5
OBSTACLE AVOIDANCE
5.1 introduction
5.2 virtual force field
The Virtual Force Field (VFF) method is our earlier real-time obstacle
avoidance method for fast-running vehicles . Unlike the methods
reviewed above, the VFF method allows for fast, continuous, and smooth
motion of the controlled vehicle among unexpected obstacles, and does
not require the vehicle to stop in front of obstacles.
The VFF Concept
The individual components of the VFF method are presented below. a.
The VFF method uses a two-dimensional Cartesian histogram grid C for
obstacle representation. Like in CMU's certainty grid concept, each cell
(i,j) in the histogram grid holds a certainty value, c(i,j), that represents the
confidence of the algorithm in the existence of an obstacle at that
location.
The histogram grid differs from the certainty grid in the way it is built and
updated. CMU's method projects a probability profile onto those cells that
are affected by a range reading; this procedure is computationally
intensive and would impose a heavy time penalty if real-time execution
on an on-board computer was attempted. Our method, on the other
hand, increments only one cell in the histogram grid for each range
reading, creating a "probability" distribution1 with only small
computational overhead. For ultrasonic sensors, this cell corresponds to
the measured distance d (see Figure 5.2.1) and lies on the acoustic axis
of the sensor. While this approach may seem to be an oversimplification,
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a probabilistic distribution is actually obtained by continuously and rapidly
sampling each sensor while the vehicle is moving. Thus, the same cell
and its neighboring cells are repeatedly incremented, as shown in Figure
5.2.2. This results in a histogramic probability distribution, in which high
certainty values are obtained in cells close to the actual location of the
obstacle.
Next, we apply the potential field idea to the histogram grid, so the
probabilistic sensor information can be used efficiently to control the
vehicle. Fig. 3 shows how this algorithm works: As the vehicle moves, a
window of wsxws cells accompanies it, overlying a square region of C.
We call this region the "active region" (denoted as C*), and cells that
momentarily belong to the active region are called "active cells" (denoted
as c*i,j).
FIGURE 5.1 INITIALLY
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FIGURE 5.2 AFTER SOME ITERATIONS
The size of the window is 33x33 cells (with a cell size of 10cmx10cm),
and the window is always centered about the robot's position. Note that a
circular window would be geometrically more appropriate, but is
computationally more expensive to handle than a square one. Each
active cell exerts a virtual repulsive forceFi,j toward the robot. The
magnitude of this force is proportional to the certainty value c*i,j and
inversely proportional to d , where d is x the distance between the cell
and the center of the vehicle, and x is a positive real number (we assume
x=2 in the following discussion). At each iteration, all virtual repulsive
forces are added up to yield the resultant repulsive force Fr.
Simultaneously, a virtual attractive force Ft of constant magnitude is
applied to the vehicle, "pulling" it toward the target. The summation of Fr
and Ft yields the resulting force vector R. In order to compute R, up to
33x33=1089 individual repulsive force vectors Fi,j must be computed and
accumulated. The computational heart of the VFF algorithm is therefore
a specially developed algorithm for the fast computation and summation
of the repulsive force vectors. Figure 5.2.3 shows this procedure.
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FIGURE 5.3 THE FORCE FIELD
5.3 Kinect based Obstacle Avoidance algorithm
The
algorithm
is
so
simple,
Pseudo code:
- initially the robot is moving forward
- update the kinect depth image
- if inside the depth image there is an object with distance less than 60
c.m
then it stops
- it looks for the farthest object found in image
- if the farthest object is in the left half then the rotation direction is anticlockwise
(to
go
in
the
farthest
object
direction)
- else if the farthest object is in the right half then the rotation direction is
clockwise
(to
go
in
the
farthest
object
direction)
- it continue rotation until no object is in distance less than 60 c.m
- then it moves forward
- go to step 2
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This Algorithm intuition is from the small mouse toy that can run and find
it's way through obstacles
(this mouse is sold in Attaba )
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