Motor equivalence and self-motion induced by different movement speeds

Abstract

This study investigated pointing movements in 3D asking two questions: (1) Is goal-directed reaching accompanied by self-motion, a component of the joint velocity vector that leaves the hand’s movement unaffected? (2) Are differences in the terminal joint configurations among different speeds of reaching motor equivalent (i.e., terminal joint configurations differ more in directions of joint space that do not produce different pointer-tip positions than in directions that do) or non-motor equivalent (i.e., terminal joint configurations differ equally or more in directions of joint space that lead to different pointer-tip positions than in directions that do not affect the pointer-tip position). Subjects reached from an identical starting joint configuration and pointer-tip location to targets at slow, moderate, and fast speeds. Ten degrees of freedom of joint motion of the arm were recorded. The relationship between changes in the joint configuration and the three-dimensional pointer-tip position was expressed by a standard kinematic model, and the range- and null subspaces were computed from the associated Jacobian matrix. (1) The joint velocity vector and (2) the difference vector between terminal joint configurations from pairs of speed conditions were projected into the two subspaces. The relative length of the two components was used to quantify the amount of self-motion and the presence of motor equivalence, respectively. Results revealed that reaches were accompanied by a significant amount of self-motion at all reaching speeds. Self-motion scaled with movement speed. In addition, the difference in the terminal joint configuration between pairs of different reaching speeds revealed motor equivalence. The results are consistent with a control system that takes advantage of motor redundancy, allowing for flexibility in the face of perturbations, here induced by different movement speeds.

Interpersonal synergies: static prehension tasks performed by two actors

“…Another method of analysis of synergies based on individual trials has been suggested recently based on measurement of deviations of a multi-element system along the UCM and ORT spaces (Scholz et al 2011; Mattos et al 2011, 2015). This method compares motor equivalent (ME, within the UCM) and non-motor equivalent (nME, within ORT) deviations of the system during quick actions.…”

Motor abundance and control structure in the golf swing

“…Another consideration is the difference in the movement speed with different events. It has been shown that as movement speed increases so does V UCM but not V Orth (Scholz, Dwight-Higgin, Lynch, Tseng, Martin, Schöner, 2011). Although the values of V UCM and V Orth are calculated separately for each event for each player, the player's values may align differently when the mean group value for the different normalisation methods.…”

Task-specific stability of abundant systems: Structure of variance and motor equivalence

“…If a system produces a desired value or time profile of a salient performance variable, large deviations in directions that keep this variable unchanged (motor equivalent, ME) are expected. Large ME deviations have been observed in several earlier studies (Scholz et al 2007;Mattos et al 2011;Scholz et al 2011;Mattos et al 2013;Mattos et al 2015).…”

“…Assuming somewhat different initial conditions and force fields across trials, one expects relatively high inter-trial variance in less stable directions and low inter-trial variance in more stable directions. Relatively recently a complementary method has been introduced based on observation of system's trajectories during quick actions (Mattos et al 2011;Scholz et al 2011). This method assumes that a neural input into the system associated with a quick action may be viewed as a perturbation expected to cause relatively large deviations of the system in directions of low-stability.…”