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Unified Control Design for Autonomous Vehicle 297

maneuvers are formulated into an integrated framework with forward tracking,
backward tracking, driving, and steering at kinematics and dynamics levels,
respectively. A nonlinear controller with a few design parameters is designed
formaneuverswithsimultaneous driving as well as steering for vehicle tracking:
in both forward tracking and backward tracking maneuvers. Tracking stability
is ensured by the proper design of a stable performance target dynamics with a
set of sufficient conditions for selecting design parameters. Simulation results
show the effectiveness of the control scheme in both tracking cases. Tracking
performance is evaluated with respect to the selection of parameters: the desired
intervehicular spacing l and the desired steering angle multiplier p. The effects
of the parameter value selections on the tracking performance are also examined
via extensive simulations.

8.2 DYNAMICS OF TRACKING MANEUVERS
8.2.1 Vehicle Kinematics and Dynamics
Consider a car-like mobile robot with front wheels for steering and rear wheels
for driving. Its kinematic model can be described by the following equation
[18,19]:

˙ q = G(θ, γ)µ (8.1)

T
where q =[x y θ γ ] is the state configuration of the vehicle with (x, y)
being the generalized coordinates of the reference point located at the center of
the rear axle, θ the heading angle of the vehicle with respect to the x-axis, and
T
γ the steering angle of the front wheels; µ =[v ω] contains the velocity v
and the steering rate ω; and

cos θ 0
 
sin θ 0
 
 
G(θ, γ) =  1  (8.2)
 tan γ 0
a
0 1
with a being the length of the vehicle.
A dynamic model of the vehicle is as in (8.3)

˙ q = G(θ, γ)µ
(8.3)
˙ µ = u
T
where u =[u m u s ] consists of the driving acceleration u m and the steering
acceleration u s homogenous to the driving and steering torques.

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c008” — 2006/3/31 — 16:43 — page 297 — #3