Page 146 - Introduction to AI Robotics

Programming a single potential field
4.4.4 4.4 Potential Fields Methodologies 129
Potential fields are actually easy to program, especially since the fields are
ego-centric to the robot. The visualization of the entire field may appear
to indicate that the robot and the objects are in a fixed, absolute coordinate
system, but they are not. The robot computes the effect of the potential field,
usually as a straight line, at every update, with no memory of where it was
previously or where the robot has moved. This should become clear through
the following examples.
A primitive potential field is usually represented by a single function. The
vector impacting the robot is computed each update. Consider the case of a
robot with a single range sensor facing forward. The designer has decided
that a repulsive field with a linear drop off is appropriate. The formula is:

(4.2) V direction = 180
(
(D d) for d = D <
V magnitude = D
0 for d > D
where D is the maximum range of the field’s effect, or the maximum dis-
tance at which the robot can detect the obstacle. (D isn’t always the detection
range. It can be the range at which the robot should respond to a stimulus.
For example, many sonars can detect obstacles 20 feet away, producing an al-
most infinitesimal response in emergent behavior but requiring the runtime
overhead of a function call. In practice, a roboticist might set a D of 2 meters.)

Notice that the formula produces a result where 0.0 V magnitude 1.0.
Below is a C code fragment that captures the repulsive field.

typedef struct {
double magnitude;
double direction;
} vector;

vector repulsive(double d, double D)
{
if (d <= D) {
outputVector.direction = -180; //turn around!
outputVector.magnitude = (D-d)/D; //linear dropoff
}
else {