Page 321 - Autonomous Mobile Robots

Unified Control Design for Autonomous Vehicle 309

T
where µ input =[v input ω input ] ,
with

v input = v +{cos(((1 + f )/2)γ ){−λl + f (d + λd)
˙
× cos(pγ − φ) + fd( ˙ θ + ˙ φ) sin(pγ − φ)}}
−1
×{cos[(p − (1 + f )/2)γ ]} (8.37)

ω input
˙ θ λ
1 + f tan γ cos(((1 + f )/2)γ )
=− − tan p − γ −
p p 2 ap cos[(p − ((1 + f )/2))γ ]
˙
×{−λl + f (d + λd) cos(pγ − φ) + fd( ˙ θ + ˙ φ) sin(pγ − φ)}
˙
f (d+λd) sin(φ − ((1 + f )/2)γ )+fd( ˙ θ + ˙ φ) cos(φ − ((1 + f )/2)γ )
+
lp cos[(p − ((1 + f )/2))γ ]
(8.38)
The above development of the kinematics-based vehicle-following control-
ler is summarized in the following theorem.

Theorem 8.1 Consider the car-like vehicle tracking maneuvers of forward
tracking, shown in Figure 8.1, and backward tracking, shown in Figure 8.2.
The kinematic motion of these tracking maneuvers is defined collectively as
the kinematics (8.1) of both vehicles and the virtual intervehicular connec-
tion (8.4). Define the tracking error ˜z in (8.5) as the difference between the
output of the follower vehicle (8.5) and the virtual intervehicular connec-
tion (8.4). The tracking target performance in ˜z is defined by the stable first
order system (8.29) and can be ensured if the nonlinear control laws (8.37) for
driving and (8.38) for steering are applied, and the following conditions are
satisfied:

• Forward tracking: f = 1


v d > 0


λ> 0

(8.39)
0 < l < d max


 π
0 < p <
2γ max
© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c008” — 2006/3/31 — 16:43 — page 309 — #15