. The system constraints were appended to the performance indicies by using penalty functions which discouraged violations. The inclusion of control variable constraints required an additional necessary condition, Pontryagin's maximum/minimum principle. Finally, steepest ascent/descent algorithms were employed to solve the non-linear two-point boundary value problems.
The optimal solutions were found to provide valuable insight into the mechanics of the golf drive and demonstrated where improvements could be made. It was concluded that the application of optimal control theory to movement studies is a useful method to investigate the biomechanics of complex human motion problems.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984.
|Date Available in IDEALS:||2014-12-16|