Are arm trajectories planned in kinematic or dynamic coordinates? An adaptation study
There are several invariant features of pointto-point human arm movements: trajectories tend to be straight, smooth, and have bell-shaped velocity profiles. One approach to accounting for these data is via optimization theory; a movement is specified implicitly as the optimum of a cost function, e.g., integrated jerk or torque change. Optimization models of trajectory planning, as well as models not phrased in the optimization framework, generally fall into two main groups-those specified in kinematic coordinates and those specified in dynamic coordinates. To distinguish between these two possibilities we have studied the effects of artificial visual feedback on planar two-joint arm movements. During self-paced point-to-point arm movements the visual feedback of hand position was altered so as to increase the perceived curvature of the movement. The perturbation was zero at both ends of the movement and reached a maximum at the midpoint of the movement. Cost functions specified by hand coordinate kinematics predict adaptation to increased curvature so as to reduce the visual curvature, while dynamically specified cost functions predict no adaptation in the underlying trajectory planner, provided the final goal of the movement can still be achieved. We also studied the effects of reducing the perceived curvature in transverse movements, which are normally slightly curved. Adaptation should be seen in this condition only if the desired trajectory is both specified in kinematic coordinates and actually curved. Increasing the perceived curvature of normally straight sagittal movements led to significant (P<0.001) corrective adaptation in the curvature of the actual hand movement; the hand movement became curved, thereby reducing the visually perceived curvature. Increasing the curvature of the normally curved transverse movements produced a significant (P<0.01) corrective adaptation; the hand movement became straighter, thereby again reducing the visually perceived curvature. When the curvature of naturally curved transverse movements was reduced, there was no significant adaptation (P>0.05). The results of the curvature-increasing study suggest that trajectories are planned in visually based kinematic coordinates. The results of the curvature-reducing study suggest that the desired trajectory is straight in visual space. These results are incompatible with purely dynamicbased models such as the minimum torque change model. We suggest that spatial perception-as mediated by vision-plays a fundamental role in trajectory planning.