Calculating Optimal Criteria for Trajectory Planning Using Observed Movement Data

Various optimal criteria have been proposed for trajectory planning in multi-joint arm movements. The minimumjerk criterion plans smooth trajectories in the extrinsic task space. The minimum-joint-angle-jerk criterion, the minimum-torque-change criterion, and the minimum-motor-command-change criterion plan smooth trajectories in the intrinsic body space. Assuming that realized trajectories reflect planned trajectories, we compared the values of above four optimal criteria calculated from observed movement data. If the value of a certain criterion is larger in a spontaneously generated movement than in some other movement, that criterion can be rejected. If, however, the value of a certain criterion is smaller in a spontaneously generated movement than in any other movement, it supports that criterion. Subjects were instructed to move their hand to a target passing through a via-point. Several via-points were given randomly to make subjects generate hand paths with various curvatures. The curvatures of the paths that have minimum values of a certain criterion are compared to curvatures of the spontaneously generated paths. The values of hand-jerk and joint-angle-jerk were obtained from measured position data. The values of torque-change were obtained using the dynamics equation of a two-joint arm model with estimated physical parameters. The values of motor-command-change were obtained from quasi-tension calculated from rectified EMG using a second-order low-pass-filter. The minimum-jerk criterion was larger in spontaneously curved movements than in movements with straighter hand paths. This result rejects the minimum-hand-jerk criterion. However, joint angle jerk was not always minimum around the hand paths predicted by the minimum-joint-angle-jerk criterion. Subjects tend to generate trajectories that have lower values of minimum-motor-command-change criterion.