Formation and control of optimal trajectory in human multijoint arm movement

Abstract

In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function C _T is defined as follows:

$$C_T = \frac{1}{2}{}^t\int\limits_0^f {\sum\limits_{i = 1}^n {\left( {\frac{{{\text{d}}z_i }}{{{\text{d}}t}}} \right)^2 {\text{d}}t,} } $$

where z _iis the torque generated by the i-th actuator (muslce) out of n actuators, and t _fis the movement time. Since this objective function critically depends on the complex nonlinear dynamics of the musculoskeletal system, it is very difficult to determine the unique trajectory which yields the best performance. We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torquechange criterion.