Quantitative examinations for human arm trajectory planning in three-dimensional space

The following two characteristics of point-to-point human arm movement on a plane have been well demonstrated: (1) The path is roughly a straight line but slightly curved. (2) The velocity profile is bell shaped with a single peak. Several models have been proposed to explain these features. Four criteria for trajectory planning based on optimal principles have been proposed: the minimum hand jerk criterion, the minimum angle jerk criterion, the minimum torque change criterion, and the minimum commanded torque change criterion. It has been shown that trajectories generated by the minimum commanded torque change model correspond well with measured trajectories in a horizontal and sagittal work space. However, it was very difficult to establish a robust method for obtaining an optimal trajectory based on the minimum commanded torque change criterion, because of the need to solve a nonlinear optimization problem. Recently, Wada and colleagues proposed a new method to stably calculate optimal trajectories based on the minimum commanded torque change criterion. The method can obtain trajectories satisfying the Euler–Poisson equations with sufficiently high accuracy. We show that optimal trajectories based on the minimum commanded torque change criterion in three-dimensional space can be calculated by applying the method. Finally, we show that the measured trajectory is closest to the minimum commanded torque change trajectory by statistical examination of many point-to-point trajectories in three-dimensional space. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(7): 43–54, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10323