Sensors and Methods for Mobile Robot Positioning

22 Part I Sensors for Mobile Robot Positioning
cot2 i
&cot2 o
' d l
(1.8)
where
2 i = relative steering angle of the inner wheel
2 o = relative steering angle of the outer wheel
l = longitudinal wheel separation
d = lateral wheel separation.
For the sake of convenience, the vehicle steering angle 2 can be thought of as the angle (relative
SA
to vehicle heading) associated with an imaginary center wheel located at a reference point P as 2
shown in the figure above. 2 can be expressed in terms of either the inside or outside steering
SA
angles (2 i or 2 o) as follows [Byrne et al., 1992]:
cot2 SA
'
d 2l %cot2 i
(1.9)
or, alternatively,
cot2 SA
' cot2 o
& d 2l .
(1.10)
Ackerman steering provides a fairly accurate odometry solution while supporting the traction and
ground clearance needs of all-terrain operation. Ackerman steering is thus the method of choice for
outdoor autonomous vehicles. Associated drive implementations typically employ a gasoline or diesel
engine coupled to a manual or automatic transmission, with power applied to four wheels through
o SA i
P 2
P 1
l
d
Y
X
Figure 1.8: In an Ackerman-steered vehicle, the extended axes for all wheels
intersect in a common point. (Adapted from [Byrne et al., 1992].)