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Technical Brief

Time-Domain Optimal Experimental Design in Human Seated Postural Control Testing

[+] Author and Article Information
M. Cody Priess

Department of Mechanical Engineering,
MSU Center for Orthopedic Research (MSUCOR),
Michigan State University,
East Lansing, MI 48824
e-mail: priessma@msu.edu

Jongeun Choi

Department of Mechanical Engineering,
Department of Electrical and Computer Engineering,
MSUCOR,
Michigan State University,
East Lansing, MI 48824
e-mail: jchoi@egr.msu.edu

Clark Radcliffe

Department of Mechanical Engineering,
MSUCOR,
Michigan State University,
East Lansing, MI 48824
e-mail: radcliffe@egr.msu.edu

John M. Popovich, Jr.

Department of Osteopathic Surgical Specialties,
MSUCOR,
Michigan State University,
East Lansing, MI 48824
e-mail: popovi16@msu.edu

Jacek Cholewicki

Department of Osteopathic Surgical Specialties,
MSUCOR,
Michigan State University,
East Lansing, MI 48824
e-mail: cholewic@msu.edu

N. Peter Reeves

Department of Osteopathic Surgical Specialties,
MSUCOR,
Michigan State University,
East Lansing, MI 48824
e-mail: reevesn@msu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 14, 2014; final manuscript received October 13, 2014; published online December 10, 2014. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 137(5), 054501 (May 01, 2015) (7 pages) Paper No: DS-14-1069; doi: 10.1115/1.4028850 History: Received February 14, 2014; Revised October 13, 2014; Online December 10, 2014

We are developing a series of systems science-based clinical tools that will assist in modeling, diagnosing, and quantifying postural control deficits in human subjects. In line with this goal, we have designed and constructed a seated balance device and associated experimental task for identification of the human seated postural control system. In this work, we present a quadratic programming (QP) technique for optimizing a time-domain experimental input signal for this device. The goal of this optimization is to maximize the information present in the experiment, and therefore its ability to produce accurate estimates of several desired seated postural control parameters. To achieve this, we formulate the problem as a nonconvex QP and attempt to locally maximize a measure (T-optimality condition) of the experiment’s Fisher information matrix (FIM) under several constraints. These constraints include limits on the input amplitude, physiological output magnitude, subject control amplitude, and input signal autocorrelation. Because the autocorrelation constraint takes the form of a quadratic constraint (QC), we replace it with a conservative linear relaxation about a nominal point, which is iteratively updated during the course of optimization. We show that this iterative descent algorithm generates a convergent suboptimal solution that guarantees monotonic nonincreasing of the cost function value while satisfying all constraints during iterations. Finally, we present successful experimental results using an optimized input sequence.

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References

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Figures

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Fig. 1

Subject on the backdrivable robot

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Fig. 2

Simplified mechanical diagram of the seated balance experiment

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Fig. 3

Block diagram of the seated balance experiment

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Fig. 4

The upper plot shows the optimal input sequence u. The lower plot shows the change in the objective function J(u;θ∧0) with increasing iteration i.

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Fig. 5

Simulated results using the optimal input u. The upper plot shows the simulated angles α1 and α2 versus time, along with their bounds. The center plot shows the differential angle α˜ versus time along with its bounds. The bottom plot shows the optimal input signal autocorrelation Ruu⋆ along with its bounds, and the original signal autocorrelation Ruu for comparison. The constraints on uh were not active during simulation.

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