Page 366 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

PRELIMINARY OBSERVATIONS 341

will not let you move the arm “through” an obstacle. Take your time—time is
not a consideration in this test.
Three examples of performance by human subjects in controlled experiments
3
are shown in Figure 7.6. Shown are the arm’s starting and target positions S and
T , along with the trajectory (dotted line) of the arm endpoint on its way from S
to T . The examples represent what one might call an “average” performance by
human subjects. 4
The reader will likely be surprised by these samples. Why is human perfor-
mance so unimpressive? After all, the subjects had complete information about
the scene, and the problem was formally of the same (rather low) complexity
as in the labyrinth test. The difference between the two sets of tests is indeed
dramatic: Under similar conditions the human subjects produced almost optimal
paths in the labyrinth (Figure 7.2) but produced rather mediocre results in the
test with the arm (Figure 7.6).
Why, in spite of seeing the whole scene with the arm and obstacles (Figure 7.5),
the subjects exhibited such low skills and such little understanding of the task.
Is there perhaps something wrong with the test protocol, or with control means
of the human interface—or is it indeed real human skills that are represented
here? Would the subjects improve with practice? Given enough time, would they
perhaps be able to work out a consistent strategy? Can they learn an existing algo-
rithm if offered this opportunity? Finally, subjects themselves might comment that
whereas the arm’s work space seemed relatively uncluttered with obstacles, in
the test they had a sense that the space was very crowded and “left no room for
maneuvering.”
The situation becomes clearer in the arm’s configuration space (C-space,
Figure 7.7). As explained in Section 5.2.1, the C-space of this revolute–revolute
arm is a common torus (see Figure 5.5). Figure 7.7 is obtained by flattening
the torus by cutting it at point T along the axes θ 1 and θ 2 . This produces
four points T in the resulting square, all identified, and two pairs of identified
C-space boundaries, each pair corresponding to the opposite sides of the C-space
square. For reference, four “shortest” paths (M-lines) between points S and T are
shown (they also appear in Figure 5.5; see the discussion on this in Section 5.2.1).
The dark areas in Figure 7.7 are C-space obstacles that correspond to the four
obstacles in Figure 7.5.
Note that the C-space is quite crowded, much more than one would think
when looking at Figure 7.5. By mentally following in Figure 7.7 obstacle outlines
across the C-space square boundaries, one will note that all four workspace
obstacles actually form a single obstacle in C-space. This simply means that
when touching one obstacle in work space, the arm may also touch some other

3 The experimental setup used in Figure 7.6c slightly differs from the other two; this played no visible
role in the test outcomes.
4 The term “average” here has no formal meaning: It signifies only that some subjects did better and
some did worse. A more formal analysis of human performance in this task will be given in the next
section. A few subjects did not finish the test and gave up, citing tiredness or hopelessness (“There
is no solution here”, “You cannot move from S to T here”...).