Point-to-Point Unconstrained Gestures: Modeling Wrist and Elbow Trajectories

Although point-to-point reaching motions have received a lot of attention, the way these movements are controlled remains incompletely resolved. Different controllers seem to be recruited depending on the task. Unconstrained reaching movements in space are strongly curved, in opposition to the widely accepted view of quasi-straightness. We argue that the curvature of the movement is due to environmental constraints that affect directly the planning of the movement. We propose a mathematical model whereby movements are planned through the combination of two concurrent controllers for the wrist and elbow in space. Coherence constraints are enforced between the two systems to simulate biomechanical constraints at the wrist, elbow and shoulder levels. External constraints, such as the presence of obstacles, are encapsulated in a virtual force which affects the planning of the movement. The predictions of the model are validated against kinematic data from human reaching motions. Four types were contrasted: intransitive versus transitive reaching motions and natural versus un-natural motions. In the un-natural case, subjects were requested to exaggeratedly elevate the elbow during the movement. In all four movements types, the movements are highly curved. The model renders with high accuracy the kinematics of the movements and accounts for the curvature as an effect of the virtual force.