Node 1
The first node measured is a four-way intersection. The hallways do not coincide here, and there is a set of couches that further interferes.
The result is that there are two meetpoints in close proximity at the intersection, and the robot homes to 3-way equidistance with a minima
distance value of approximately 65 inches while recording a fourth minima at about 71 inches.
Minima
We can see from the first figure that the observed minima values ranged from 62.6 to 72.8 inches.The overall mean minima value was 66.8 inches, with a standard deviation of 2.2 inches.
We can see from the second figure that the mean minima values (mean per sample) ranged from 65.4 to 68.0 inches.
The standard deviation of mean minima values was 0.4 inches.
Therefore, we have SIGMA_DIST = 0.4 (inches).
Edge angles
The relative edge angles of the meetpoint were about 80, 90, 90 and 100 degrees, as shown in the first figure.From the second figure we see that the asymmetry mean was 23.8 degrees, with a standard deviation of 7.0 degrees.
Therefore, we have SIGMA_SYM = 7.0 (degrees).
Node 2
The second node measured is a three-way intersection with two concrete corners and wooden slats on the wall.
The equidistant minima distance is approximately 59 inches.
Minima
We can see from the first figure that the observed minima values ranged from 57.6 to 61.7 inches.The overall mean minima value was 58.9 inches, with a standard deviation of 0.7 inches.
We can see from the second figure that the mean minima values (mean per sample) ranged from 57.8 to 61.3 inches.
The standard deviation of mean minima values was 0.6 inches.
Therefore, we have SIGMA_DIST = 0.6 (inches).
Edge angles
The relative edge angles of the meetpoint were about 120, 120, and 120 degrees, as shown in the first figure.From the second figure we see that the asymmetry mean was 7.8 degrees, with a standard deviation of 2.1 degrees.
Therefore, we have SIGMA_SYM = 2.1 (degrees).
Node 3
The third node measured is a three-way intersection where three hallways of different widths merge.
This intersection occurs in front of the elevators and is one of the two largest scale meetpoints on the sixth floor.
The equidistant minima distance is approximately 85 inches.
Minima
We can see from the first figure that the observed minima values ranged from 82.1 to 87.0 inches.The overall mean minima value was 85.2 inches, with a standard deviation of 0.9 inches.
We can see from the second figure that the mean minima values (mean per sample) ranged from 82.5 to 86.3 inches.
The standard deviation of mean minima values was 0.9 inches.
Therefore, we have SIGMA_DIST = 0.9 (inches).
Edge angles
The relative edge angles of the meetpoint were about 90, 125, and 125 degrees, as shown in the first figure.From the second figure we see that the asymmetry mean was 33.4 degrees, with a standard deviation of 7.2 degrees.
Therefore, we have SIGMA_SYM = 7.2 (degrees).
Node 4
The fourth node measured is a three-way intersection with two concrete corners and a concrete wall.
The intersection occurs where the narrow corridor meets the 6300 corridor.
The equidistant minima distance is approximately 51 inches.
Minima
We can see from the first figure that the observed minima values ranged from 50.5 to 52.6 inches.The overall mean minima value was 51.7 inches, with a standard deviation of 0.4 inches.
We can see from the second figure that the mean minima values (mean per sample) ranged from 50.8 to 52.2 inches.
The standard deviation of mean minima values was 0.3 inches.
Therefore, we have SIGMA_DIST = 0.3 (inches).
Edge angles
The relative edge angles of the meetpoint were about 110, 110, and 140 degrees, as shown in the first figure.From the second figure we see that the asymmetry mean was 33.7 degrees, with a standard deviation of 5.7 degrees.
Therefore, we have SIGMA_SYM = 5.7 (degrees).
Discussion:
Tabulating the data from prior runs and this we have the following:
| Material | EQ DIST | SIGMA_DIST | MEAN SYM | SIGMA_SYM |
| cardboard | 28" | 0.3" | 13.7° | 3.7° |
| cardboard | 28" | 0.3" | 8.4° | 3.0° |
| drywall | 38" | 0.2" | 15.5° | 3.9° |
| concrete | 51" | 0.3" | 33.7° | 5.7° |
| wood & concrete | 59" | 0.6" | 7.8° | 2.1° |
| concrete | 65" | 0.4" | 23.8° | 7.0° |
| concrete | 85" | 0.9" | 33.4° | 7.2° |
For a given material, as the equidistant minima distance (meetpoint scale) increases, we see that SIGMA_DIST also increases.
The exception to this trend occurs when changing materials; note that concrete is better than wood & concrete
and drywall is better than cardboard for consistent ultrasonic range measurements.
The angular symmetry standard deviation (SIGMA_SYM) varies more directly with the angular configuration
of the meetpoints than with material. We still see a correspondence with meetpoint scale overall,
but notice that SIGMA_SYM is similar for meetpoints with EQ DIST values of 51" and 85".
I feel that we may require a different measure for angular data than distance to symmetry.
With the collected data, I will use a matrix of relative angle differences to compute new data for comparisons.
