Reconstruction of the Unknown Optimization Cost Functions from Experimental Recordings During Static Multi-Finger Prehension

Abstract

The goal of the research is to reconstruct the unknown cost (objective) function(s) presumably used by the neural controller for sharing the total force among individual fingers in multifinger prehension. The cost function was determined from experimental data by applying the recently developed Analytical Inverse Optimization (ANIO) method (Terekhov et al. 2010). The core of the ANIO method is the Theorem of Uniqueness that specifies conditions for unique (with some restrictions) estimation of the objective functions. In the experiment, subjects (n = 8) grasped an instrumented handle and maintained it at rest in the air with various external torques, loads, and target grasping forces applied to the object. The experimental data recorded from 80 trials showed a tendency to lie on a 2-dimensional hyperplane in the 4-dimensional finger-force space. Because the constraints in each trial were different, such a propensity is a manifestation of a neural mechanism (not the task mechanics). In agreement with the Lagrange principle for the inverse optimization, the plane of experimental observations was close to the plane resulting from the direct optimization. The latter plane was determined using the ANIO method. The unknown cost function was reconstructed successfully for each performer, as well as for the group data. The cost functions were found to be quadratic with nonzero linear terms. The cost functions obtained with the ANIO method yielded more accurate results than other optimization methods. The ANIO method has an evident potential for addressing the problem of optimization in motor control.