Visualizing potential fields

Visualizing potential fields

The first tenet of a potential fields architecture is that the motor action of a
behaviormust be represented as a potential field. Apotential field is an array,
or field, of vectors. As described earlier, a vector is a mathematical construct
which consists of a magnitude and a direction. Vectors are often used to
represent a force of some sort. They are typically drawn as an arrow, where
the length of the arrow is the magnitude of the force and the angle of the
arrowis the direction. Vectors are usually representedwith a boldface capital
letter, for example, V. A vector can also be written as a tuple (m; d), wherem
stands for magnitude and d for direction. By convention the magnitude is a
real number between 0.0 and 1, but the magnitude can be any real number.
ARRAY REPRESENTING The array represents a region of space. In most robotic applications, the
A FIELD space is in two dimensions, representing a bird’s eye view of the world just
like a map. The map can be divided into squares, creating a (x,y) grid. Each
element of the array represents a square of space. Perceivable objects in the
world exert a force field on the surrounding space. The force field is analogous
to a magnetic or gravitation field. The robot can be thought of as a
particle that has entered the field exuded by an object or environment. The
vector in each element represents the force, both the direction to turn and the
magnitude or velocity to head in that direction, a robot would feel if it were
at that particular spot. Potential fields are continuous because it doesn’t matter
how small the element is; at each point in space, there is an associated
vector.
Fig. 4.12 shows how an obstacle would exert a field on the robot and make
it run away. If the robot is close to the obstacle, say within 5meters, it is inside
the potential field andwill fell a force thatmakes itwant to face directly away
from the obstacle (if it isn’t already) and move away. If the robot is not within
range of the obstacle, it just sits there because there is no force on it. Notice
that the field represents what the robot should do (the motor schema) based
on if the robot perceives an obstacle (the perceptual schema). The field isn’t
concerned with how the robot came to be so close to the obstacle; the robot
feels the same force if it were happening to move within range or if it was
just sitting there and someone put their hand next to the robot.