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.

Optimization in simulations of human movement planning

“…First, there always exist feasible solutions to (10), and also at least one optimal solution. Further, it is easy to show that each optimal solution (local or global) of (10) always satisfies the Karush-Kuhn-Tucker ('KKT') conditions.…”

“…This means that the objective function in (10) and (11) can be interpreted as the (non-smooth) merit function:…”

“…the longest or highest jump, given a set of capacities in a specific system. A second optimization setting is the best fit procedures, where a movement of the chosen model either should resemble a recorded movement [6][7][8], or should be used to deduce the neural motor control strategy [9,10].…”

Activation dynamics in the optimization of targeted movements

“…A wider concept, an 'inverse optimization', is used in e.g., [20,21], where recorded movements are used in order to deduce the neural motor control strategy, parameterizing the cost function.…”

Temporal finite element formulation of optimal control in mechanisms

“…A wider concept, an inverse optimization, is used in e.g. [25,26], where recorded movements are used in order to deduce the neural motor control strategy, parameterizing the objective function.…”