Page 445 - Automotive Engineering Powertrain Chassis System and Vehicle Body

CHAP TER 1 4. 2 Decisional architecture

The following control commands of the steering angle
f and locomotion velocity v provide the parallel parking
manoeuvre (Paromtchik and Laugier, 1996b):

k
fðtÞ¼ f max f AðtÞ; 0 t T; (14.2.9)
vðtÞ¼ v max k v BðtÞ; 0 t T; (14.2.10)

where f max > 0 and v max > 0 the admissible magnitudes
of the steering angle and locomotion velocity re- Fig. 14.2-16 Shape of a parallel forward/backward motion.
spectively, k f ¼ 1 corresponds to a right side (þ1) or
left side ( 1) parking place relative to the traffic lane, where f _ max and f max are the maximal admissible steering
€
k v ¼ 1 corresponds to forward (þ1) or backward ( 1) rate and acceleration respectively for the steering wheel
motion. Therefore, servo-system. The value of T * min gives duration of the full
turn of the steering wheels from f max to f max or vice
8 1; 0 t < t ; * *
0
< pðt t Þ versa, i.e. one can choose T ¼ T min .
0
0
0
AðtÞ¼ cos ; t t T t ; (14.2.11) The value of T is lower-bounded by the constraints on
: T * the velocity v max and acceleration _ v max and by the con-
0
1; T t < t T; dition T < T. When the control command (14.2.10) is
*

4pt applied, the lower bound of T is:
BðtÞ¼ 0:5 1 cos ; 0 t T; (14.2.12)
T 2pv ðD1Þ
0
T min ¼ max ; T * ; (14.2.14)
0
*
where t ¼ T T * ; T < T: The shape of the type of paths _ v max
2
that corresponds to the controls (Equations 14.2.11 and where v ðD1Þ v max ; empirically obtained function,
0
14.2.12) is shown in Fig. 14.2-16. serves to provide a smooth motion of the vehicle when
The commands (Equations 14.2.9 and 14.2.10) are
open-loop in the (x, y, q)-coordinates. The steering wheel the available distance D1 is small. aims to obtain the
The computation of T and f
max
servo-system and locomotion servo-system must execute maximal values such that the following ‘longitudinal’ and
the commands (Equations 14.2.9 and 14.2.10), in order ‘lateral’ conditions are still satisfied:
to provide the desired (x, y)-path and orientation q of the
vehicle. The resulting accuracy of the motion in the (x, y, q)- jðx T x 0 Þcosq þðy T y 0 Þsinq jhD1; (14.2.15)
0
0
coordinates depends on the accuracy of these servo-
systems. Possible errors are compensated by subsequent jðx 0 x T Þsinq 0 þðy T y 0 Þcosq 0 jhD2: (14.2.16)
iterative motions. Using the maximal values of T and f assures that
max
For each pair of successive motions (i, iþ1), the co- the longitudinal and, especially, lateral displacement of
efficient k v in Equation 14.2.10 has to satisfy the equa- the vehicle is maximal within the available free parking
tion k v;iþ1 ¼ k v;i that alternates between forward and
space. The computation is carried out on the basis of the
backward directions. Between successive motions, when
model (Equation 14.2.1) when the commands (Equa-
the velocity is null, the steering wheels turn to the op-
tions 14.2.9 and 14.2.10) are applied. In this computa-
posite side in order to obtain a suitable steering angle
tion, the value of v max must correspond to a safety
f max or f max to start the next iterative motion. requirement for parking manoeuvres, e.g. v max ¼ 0:75 m/s
In this way, the form of the commands in Equations was found empirically.
14.2.9 and 14.2.10 is defined by Equations 14.2.11 At each iteration i the parallel parking algorithm is
and 14.2.12 respectively. In order to evaluate Equations summarized as follows:
14.2.9 14.2.12 for the parallel parking manoeuvre, the
)
durations T and T, the magnitudes f max and v max must 1. Obtain available longitudinal and lateral displace-
be known. ments D1 and D2 respectively by processing the
The value of T is lower-bounded by the kinematic sensor data.
)
and dynamic constraints of the steering wheel servo- 2. Search for maximal values T and f max by evaluating
system. When the control command (Equation 14.2.9)is the model (Equation 14.2.1) with controls (Equa-
)
applied, the lower bound of T is: tions 14.2.9 and 14.2.10) so that the conditions
(Equations 14.2.15 and 14.2.16) are still satisfied.
( s ffiffiffiffiffiffiffiffiffiffi)
f max f max 3. Steer the vehicle by controls (Equations 14.2.9 and
*
T min ¼ p max € ; € ; (14.2.13) 14.2.10) while processing the range data for collision
f
f
max
max
avoidance.
452