An analytical approach to the problem of inverse optimization with additive objective functions

An application to human prehension

Alexander V. Terekhov, Yakov B. Pesin, Xun Niu, Mark Latash, Vladimir M. Zatsiorsky

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.

Original language English (US) 423-453 31 Journal of Mathematical Biology 61 3 https://doi.org/10.1007/s00285-009-0306-3 Published - Jan 1 2010

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Inverse Optimization
system optimization
Objective function
Fingers
Torque
Sharing
torque
Muscles
Inverse Problem
methodology
Experimental Data
Optimization Problem
muscles
Grasping
Human
Linear Constraints
Muscle
Uniqueness
Predict

All Science Journal Classification (ASJC) codes

• Modeling and Simulation
• Agricultural and Biological Sciences (miscellaneous)
• Applied Mathematics

Cite this

title = "An analytical approach to the problem of inverse optimization with additive objective functions: An application to human prehension",
abstract = "We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.",
author = "Terekhov, {Alexander V.} and Pesin, {Yakov B.} and Xun Niu and Mark Latash and Zatsiorsky, {Vladimir M.}",
year = "2010",
month = "1",
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doi = "10.1007/s00285-009-0306-3",
language = "English (US)",
volume = "61",
pages = "423--453",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Verlag",
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}

An analytical approach to the problem of inverse optimization with additive objective functions : An application to human prehension. / Terekhov, Alexander V.; Pesin, Yakov B.; Niu, Xun; Latash, Mark; Zatsiorsky, Vladimir M.

In: Journal of Mathematical Biology, Vol. 61, No. 3, 01.01.2010, p. 423-453.

Research output: Contribution to journalArticle

TY - JOUR

T1 - An analytical approach to the problem of inverse optimization with additive objective functions

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AU - Pesin, Yakov B.

AU - Niu, Xun

AU - Latash, Mark

AU - Zatsiorsky, Vladimir M.

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N2 - We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.

AB - We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.

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