Optimal control of joint torques using direct collocation to maximize ball carry distance in a golf swing
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Optimal control of joint torques using direct collocation to maximize ball carry distance in a golf swing Colin Brown1 · William McNally1 · John McPhee1
Received: 5 August 2019 / Accepted: 12 March 2020 © Springer Nature B.V. 2020
Abstract Forward dynamics golf swing simulations are important to gain insight into how a golfer should swing a particular club and which design improvements should be considered by golf club manufacturers. A new method of optimizing a four degree-of-freedom (DoF) biomechanical golfer model swinging a flexible shaft with a rigid clubhead was developed using a direct orthogonal collocation approach. The kinematic and kinetic results of the simulation confirm previous findings on optimal joint angle trajectories, shaft deflection patterns, and joint torque profiles in a golf swing. This optimization approach is a promising development in biomechanics research, and future work will implement this method in three-dimensional swing models that have been shown to have higher robustness and fidelity. Keywords Golf swing · Forward dynamics · Optimal control · Direct collocation
1 Introduction The human body can be described as a multibody system, and multibody biomechanics is an evolved area of research in sports engineering and rehabilitation, particularly in golf. Golf was recently cited by National Allied Golf Associations to have an economic impact of over $19 billion per year in Canada alone [1]. Research in improving golf club design is of great interest to the industry, as well as improving biomechanical models of golf swings. By modeling the golf swing, insights can be made into how the golfer should swing a particular club and which improvements should be considered in golf club design. Over the last 40 years, models of the golf swing have been developed for use in inverse dynamic simulations, which require input experimental data, and forward dynamic simulations, which require the input of unoptimized or optimized torques [2]. One of the first golf swing models produced to gain insight into the biomechanics of the swing was the double pendulum by Cochran and Stobbs [3], in which two links represented the arms and the club. This study found that a well-coordinated swing could be produced with a passive wrist
B C. Brown
[email protected]
1
University of Waterloo, 200 University Ave. W, Waterloo, ON N2L 3G1, Canada
C. Brown et al.
joint, as the club could be accelerated naturally by the centrifugal force acting on its center of gravity. The validity of the double pendulum model was verified in a comprehensive forward dynamic analysis by Jorgensen [4], in which the Lagrangian method was used to generate the differential equations of motion. Jorgensen generated solutions to these differential equations by inputing a constant torque at the shoulder and wrist and also found that a passive or low active torque produced a natural downswing with high clubhead velocity. This effect was also confirmed in a forward dynamic study of the double pendulum model by Lampsa, in which joint
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