Analysis of an optimal control model of multi-joint arm movements

Abstract

Abstract. In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and ½ show an 'N' shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement.When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements.

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Energy Optimal Trajectories in Human Arm Motion Aiming for Assistive Robots

“…One effective approach to investigating the planning mechanism is to examine the mechanical and physiological properties of a muscle, and to investigate the behavior of individual muscles in human arm trajectories (Kashima et al, 2002), (Fagg et al, 2002), (Georgopoulos et al, 1986). Different optimization criteria based on the minimum energy were proposed (Alexander, 1997), (Buchanan and Shreeve, 1996), (Lan, 1997). A minimum energy cost hypothesis for human arm trajectories was presented and tested (Alexander, 1997).…”

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“…Hierarchical model [15] , neural network [12] [13] [20] , optimal control [1] [10] , adaptive control [6] [11] , iterative learning [14] , and combination of these methods [17] have been applied in various motion controls of the human arm. So far most of the studies have focused on the arm movement control on the horizontal plane, with gravity compensation.…”