The Curvature of Hand Paths in Multi-joint Movements: Examinations of Computational Theories for Trajectory Planning

In multi-joint movements, possible trajectories for a given target are infinite, but actually have certain invariant features. It has been discussed whether trajectories of the human arm are planned in an extrinsic space or in an intrinsic space. Hand paths planned in the former are predicted to be always straight, while those in the latter are generally curved. Both Uno et al. and Osu et al. reported that actual hand paths tended to significantly curve for some specific arm postures, movement distances, and movement durations. We have extended the previous studies by using various initial and final positions located within a workspace and examined if the curvature of a trajectory quantitatively varies with arm posture when subjects make point to point reaching movements on a horizontal plane. Curvatures of measured hand trajectories were linearly estimated using two models, hand position and hand translation, which are represented by extrinsic coordinates, and other two models, joint angle and joint rotation, which are represented by intrinsic coordinates. In experiment I and II, movement durations were restricted, and in experiment III. movement durations were flexible and added to parameters. Movement durations and joint rotation significantly contributed to curvature. We succeeded in predicting the curvature of hand paths by using the arm posture before and after a movement. The results suggest that trajectory curvature depends on arm posture and is in accordance with predictions made under planning in the intrinsic space, rather than that in the extrinsic space. Furthermore, the result that a longer movement duration causes a larger curvature is in agreement with the predictions of Uno and Kawato, in which a longer movement duration makes paths expand toward the outer side because of an effectively larger viscosity ratio.