2Department of Physiology Northwestern University School of Medicine
The observation that human reaching movements often exhibit bell-shaped tangential velocity profiles and straight paths has been interpreted by many to mean that a detailed trajectory of the arm must be planned prior to movement execution. Here, we present a simple model of pulse-step reach control that does not maintain an explicit representation of the trajectory to be followed.
The arm model consists of a shoulder and an elbow joint, positioned such that movements are made in the horizontal plane. The joints are actuated by two pairs of opposing muscles, each of which is regulated by a stretch reflex. Voluntary commands control the thresholds of the reflexes. Although two opposing muscles produce a unique joint equilibrium position, the dynamics of the stretch reflex creates a "stiction region" around the equilibrium. Once the joint enters this region, it slows rapidly, effectively halting the joint's movement. This formulation of muscle/reflex dynamics has the advantage of allowing rapid arm movements while limiting the potential for oscillations around the end-point of movement.
For a given start and target position, the control program is represented by a pair of open-loop, pulse-step commands that are sent to the muscle pairs actuating the two joints. The pulse-step program is specified by a set of seven parameters: magnitudes of the joint pulse and step commands (4 parameters), relative initiation time of the elbow and shoulder pulses (1), and the times of transition from pulse to step (2). A hierarchical search process is used to find the appropriate set of parameters for a given movement. The search is guided by the error in the movement endpoint, and a measure of the straightness of the movement.
Despite the low dimensionality of the motor program representation, it is often possible to achieve a bell-shaped velocity profile and an approximately straight path. This approach is similar Karniel and Inbar (1997), with a critical difference being that only the agonist muscle bursts are specified directly. The braking antagonist burst naturally falls out of the stretch reflex model. In continuing work, we are examining biologically-realistic mechanisms for representing and updating the control program.
Keywords: reach control model, pulse-step control, stretch reflex
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