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314 Autonomous Mobile Robots

as its derivatives ˙ φ and ¨ φ. These requirements are vital and also implemented
in other vehicle-following systems. For example, the inclusion of relative dis-
tance, velocity, and even acceleration in the controller have been well known
and implemented in longitudinal controls in order to improve the stability of
the tracking system [4,5,10]. Likewise, for steering control, the controllers
developed based on kinematic models generally need the relative angle and/or
its first derivative [2,10] whereas those based on dynamics model [11,12,20]
may or may not require the second derivative.
In practice, the relative distance and angle can be measured by a ranging
sensor. Relative velocities and particularly relative accelerations are more diffi-
cult to obtain. In general, there are two ways of getting those measurements. The
first one is to utilize a wireless communication channel to transmit the vehicu-
lar measurements such as velocity, acceleration, and yaw rate of the leader
vehicle to the follower vehicle [5,10]. The relative velocities and/or accelera-
tions are computed based on the geometric and dynamic relationships of the
two vehicles. The second way relies on the high accuracy of the ranging sensor
to estimate the derivatives using numerical calculations or derivative filtering
[2,12]. This method is less accurate than the first one but more suitable for
low-speed applications and does not require a communication channel.

8.4 TRACKING PERFORMANCE EVALUATION
The nonlinear controller developed in the previous section needs verification
and the effects of parameter selections are to be evaluated. In this section, we
focus on the effects and evaluations of the design parameters l and p for the
dynamics-based controller. The closed-loop system’s parameters λ and ξ are set
as constants of 1 and 0.5, respectively. Different sets of design parameters (l, p)
are tested for both look-ahead and look-behind tracking control.
Some limits are chosen based on the real physical limits of our test-bed
car-like vehicle. The steering angle of the vehicle is limited as |γ |≤ γ max =
π/9 rad (=20 ). Other limits are chosen as follows: d max = 8 m as the reliable
◦
range of the sensing; l min = 1 m for safety stopping; and p min = 0.1 for some
minimum sensitivity to steering.
The evaluation is carried out by numerical simulation using the platform
® 2
integrating ADAMS ®1 and Simulink . The ADAMS is a mechanical proto-
typing package and is used to construct two mobile robot vehicles. Simulink
is used to model the proposed nonlinear tracking controller. The integration
of these two powerful simulation platforms produces a simulation platform
for mobile robotics and associated advance control designs. It has the bene-
fits of doing away with the dynamic modeling of vehicles and the motions are

1
Registered trademark of MSC Software Corporation.
2 Registered trademark of The MathWorks, Inc.

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c008” — 2006/3/31 — 16:43 — page 314 — #20