Minimum-jerk, two-thirds power law, and isochrony: converging approaches to movement planning.

Two approaches to the study of movement planning were contrasted. Data on the drawing of complex two-dimensional trajectories were used to test whether the covariations of the kinematic and geometrical parameters of the movement formalized by the two-thirds power law and by the isochrony principle (P. Viviani & R. Schneider, 1991) can be derived from the minimum-jerk model hypothesis (T. Flash & N. Hogan, 1985). The convergence of the 2 approaches was satisfactory insofar as the relation between tangential velocity and curvature is concerned (two-thirds power law). Global isochrony could not be deduced from the optimal control hypothesis. Scaling of velocity within movement subunits can instead be derived from the minimum-jerk hypothesis. The implications vis-à-vis the issue of movement planning are discussed with an emphasis on the representation used by the motor control system for coding the intended trajectories.