Research Papers

Dynamic Optimization of Human Running With Analytical Gradients

[+] Author and Article Information
Hyun-Joon Chung, Jasbir S. Arora, Karim Abdel-Malek

Center for Computer-Aided Design (CCAD),
The University of Iowa,
Iowa City, IA 52242

Yujiang Xiang

Assistant Professor
Department of Mechanical Engineering,
University of Alaska Fairbanks,
Fairbanks, AK, 99775
e-mail: yujxiang@gmail.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 25, 2013; final manuscript received May 9, 2014; published online January 12, 2015. Assoc. Editor: Jozsef Kovecses.

J. Comput. Nonlinear Dynam 10(2), 021006 (Mar 01, 2015) (18 pages) Paper No: CND-13-1228; doi: 10.1115/1.4027672 History: Received September 25, 2013; Revised May 09, 2014; Online January 12, 2015

The optimization-based dynamic prediction of 3D human running motion is studied in this paper. A predictive dynamics method is used to formulate the running problem, and normal running is formulated as a symmetric and cyclic motion. Recursive Lagrangian dynamics with analytical gradients for all the constraints and objective function are incorporated in the optimization process. The dynamic effort is used as the performance measure, and the impulse at the foot strike is also included in the performance measure. The joint angle profiles and joint torque profiles are calculated for the full-body human model, and the ground reaction force (GRF) is determined. Several cause-and-effect cases are studied, and the formulation for upper-body yawing motion is proposed and simulated. Simulation results from this methodology show good correlation with experimental data obtained from human subjects and the existing literature.

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Fig. 3

Global degree of freedom descriptions

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Fig. 4

Branch descriptions in body frame

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Fig. 5

Local coordinate system of human model based on DH method

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Fig. 6

Description of ZMP

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Fig. 8

Model of running phase

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Fig. 9

Description of foot model: (a) side view and (b) top view

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Fig. 10

Foot support phase and support region: (a) foot strike, (b) midsupport, (c) toe off

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Fig. 11

Key points for the foot location constraint

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Fig. 12

Points for ground penetration constraint: (a) foot-strike instant, (b) midsupport phase, (c) toe-off phase

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Fig. 13

Points for ground penetration constraint: (a) foot-strike instant, (b) midsupport phase (c) toe-off phase; the green points are in contact and the red points are not in contact

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Fig. 14

Six points of foot for ground penetration constraint

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Fig. 15

Description of initial rear heel position

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Fig. 21

Running simulations: (a) without armor, (b) with armor

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Fig. 20

Armor attached at legs

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Fig. 19

Vertical ground reaction force

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Fig. 18

Knee joint torque profiles

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Fig. 17

Running snapshot (3.0 m/s)

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Fig. 28

Snapshot with upper-body motion formulation

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Fig. 29

Snapshot with upper-body motion formulation—top view

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Fig. 30

Knee joint torque profiles with upper-body motion

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Fig. 31

Vertical ground reaction force with upper-body motion

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Fig. 32

Running validation—six determinants

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Fig. 22

Knee joint angles with and without armor

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Fig. 23

Knee joint torque with and without armor

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Fig. 24

Vertical ground reaction force with and without armor

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Fig. 25

Knee joint torque in different running speeds

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Fig. 26

Vertical ground reaction force in different running speeds

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Fig. 27

Arm–leg coupling motion




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