Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel;
J Neurophysiol. 2014 Mar;111(5):954-68. doi: 10.1152/jn.00132.2013. Epub 2013 Nov 20.
Surface-constrained motion, i.e., motion constraint by a rigid surface, is commonly found in daily activities. The current work investigates the choice of hand paths constrained to a concave hemispherical surface. To gain insight regarding paths and their relationship with task dynamics, we simulated various control policies. The simulations demonstrated that following a geodesic path (the shortest path between 2 points on a sphere) is advantageous not only in terms of path length but also in terms of motor planning and sensitivity to motor command errors. These stem from the fact that the applied forces lie in a single plane (that of the geodesic path). To test whether human subjects indeed follow the geodesic, and to see how such motion compares to other paths, we recorded movements in a virtual haptic-visual environment from 11 healthy subjects. The task comprised point-to-point motion between targets at two elevations (30° and 60°). Three typical choices of paths were observed from a frontal plane projection of the paths: circular arcs, straight lines, and arcs close to the geodesic path for each elevation. Based on the measured hand paths, we applied k-means blind separation to divide the subjects into three groups and compared performance indicators. The analysis confirmed that subjects who followed paths closest to the geodesic produced faster and smoother movements compared with the others. The "better" performance reflects the dynamical advantages of following the geodesic path and may also reflect invariant features of control policies used to produce such a surface-constrained motion.
约束表面运动，即受到刚性表面约束的运动，在日常活动中很常见。本研究调查了受约束于凹半球表面的手路径选择。为了深入了解路径及其与任务动力学的关系，我们模拟了各种控制策略。模拟结果表明，遵循测地线路径（球面上两点之间的最短路径）不仅在路径长度方面具有优势，而且在运动规划和对运动指令误差的敏感性方面也具有优势。这是因为所施加的力位于单个平面（测地线路径所在的平面）上。为了测试人类受试者是否确实遵循测地线路径，并观察这种运动与其他路径的比较，我们从 11 名健康受试者那里记录了在虚拟触觉视觉环境中的运动。任务包括在两个高度（30°和 60°）的目标之间进行点对点运动。从路径的正面投影观察到三种典型的路径选择：对于每个高度，圆弧、直线和接近测地线的弧线。基于测量的手路径，我们应用 k-均值盲分离将受试者分为三组，并比较性能指标。分析证实，与其他路径相比，遵循最接近测地线路径的受试者产生了更快、更平滑的运动。“更好”的性能反映了遵循测地线路径的动力学优势，也可能反映了用于产生这种约束表面运动的控制策略的不变特征。
