Sternad D, Schaal S
Department of Kinesiology, Pennsylvania State University, University Park 16802, USA.
Exp Brain Res. 1999 Jan;124(1):118-36. doi: 10.1007/s002210050606.
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, remains an open question. In this context, two hypotheses of movement segmentation of endpoint trajectories in three-dimensional human drawing movements are reexamined: (1) the stroke-based segmentation hypothesis based on the results that the proportionality coefficient of the two-thirds power law changes discontinuously with each new "stroke," and (2) the segmentation hypothesis inferred from the observation of piecewise planar endpoint trajectories of three-dimensional drawing movements. In two experiments human subjects performed a set of elliptical and figure eight patterns of different sizes and orientations using their whole arm in three dimensions. 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 to those 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 (DOF) 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.
虽然人们普遍认为复杂运动由一系列更简单的单元组成，但定义这些动作单元或运动基元的探索仍然是一个悬而未决的问题。在此背景下，重新审视了三维人体绘画运动中端点轨迹的两种运动分割假设：（1）基于三分之二幂律的比例系数随每个新“笔画”不连续变化的结果的基于笔画的分割假设，以及（2）从三维绘画运动的分段平面端点轨迹观察中推断出的分割假设。在两个实验中，人类受试者使用他们的整个手臂在三维空间中执行了一组不同大小和方向的椭圆形和数字八图案。分析了端点轨迹的运动学特征和手臂的七个关节角度。虽然端点轨迹产生了与文献中报道的类似的分割特征，但关节角度分析显示没有明显的分割，而是连续的振荡模式。通过用正弦轨迹逼近人类受试者的关节角度数据，并在一个7自由度（DOF）拟人机器人手臂上实现这个模型，结果表明这样一种连续运动策略可以产生与上述分割假设所观察到的完全相同的特征。端点轨迹这种明显分割的起源可追溯到人类手臂正向运动学的非线性变换。所呈现的结果表明，离散运动生成的原理可能不像之前所认为的那样容易与节奏运动的原理相协调，而将非线性模式生成器推广到手臂运动可以为解决动作单元问题提供一个有趣的替代方法。
