Research Papers

Constrained Dynamic Optimization of Sit-to-Stand Motion Driven by Bézier Curves

[+] Author and Article Information
Valerie Norman-Gerum

Systems Design Engineering,
University of Waterloo,
200 University Avenue West,
Waterloo, ON N2 L 3G1, Canada
e-mail: normangerum@uwaterloo.ca

John McPhee

ASME Fellow
Systems Design Engineering,
University of Waterloo,
200 University Avenue West,
Waterloo, ON N2 L 3G1, Canada
e-mail: mcphee@uwaterloo.ca

1Corresponding author.

Manuscript received May 28, 2018; final manuscript received August 30, 2018; published online October 23, 2018. Assoc. Editor: Guy M. Genin.

J Biomech Eng 140(12), 121011 (Oct 23, 2018) (7 pages) Paper No: BIO-18-1252; doi: 10.1115/1.4041527 History: Received May 28, 2018; Revised August 30, 2018

The purpose of this work is twofold: first, to synthesize a motion pattern imitating sit-to-stand (STS) and second, to compare the kinematics and dynamics of the resulting motion to healthy STS. Predicting STS in simulation inspired the creation of three models: a biomechanical model, a motion model, and performance criteria as a model of preference. First, the human is represented as three rigid links in the sagittal plane. This model captures aspects of joint, foot, and buttocks physiology, which makes it the most comprehensive planar model for predicting STS to date. Second, candidate STS trajectories are described geometrically by a set of Bézier curves which seem well suited to predictive biomechanical simulations. Third, with the assumption that healthy people naturally prioritize mechanical efficiency, disinclination to a motion is described as a cost function of joint torques, and for the first time, physical infeasibility including slipping and falling. This new dynamic optimization routine allows for motions of gradually increasing complexity while the model's performance is improving. Using these models and optimal control strategy together has produced gross motion patterns characteristic of healthy STS when compared with normative data from the literature.

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Fig. 1

A schematic of the three-link sagittal plane model while seated

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Fig. 2

Three Bézier curves describing a STS motion with sitting, motion and standing components

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Fig. 3

Iterative routine to determine an optimal STS

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Fig. 4

Joint torques for optimal STS from a 46 cm chair compared to joint torque strengths [18]

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Fig. 5

Optimal STS from a 46 cm chair

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Fig. 6

Evenly spaced snapshots of predicted STS

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Fig. 7

Predicted STS event timing from three chairs compared to experimental means, standard deviations, and ranges [15]

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Fig. 8

STS joint angle profiles as predicted from three chairs compared to experimental STS from a 46 cm chair [35]

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Fig. 9

Maximum flexion angular velocity of the hip

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Fig. 10

Free-body diagram of the foot



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