Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

Terekhov, Alexander V.; Zatsiorsky, Vladimir M.

doi:10.1007/s00422-011-0421-2

Cited by 24 publications

(37 citation statements)

References 78 publications

(102 reference statements)

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“…A. The first-order coefficients are not presented here because they cannot be identified unambiguously (for details see Terekhov, Pesin, et al, 2010; Terekhov & Zatsiorsky, 2011). …”

Section: Resultsmentioning

confidence: 99%

“…A brief description of the method is provided in Appendix A. A detailed description of the ANIO approach is available in (Terekhov, Pesin, et al, 2010; Terekhov & Zatsiorsky, 2011), a more brief description is also provided in (Park et al, 2010; Park, Sun, et al, 2011; Park, Zatsiorsky, & Latash, 2011; Park, Singh, et al, 2012; Niu, Latash, & Zatsiorsky, 2012; Niu, Terekhov, Latash, & Zatsiorsky, 2012). …”

Section: Methodsmentioning

confidence: 99%

“…Here we present the Uniqueness Theorem for the case of four variables and two constraints. The general case can be found in (Terekhov, Pesin, et al, 2010; Terekhov & Zatsiorsky, 2011). …”

Section: Uniqueness Theoremmentioning

confidence: 99%

“…A priori it is difficult to say which of them is more likely to be used in stabilization and/or optimization. To address this question we will use two complementary methods – the analytical inverse optimization (ANIO; Terekhov, Pesin, Niu, Latash, & Zatsiorsky, 2010; Terekhov & Zatsiorsky, 2011) and uncontrolled manifold analysis (UCM; Scholz & Schöner, 1999; Latash, Scholz, & Schöner, 2002). …”

Section: Introductionmentioning

confidence: 99%

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Optimization and Variability of Motor Behavior in Multifinger Tasks: What Variables Does the Brain Use?

Martin

Terekhov

Latash

et al. 2013

Journal of Motor Behavior

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The neural control of movement has been described using different sets of elemental variables. Two possible sets of elemental variables have been suggested for finger pressing tasks: the forces of individual fingers and the finger commands (also called “finger modes” or “central commands”). In this study we analyze which of the two sets of the elemental variables is more likely used in the optimization of the finger force sharing and which set is used for the stabilization of performance. We used two recently developed techniques – the analytical inverse optimization (ANIO) and the uncontrolled manifold (UCM) analysis – to evaluate each set of elemental variables with respect to both aspects of performance. The results of the UCM analysis favored the finger commands as the elemental variables used for performance stabilization, while ANIO worked equally well on both sets of elemental variables. A simple scheme is suggested as to how the CNS could optimize a cost function dependent on the finger forces, but for the sake of facilitation of the feed-forward control it substitutes the original cost function by a cost function, which is convenient to optimize in the space of finger commands.

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“…A. The first-order coefficients are not presented here because they cannot be identified unambiguously (for details see Terekhov, Pesin, et al, 2010; Terekhov & Zatsiorsky, 2011). …”

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…Here we present the Uniqueness Theorem for the case of four variables and two constraints. The general case can be found in (Terekhov, Pesin, et al, 2010; Terekhov & Zatsiorsky, 2011). …”

Section: Uniqueness Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization and Variability of Motor Behavior in Multifinger Tasks: What Variables Does the Brain Use?

Martin

Terekhov

Latash

et al. 2013

Journal of Motor Behavior

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“…These are extreme forms of the types of changes used in the present experiments that force us to consider how a theory of optimal control can be tested experimentally. If a body of experimental data is used to infer or even compute performance criteria (Terekhov and Zatsiorsky, 2011), those same data cannot be used to test the hypothesis that performance is optimal. Changing the musculoskeletal system as was done in these experiments provides an opportunity for such tests that, in the event, consistently failed.…”

Section: Does Optimal Control Operate Over Longer Time Periods Than Amentioning

confidence: 99%

Muscle Coordination Is Habitual Rather than Optimal

Rugy¹,

Loeb²,

Carroll³

2012

J. Neurosci.

201

163

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When sharing load among multiple muscles, humans appear to select an optimal pattern of activation that minimizes costs such as the effort or variability of movement. How the nervous system achieves this behavior, however, is unknown. Here we show that contrary to predictions from optimal control theory, habitual muscle activation patterns are surprisingly robust to changes in limb biomechanics. We first developed a method to simulate joint forces in real time from electromyographic recordings of the wrist muscles. When the model was altered to simulate the effects of paralyzing a muscle, the subjects simply increased the recruitment of all muscles to accomplish the task, rather than recruiting only the useful muscles. When the model was altered to make the force output of one muscle unusually noisy, the subjects again persisted in recruiting all muscles rather than eliminating the noisy one. Such habitual coordination patterns were also unaffected by real modifications of biomechanics produced by selectively damaging a muscle without affecting sensory feedback. Subjects naturally use different patterns of muscle contraction to produce the same forces in different pronation-supination postures, but when the simulation was based on a posture different from the actual posture, the recruitment patterns tended to agree with the actual rather than the simulated posture. The results appear inconsistent with computation of motor programs by an optimal controller in the brain. Rather, the brain may learn and recall command programs that result in muscle coordination patterns generated by lower sensorimotor circuitry that are functionally "good-enough."

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Optimality versus variability: effect of fatigue in multi-finger redundant tasks

et al. 2011

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We used two methods to address two aspects of multi-finger synergies and their changes after fatigue of the index finger. Analytical inverse optimization (ANIO) was used to identify cost functions and corresponding spaces of optimal solutions over a broad range of task parameters. Analysis within the uncontrolled manifold (UCM) hypothesis was used to quantify co-variation of finger forces across repetitive trials that helped reduce variability of (stabilized) performance variables produced by all the fingers together. Subjects produced steady-state levels of total force and moment of force simultaneously as accurately as possible by pressing with the four fingers of the right hand. Both before- and during-fatigue, the subjects performed single trials for many force-moment combinations covering a broad range; the data were used for the ANIO analysis. Multiple trials were performed at two force-moment combinations; these data were used for analysis within the UCM hypothesis. Fatigue was induced by 1-min maximal voluntary contraction (MVC) exercise by the index finger. Principal component (PC) analysis showed that the first two PCs explained over 90% of the total variance both before and during fatigue. Hence, it was concluded that experimental observations formed a plane in the four-dimensional finger force space both before and during fatigue conditions. Based on this conclusion, quadratic cost functions with linear terms were assumed. The dihedral angle between the plane of optimal solutions and the plane of experimental observations was very small (a few degrees); it increased during fatigue. There was an increase with fatigue of the coefficient at the quadratic term for the index finger force balanced by a drop in the coefficients for the ring and middle fingers. Within each finger pair (index-middle and ring-little), the contribution of the “central” fingers to moment production increased during fatigue. An index of antagonist moment production dropped with fatigue. Fatigue led to higher co-variation indices during pronation tasks (index finger is an agonist) but opposite effects during supination tasks. The results suggest that adaptive changes in co-variation indices that help stabilize performance may depend on the role of the fatigued element, agonist or antagonist.

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Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

Cited by 24 publications

References 78 publications

Optimization and Variability of Motor Behavior in Multifinger Tasks: What Variables Does the Brain Use?

Optimization and Variability of Motor Behavior in Multifinger Tasks: What Variables Does the Brain Use?

Muscle Coordination Is Habitual Rather than Optimal

Optimality versus variability: effect of fatigue in multi-finger redundant tasks

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