Page 72 - Introduction to Autonomous Mobile Robots

Mobile Robot Kinematics

Y R 57

β(t)
B
d
Robot chassis
ϕ, r
A
l v
α
d
X
P R
Figure 3.6
A castor wheel and its parameters.

·
·
sin ( α + β) – cos ( α + β) –()cos β R θ()ξ – rϕ = 0 (3.17)
l
I
The castor geometry does, however, have significant impact on the sliding constraint.
The critical issue is that the lateral force on the wheel occurs at point A because this is the
attachment point of the wheel to the chassis. Because of the offset ground contact point rel-
ative to , the constraint that there be zero lateral movement would be wrong. Instead, the
A
constraint is much like a rolling constraint, in that appropriate rotation of the vertical axis
must take place:

·
·
cos ( α + β) sin ( α + β) d + lsin β R θ()ξ + dβ = 0 (3.18)
I
In equation (3.18), any motion orthogonal to the wheel plane must be balanced by an
equivalent and opposite amount of castor steering motion. This result is critical to the suc-
·
β
cess of castor wheels because by setting the value of any arbitrary lateral motion can be
acceptable. In a steered standard wheel, the steering action does not by itself cause a move-
ment of the robot chassis. But in a castor wheel the steering action itself moves the robot
chassis because of the offset between the ground contact point and the vertical axis of rota-
tion.