Page 98 - Introduction to Autonomous Mobile Robots
P. 98
Mobile Robot Kinematics
Y =Y I 83
G
x ˆ
β
goal
X =X I
G
Y R
ρ
α
X R
v
θ
ω ∆x
Figure 3.19
Robot kinematics and its frames of interests.
The task of the controller layout is to find a control matrix , if it exists
K
k 11 k 12 k 13
,
(
K = with k = kt e) (3.45)
ij
k 21 k 22 k 23
such that the control of vt() and ω t()
R
vt() ⋅ x
ω t() = Ke = K y (3.46)
θ
drives the error toward zero. 2
e
lim et() = 0 (3.47)
t → ∞
2. Remember that v(t) is always heading in the X direction of the robot’s reference frame due to the
R
nonholonomic constraint.
