Sensors and Methods for Mobile Robot Positioning

140 Part II Systems and Methods for Mobile Robot Positioning
increases (or reduces) the amount of rotation when going in the other direction. Examples for Type
A and Type B errors are shown in Figure 5.9.
ccw
Nominal square path
ccw
Nominal square path
Robot
Robot
Nominal square path
cw
y
Nominal square path
cw
x
a. \designer\book\deadre53.ds4, .wmf, 06/15/95 b.
Figure 5.9: Type A and Type B errors in the ccw and cw directions. a. Type A
errors are caused only by the wheelbase error E b. b. Type B errors are caused
only by unequal wheel diameters (E d).
Figure 5.9a shows a case where the robot turned four times for a nominal amount of 90 degrees
per turn. However, because the actual wheelbase of the vehicle was larger than the nominal value,
the vehicle actually turned only 85 degrees in each corner of the square path. In the example of
Figure 5.9 the robot actually turned only total = 4×85( = 340(, instead of the desired nominal = 360(.
One can thus observe that in both the cw and the ccw experiment the robot ends up turning less than
the desired amount, i.e.,
| | < | | and | | < | | .
total, cw nominal total, ccw nominal
Hence, the orientation error is of Type A.
In Figure 5.9b the trajectory of a robot with unequal wheel diameters is shown. This error
expresses itself in a curved path that adds to the overall orientation at the end of the run in ccw
direction, but it reduces the overall rotation in the ccw direction, i.e.,
| | > | | but | | < | | .
total, ccw nominal total,cw nominal