Conflict Detection(Batcher’s Algorithm)

• Identifying two lines for a plane in (time axis)-(x axis) coordinate plane. – Suppose the current coordinate location of plane is

(X,Y) on x-y plane. The height is missing here.– The point (0 , X – 1.5) is a point on vertical X-axis on

this planar graph and is an initial point on lower line. – The point (0 , X + 1.5) is a point on the vertical X-axis

on this planar graph and is an initial point on upper line.

– We assume that the plane continues with same velocity, so that in k half-seconds, it will be in position (X+k*DX, Y+k*DY) on x-y plane.

– At T = 20 minutes, the point (20 , X – 1.5 + 20*120*DX) will be on lower line and (20 , X + 1.5 + 20*120*DX) will be on upper line.

Conflict Detection Algorithm (2)– The two points on each line determine the upper and

lower line (see next slide). • The two lines for the (T axis)-(Y axis) plane can

be determined similarly. • If the height of plane is changing by DH each 0.5

second, the two lines for (T axis)-(H axis) is determined similarly.– If the plane has a constant height H, then the two

lines on (T axis)-(H axis) will be horizonal lines going through (0, H+1000 feet) and (0, H-1000 feet) respectively.

• On the next slide, we show the safety zone overlap for two planes A and B in x-dimension.

Conflict Detection (3)

Conflict Detection (4)• These two planes only have a potential

conflict if their safety spaces overlap in all three dimensions at a common time.

• To test for a potential conflict, first determine the biggest min-time on all three graphs and the smallest max-time for planes A and B on all three graphs. – If across the three dimensions, the biggest

min-time is smaller than the smallest max-time, there is a potential conflict