Page 365 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

340 HUMAN PERFORMANCE IN MOTION PLANNING

front of the computer screen, and controls the arm motion using the computer
mouse. The first link, l 1 , of the arm rotates about its joint J 0 located at the fixed
base of the arm. The joint of the second link, J 1 , is attached to the first link,
and the link rotates about point J 1 , which moves together with link l 1 . Overall,
the arm looks like a human arm, except that the second link, l 2 , has a piece that
extends outside the “elbow” J 1 . (This kinematics is quite common in industrial
and other manipulators.) And, of course, the arm moves only in the plane of
the screen.
How does one control the arm motion in this setup? By positioning the cursor
on link l 1 and holding down the mouse button, the subject will make the link
rotate about joint J 0 and follow the cursor. At this time link l 2 will be “frozen”
relative to link l 1 and hence move with it. Similarly, positioning the cursor on
link l 2 and holding down the mouse button will make the second link rotate about
joint J 1 , with link l 1 being “frozen” (and hence not moving at all). Each such
motion causes the appropriate link endpoint to rotate on a circular arc.
Or—this is another way to control the arm motion—one can position the
cursor at the endpoint P of link l 2 and drag it to whatever position in the arm
workspace one desires, instantaneously or in a smooth motion. The arm endpoint
will follow the cursor motion, with both links moving accordingly. During this
motion the corresponding positions of both links are computed automatically in
real time, using the inverse kinematics equations. (Subjects are not told about
this mechanism, they just see that the arm moves as they expect.) This second
option allows one to control both links motion simultaneously. It is as if someone
moves your hand on the table—your arm will follow the motion.
We will assume that, unlike in the human arm, there are no limits to the motion
of each joint in Figure 7.5. That is, each link can in principle rotate clockwise
or counterclockwise indefinitely. Of course, after every 2π each link returns to
its initial position, so one may or may not want to use this capability. [Looking
ahead, sometimes this property comes in handy. When struggling with moving
around an obstacle, a subject may produce more than one rotation of a link.
Whether or not the same motion could be done without the more-than-2π link
rotation, not having to deal with a constraint on joint angle limits makes the test
psychologically easier for the subject.]
The difficulty of the test is, of course, that the arm workspace contains obsta-
cles. When attempting to move the arm to a specified target position, the subjects
will need to maneuver around those obstacles. In Figure 7.5 there are four obsta-
cles. One can safely guess, for example, that obstacle O 1 may interfere with the
motion of link l 1 and that the other three obstacles may interfere with the motion
of link l 2 .
Similar to the test with a labyrinth, in the arm manipulator test with complete
information the subject is given the equivalent of the bird’s-eye view: One has a
complete view of the arm and the obstacles, as shown in Figure 7.5. Imagine you
are that subject. You are asked to move the arm, collision-free, from its starting
position S to the target position T . The arm may touch an obstacle, but the system