Page 65 - Introduction to Autonomous Mobile Robots

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Y I Chapter 3

X R

θ
Y R

X I

Figure 3.2
The mobile robot aligned with a global axis.

cos θ sin θ 0
R θ() = – sin θ cos θ 0 (3.2)
0 0 1

This matrix can be used to map motion in the global reference frame X Y,{ I I } to motion
·
in terms of the local reference frame X Y,{ R R } . This operation is denoted by R θ()ξ I
because the computation of this operation depends on the value of : θ

· π ·
ξ = R ---()ξ I (3.3)
R
2
π
For example, consider the robot in figure 3.2. For this robot, because θ = --- we can
2
easily compute the instantaneous rotation matrix R:

01 0
π
R ---() = –0 0 (3.4)
1
2
00 1