ARE COMPLEX CONTROL SIGNALS REQUIRED FOR HUMAN ARM MOVEMENT

It has been proposed that the control signals underlying voluntary hum an arm movement have a ''complex'' nonmonotonic time-varying form, and a number of empirical findings have been offered in support of this i dea. In this paper, we address three such findings using a model of tw o-joint arm motion based on the lambda version of the equilibrium-poin t hypothesis. The model includes six one-and two-joint muscles, reflex es, modeled control. signals, muscle properties, and limb dynamics. Fi rst, we address the claim that ''complex'' equilibrium trajectories ar e required to account for nonmonotonic joint impedance patterns observ ed during multijoint movement. Using constant-rate shifts in the neura lly specified equilibrium of the limb and constant cocontraction comma nds, we obtain patterns of predicted joint stiffness during simulated multijoint movements that match the nonmonotonic patterns reported emp irically. We then use the algorithm proposed by Gomi and Kawato to com pute a hypothetical equilibrium trajectory from simulated stiffness, v iscosity, and Limb kinematics. Like that reported by Gomi and Kawato, the resulting trajectory was nonmonotonic, first leading then lagging the position of the limb. Second, we address the claim that high level s of stiffness are required to generate rapid single-joint movements w hen simple equilibrium shifts are used. We compare empirical measureme nts of stiffness during rapid single-joint movements with the predicte d stiffness of movements generated using constant-rate equilibrium shi fts and constant cocontraction commands. Single-joint movements are si mulated at a number of speeds, and the procedure used by Bennett to es timate stiffness is followed. We show that when the magnitude of the c ocontraction command is scaled in proportion to movement speed, simula ted joint stiffness varies with movement speed in a manner comparable with that reported by Bennett. Third, we address the related claim tha t nonmonotonic equilibrium shifts are required to generate rapid singl e-joint movements. Using constant-rate equilibrium shifts and constant cocontraction commands, rapid single-joint movements are simulated in the presence of external torques. We use the procedure reported by La tash and Gottlieb to compute hypothetical equilibrium trajectories fro m simulated torque and angle measurements during movement. As in Latas h and Gottlieb, a nonmonotonic function is obtained even though the co ntrol signals used in the simulations are constant-rate changes in the equilibrium position of the limb. Differences between the ''simple'' equilibrium trajectory proposed in the present paper and those that ar e derived from the procedures used by Gomi and Kawato and Latash and G ottlieb arise from their use of simplified models of force generation.