Page 200 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

MINIMUM TIME STRATEGY 175

4.3.8 Examples
The performance of Minimum Time Strategy algorithm is illustrated in
Figure 4.12. The examples shown are computer simulations. The robot mass
m and constraints on control parameters p and q are the same for all examples:
p max = q max , p max /m = 1. The generated paths are shown in thicker lines. For
the purpose of comparison, also shown (in a thin line) are paths produced under
the same conditions by a kinematic algorithm VisBug.
The radius of vision r v is the same in both Figures 4.12a and 4.12b. The
difference is in the environment: In Figure 4.12b there are additional obstacles;
that is, the robot suddenly uncovers them at a close distance when turning around
a corner. Note that in Figure 4.12b the path becomes tighter and shorter, though
it takes longer: Measured in the number of steps, the path in Figure 4.12a takes
242 steps, and the path in Figure 4.12b takes 278 steps. One can say the robot
becomes more cautious in Figure 4.12b.
A similar pair of examples shown in Figures 4.12c and 4.12d illustrates the
effect of the radius of vision r v : Here it is twice as big as the radius of vision
in Figures 4.12a and 4.12b. The times to execute the path here are 214 and 244
steps, respectively, shorter than in the corresponding examples in Figures 4.12a
and 4.12b. The examples thus demonstrate that better sensing (larger r v ) results
in shorter time to complete the task: More crowded space results in longer time,
though possibly in shorter paths.
Note that in some points the algorithm found it necessary to make use of
the stopping path; those points are usually easy to recognize from the sharp
turns in the path. For example, in Figure 4.12a the robot came to a halt at
points A and D, and in Figure 4.12b it stopped at points A–F. The algorithm’s
performance in a more complicated environment is shown in Figures 4.12e and
4.12f. In Figure 4.12f the radius of vision r v is significantly larger than that
in Figure 4.12e. Note again that richer input information provided by a larger
sensing range is likely to translate into shorter paths.