Page 87 - Introduction to Autonomous Mobile Robots

Chapter 3
72
Recall that in the case of mobility, an increase in the rank of C β() implied more kine-
1 s
matic constraints and thus a less mobile system. In the case of steerability, an increase in
β
the rank of C () implies more degrees of steering freedom and thus greater eventual
1s s
β
maneuverability. Since C β() includes C () , this means that a steered standard wheel
1 s 1s s
can both decrease mobility and increase steerability: its particular orientation at any instant
imposes a kinematic constraint, but its ability to change that orientation can lead to addi-
tional trajectories.
The range of δ can be specified: 0 ≤ δ ≤ 2 . The case δ = 0 implies that the robot
s s s
has no steerable standard wheels, N = 0 . The case δ = 1 is most common when a robot
s
s
configuration includes one or more steerable standard wheels.
For example, consider an ordinary automobile. In this case N = 2 and N = 2 . But
f s
the fixed wheels share a common axle and so rank C = 1 . The fixed wheels and any
1f
one of the steerable wheels constrain the ICR to be a point along the line extending from
the rear axle. Therefore, the second steerable wheel cannot impose any independent kine-
β
matic constraint and so rank C () = 1 . In this case δ = 1 and δ = . 1
1s s m s
The case δ = 2 is only possible in robots with no fixed standard wheels: N = . 0
s f
Under these circumstances, it is possible to create a chassis with two separate steerable
standard wheels, like a pseudobicycle (or the two-steer) in which both wheels are steerable.
Then, orienting one wheel constrains the ICR to a line while the second wheel can con-
strain the ICR to any point along that line. Interestingly, this means that the δ = 2
s
implies that the robot can place its ICR anywhere on the ground plane.
3.3.3 Robot maneuverability
The overall degrees of freedom that a robot can manipulate, called the degree of maneuver-
ability δ M , can be readily defined in terms of mobility and steerability:

δ = δ + δ (3.42)
M m s
Therefore maneuverability includes both the degrees of freedom that the robot manipu-
lates directly through wheel velocity and the degrees of freedom that it indirectly manipu-
lates by changing the steering configuration and moving. Based on the investigations of the
previous sections, one can draw the basic types of wheel configurations. They are depicted
in figure 3.14
Note that two robots with the same δ M are not necessarily equivalent. For example, dif-
ferential drive and tricycle geometries (figure 3.13) have equal maneuverability δ M = . 2
In differential drive all maneuverability is the result of direct mobility because δ m = 2 and
δ = 0 . In the case of a tricycle the maneuverability results from steering also: δ m = 1
s
and δ = 1 . Neither of these configurations allows the ICR to range anywhere on the
s
plane. In both cases, the ICR must lie on a predefined line with respect to the robot refer-