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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