Invariances and controlled variables in human arm movement

Resumo

The main question of this thesis is the origin of the correlation between speed and curvature in human hand movement, or why does the hand move slower in curves? The phenomenon is known since the late 19th century, and was formalized in the late 20th century as the “speed-curvature power law” or “the 2/3 power law”. It has often been studied, since it is one of the few invariances found in hand movement. There is no consensus about its origin, and the attempts to explain it can be placed into roughly three approaches. First, the cortical origin hypotheses assume that the cortical structures optimize movement trajectories according to a criterion (such as minimal jerk) and the movement system then executes the planned trajectory. The second group of approaches assumes interaction: the power law depends on the interaction between the brain, the hand, and the environment; it arises from low-pass filtering properties of the arm or from differences in the environment, such as moving the hand through air or water. Finally, the third approach attempts to explain away the power law as a purely statistical artifact, arising from mistakes in the measurement process or the calculation of variables. To answer this question, we have considered all three approaches, using mathematical analysis of generated trajectories, human behavioral experiments, and numerical and robotic modelling. We showed that the power law is not mathematically trivial, but that there is a statistical artifact if angular speed is used instead of tangential speed. We argued against the claim that mechanical work is minimal in the 2/3 power law, and explored the relationship between the angular frequency of a curve, its power law exponent and the minimization of jerk. Applying the theory of hierarchical control, we built a robot arm and showed how the interaction between the artificial perception, simple controllers, low-pass-filtering physical arm, and the unpredictable environment may result in the power law when drawing ellipses. The robot, however, produced smaller and phase-delayed elliptic trajectories compared to humans in similar tasks. In behavioral experiments with humans, we found that the most likely visual features used when tracking targets along elliptic trajectories are the phase and size difference. We created a numerical simulation of sensorimotor feedback loops using those features as controlled variables. When performing the same tasks as human participants, the simulation drew ellipses of the correct size and without phase delay, and also reproduced the exponents of the speed-curvature power law. Taken together, the papers show significant progress toward understanding the origins of the speed-curvature power law, and suggest further testable hypotheses on the neural mechanisms of sensorimotor control in human arm and hand movement. Specifically, it appears that the power law in drawing ellipses can be explained by a hypothesis in the interaction approach - the power law emerges in the interaction of the low-pass filtering in the sensorimotor system, and higher-level visual controlled variables, such as the phase difference and the size difference. Additionally, we developed a free open-source movement tracking application for Android tablets to facilitate hand movement research outside the lab. Further, we built a prototype robot model of two antagonistic muscles for simultaneous control of joint angle and muscle tone. This is an initial step toward a more complex electromechanical model of the human arm that could be used to integrate and further verify the hypotheses generated by the present thesis.