Segmentation of endpoint trajectories does not imply segmented control

Abstract

Abstract:While it is generally assumed that complex movements consist of a sequence of simpler units, the quest to define these units of action, or movement primitives, still remains an open question. In this context, two hypotheses of movement segmentation of endpoint trajectories in 3D human drawing movements are re-examined: (1) the strokebased segmentation hypothesis based on the results that the proportionality coefficient of the 2/3 power law changes discontinuously with each new "stroke", and (2) the segmentation hypothesis inferred from the observation of piecewise planar endpoint trajectories of 3D drawing movements. In two experiments human subjects performed a set of elliptical and figure-8 patterns of different sizes and orientations using their whole arm in 3D. The kinematic characteristics of the endpoint trajectories and the seven joint angles of the arm were analyzed. While the endpoint trajectories produced similar segmentation features as reported in the literature, analyses of the joint angles show no obvious segmentation but rather continuous oscillatory patterns. By approximating the joint angle data of human subjects with sinusoidal trajectories, and by implementing this model on a 7-degree-of-freedom anthropomorphic robot arm, it is shown that such a continuous movement strategy can produce exactly the same features as observed by the above segmentation hypotheses. The origin of this apparent segmentation of endpoint trajectories is traced back to the nonlinear transformations of the forward kinematics of human arms. The presented results demonstrate that principles of discrete movement generation may not be reconciled with those of rhythmic movement as easily as has been previously suggested, while the generalization of nonlinear pattern generators to arm movements can offer an interesting alternative to approach the question of units of action.

Complex Unconstrained Three-Dimensional Hand Movement and Constant Equi-Affine Speed

“…Nevertheless, additional claims that this segmentation may reflect central segmented control (Viviani 1986;Viviani and Cenzato 1985) were contrasted with results suggesting this segmentation to be epiphenomenal to continuous smooth minimum-jerk control at the hand level (Richardson and Flash 2002) or to nonlinear transformations of the forward kinematics of human arms that perform smooth multijoint rotations, which are governed by continuous control (Dounskaia 2007;Sternad and Schaal 1999). It will therefore be interesting to test what type of segmentation is implied by the one-sixth or curvature-torsion power laws and how much more of the variance in the speed profile might be explained by geometry under the assumption of movement segmentation.…”

“…As noted in the INTRODUCTION, a few studies demonstrated that for the planar case, the exponent of the -PL may change systematically with the path (Sternad and Schaal 1999;Wann et al 1988). Of special interest is the study by Schaal and Sternad (2001), which investigates the 2/3-PL for unconstrained ellipse tracing in 3D space.…”

“…If movement at constant equi-affine speed is indeed the guiding principle and the 2/3-PL is just a special case, we would expect general 3D movement to conform to 3D constant equi-affine speed instead of to the 2/3-PL. This was in fact demonstrated when it was shown that the 2/3-PL does not sufficiently explain general 3D drawing movements-the less planar the path is, the less the power law is obeyed (Pollick and Ishimura 1996;Schaal and Sternad 2001;Sternad and Schaal 1999). Yet does the novel 3D power law describe 3D movements better than the 2/3-PL?…”

Spatial constant equi-affine speed and motion perception

“…The most striking may be the systematic deviations in the production of the paradigmatic shape on which the two-thirds power law was initially demonstrated, the planar ellipse (Wann et al 1988), especially when it is traced freely in space (Sternad and Schaal 1999). The same holds for motion perception, where what subjects perceive as the most uniform speed profile was found to depend on the eccentricity the elliptical paths (Viviani and Stucchi 1992;Levit-Binnun et al 2006).…”

Towards Testable Neuromechanical Control Architectures for Running

“…The appeal to optimality may confound the development of more fundamental compositional principles. For example, arguments for the "power law" [64,77], and, more particularly, that the observed episodic power law trajectories constitute the alphabet of a "motor language" have been shown to be equally well explained as artifacts of nonlinear kinematics [70,75].…”