Page 69 - Introduction to Autonomous Mobile Robots

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Y R Chapter 3

β

Robot chassis
ϕ, r
l A v
α

X
P R
Figure 3.4
A fixed standard wheel and its parameters.

Under these assumptions, we present two constraints for every wheel type. The first con-
straint enforces the concept of rolling contact – that the wheel must roll when motion takes
place in the appropriate direction. The second constraint enforces the concept of no lateral
slippage – that the wheel must not slide orthogonal to the wheel plane.

3.2.3.1 Fixed standard wheel
The fixed standard wheel has no vertical axis of rotation for steering. Its angle to the chassis
is thus fixed, and it is limited to motion back and forth along the wheel plane and rotation
around its contact point with the ground plane. Figure 3.4 depicts a fixed standard wheel A
and indicates its position pose relative to the robot’s local reference frame X Y,{ R R } . The
α
A
l
position of is expressed in polar coordinates by distance and angle . The angle of the
β
wheel plane relative to the chassis is denoted by , which is fixed since the fixed standard
wheel is not steerable. The wheel, which has radius , can spin over time, and so its rota-
r
tional position around its horizontal axle is a function of time : t ϕ t() .
The rolling constraint for this wheel enforces that all motion along the direction of the
wheel plane must be accompanied by the appropriate amount of wheel spin so that there is
pure rolling at the contact point:
·
·
l
sin ( α + β) – cos ( α + β) –()cos β R θ()ξ – rϕ = 0 (3.12)
I