Optimal Impedance Control for Task Achievement in the Presence of Signal-Dependent Noise

Abstract

There is an infinity of impedance parameter values, and thus different co-contraction levels, that can produce similar movement kinematics from which the CNS must select one. Although signal-dependent noise (SDN) predicts larger motor-command variability during higher co-contraction, the relationship between impedance and task performance is not theoretically obvious and thus was examined here. Subjects made goal-directed, single-joint elbow movements to either move naturally to different target sizes or voluntarily co-contract at different levels. Stiffness was estimated as the weighted summation of rectified EMG signals through the index of muscle co-contraction around the joint (IMCJ) proposed previously. When subjects made movements to targets of different sizes, IMCJ increased with the accuracy requirements, leading to reduced endpoint deviations. Therefore without the need for great accuracy, subjects accepted worse performance with lower co-contraction. When subjects were asked to increase co-contraction, the variability of EMG and torque both increased, suggesting that noise in the neuromotor command increased with muscle activation. In contrast, the final positional error was smallest for the highest IMCJ level. Although co-contraction increases the motor-command noise, the effect of this noise on the task performance is reduced. Subjects were able to regulate their impedance and control endpoint variance as the task requirements changed, and they did not voluntarily select the high impedance that generated the minimum endpoint error. These data contradict predictions of the SDN-based theory, which postulates minimization of only endpoint variance and thus require its revision.

Task Performance is Prioritized Over Energy Reduction

“…This matches with previous work [31][32][33], where subjects performed a positioning task with elbow rotations and used increased stiffness as the target circle size decreased. In general, this finding of increased stiffness with greater accuracy requirement correlated with Hogan's theory of robotic manipulation and impedance control [18].…”

Motor Memory and Local Minimization of Error and Effort, Not Global Optimization, Determine Motor Behavior

“…However, tasks used in motor control experiments such as reaching movements (Morasso 1981;Osu et al 2003;Uno et al 1989), force field learning (Burdet et al 2001;Shadmehr and Mussa-Ivaldi 1994), and movements through via-points (Flash and Hogan 1985;Uno et al 1989) are limited in their ability to differentiate effort from error minimization (O'Sullivan et al 2009): Noise and thus error generally increase monotonically with motor command (Jones et al 2002;Osu et al 2004), such that error and effort are in one-to-one relationship. These tasks thus feature a single optimum of error and effort in which optimization has been computed using linear optimal control (Todorov and Jordan 2002) or nonlinear optimization with constraints (Biess et al 2007) or by gradient descent (Franklin et al 2008).…”

Movement curvature planning through force field internal models

“…Another class of reaching models are stochastic models that take into account the noise inherent to the motor system. It has been consistently observed that the standard deviation of neuromotor commands increases with its mean (Sutton and Sykes 1967;Schmidt et al 1979;Clamman 1969;Matthews 1996;St-Amant et al 1998;Clancy and Hogan 1999;Osu et al 2004). In line with this evidence, it was suggested that the brain minimizes the variance of the final arm position in the presence of such signal-dependent motor noise (Harris and Wolpert 1998;Hamilton et al 2002).…”