Control of Three- and Four-Joint Arm Movement: Strategies for a Manipulator with Redundant Degrees of Freedom

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Abstract
Control of arm movements when the number of joints exceeds the degrees of freedom necessary for the task requires a strategy for selecting specific arm configurations out of an infinite number of possibilities. This report reviews strategies used by human subjects to control the shoulder, elbow, and wrist (three degrees of freedom) while moving a pointer to positions in a horizontal plane (two degrees of freedom). Analysis of final arm configurations assumed when the pointer was at the target showed the following: (a) Final arm configurations were virtually independent of the configuration at the start of the pointing movement, (b) subjects avoided configurations subjectively felt to be uncomfortable (e.g., those with extreme flexion or extension of the wrist), and (c) the results could be simulated by assigning hypothetical cost functions to each joint and selecting the arm configuration that minimized the sum of the costs. The fitted cost functions qualitatively agreed with psychophysically determined comfort; they appeared to depend on joint angle and on muscular effort. Simple neural networks can learn implicit representations of these cost functions and use them to specify final arm configurations. The minimum cost principle can be extended to movements that use the fingers as a fourth movable segment. For this condition, however, experiments showed that final configurations of the arm depended upon initial configurations. Analysis of movement trajectories for arms with three degrees of freedom led to a control model in which the minimum cost principle is augmented by a mechanism that distributes required joint movements economically among the three joints and a mechanism that implements a degree of mass-spring control.

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