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4 The Reactive Paradigm
radial lines extending outward from the object). Tangential fields can “spin”
either clockwise or counterclockwise; Fig. 4.13 shows a clockwise spin. They
are useful for directing a robot to go around an obstacle, or having a robot
investigate something.

4.4.2 Magnitude profiles
Notice that in Fig. 4.13, the length of the arrows gets smaller closer to the
object. The way the magnitude of vectors in the field change is called the
MAGNITUDE PROFILE magnitude profile. (The term “magnitude profile” is used here because the
term “velocity profile” is used by control engineers to describe how a robot’s
motors actually accelerate and decelerate to produce a particular movement
without jerking.)
Consider the repulsive field in Fig. 4.12. Mathematically, the field can be
represented with polar coordinates and the center of the field being the origin
(0,0):

(4.1) V direction =
= c
V magnitude

In that case, the magnitude was a constant value, c: the length of the ar-
rows was the same. This can be visualized with a plot of the magnitude
shown in Fig. 4.14a.
This profile says that the robot will run away (the direction it will run
is ) at the same velocity, no matter how close it is to the object, as long
as it is in the range of the obstacle. As soon as the robot gets out of range
of the obstacle, the velocity drops to 0.0, stopping the robot. The field is
essentially binary: the robot is either running away at a constant speed or
stopped. In practice there is a problem with a constant magnitude. It leads
to jerky motion on the perimeter of the range of the field. This is illustrated
when a robot is heading in a particular direction, then encounters an obsta-
cle. It runs away, leaving the field almost immediately, and turns back to its
original path, encounters the field again, and so on.
Magnitude profiles solve the problem of a constant magnitude. They also
REFLEXIVITY make it possible for a robot designer to represent reflexivity (that a response
should be proportional to the strength of a stimulus) and to create interesting
responses. Now consider the profile in Fig. 4.13c. It can be described as how