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Minimum-torque posture control
The positioning component of the human arm has four kinematic degrees of freedom (DOF), three of which are used to position the end-effector. The fourth DOF, here denoted $\gamma,$ does not affect the hand position (it exclusively affects the elbow position) and may thus be considered redundant. It may be hypothesized that, in the absence of any other constraints, $\gamma$ is chosen such that some task related cost is minimized. In this work, we investigate the particular hypothesis that $\gamma$ is chosen such that the sum of the squared torques at the shoulder and elbow is minimal. A particular feature of this minimum principle is that it associates costs with both movement and static posture. This feature distinguishes the minimum-torque principle from zero-static-cost (ZSC) principles such as the well-known minimum-jerk (Flash and Hogan, 1985) and minimum-torque-change (Uno, Kawato, & Suzuki, 1989) principles. The main objectives of this work are to (1) reject the validity of ZSC principles and (2) to expose the predictions that arise from the minimum-torque principle and to compare these predictions with observed behavior. Human performance is assessed in tasks which consist of the following three components: (1) A movement that places the end-effector in a specified position, (2) a period of posture maintenance of specified duration, and (3) a movement that returns the arm to its initial position. Only one dependent variable is considered: the $\gamma$ associated with the static posture adopted during the posture maintenance period. Performances from three experiments are analyzed. The results of the first experiment disconfirm the validity of ZSC principles, the results of the second experiment are ambiguous, and the results of the third experiment provide some evidence in support of the minimum-torque principle.
Engelbrecht, Sascha E, "Minimum-torque posture control" (1997). Doctoral Dissertations Available from Proquest. AAI9721446.