Computational Intelligence - August 2013 - 34

as a distance sensor because it provides
more reliable and robust values. The maximum sensor range is approximately 4.7 m,
with 1 degree of angular resolution and 1
mm of linear resolution. Suppose that the
r ight wall-following task is perfor med.
Fig. 5( b) shows the counterclockwisescanned laser sensor readings in the four
angular ranges (in the right front quadrant)
L 1 ! [- 23c, 0c], L 2 ! [- 45c, - 23c], L 3 ! [- 68c, - 45c], and
L 4 ! [- 90c, - 68c] . The laser sensor values are scaled to be
within the range [0, 1]. The minimum sensor value in each
of the four laser regions serves as an input to the FC
described in (1). The outputs of the FC are the robot steering angle i ! [- 180c, 180c] and the robot forward speed
v ! [0.35, 0.55] m/s. That is, the ith rule in the FC is of the
following form:
Rule R i : If L 1 (t) is A i1 and f and L 4 (t) is A i4 , then i (t) is
i1
a and v (t) is a i2 .
To connect the robot fuzzy control problem to the
MO-RACACO, the two key factors are representation of
the optimized FC as an individual in the MO-RACACO
and performance evaluation of each individual. For the first
factor, all of the antecedent parameters m ij and v ij in the
fuzzy sets A ij, j = 1, f, 4, and the consequent parameters
a i1 and a i2 in the ith rule are optimized through the MORACACO. Each solution vector S j in the MO-RACACO
represents a robot FC and is described by (5) and (6) with
n = 4 and c = 2 . The second factor is introduced in the
next section.

A well-controlled robot should satisfy the multiple
objectives of maintaining a proper distance from
the wall being followed, making smooth turns
and changes in steering angles, and moving at
a high speed.
The constraint v ij $ 0.05 is imposed on the new v ij value to
avoid the generation of a too small or negative width of a fuzzy
set. If this constraint is violated, the new v ij value is set to 0.05.
uk
For the null solution vector s j in the inactive rule R k,
k
t
the new rule solution vector s j is also a null vector. The final
new solution vector after the operation in phase three is thus
t
t1
t Mu
S j = 8 s j , f, s j B , j = 1, f, N. As stated previously, the performance of each of these N new solutions is compared with
that of each of the original N solutions, and only the top N
ranked solutions are reserved.
IV. Multi-Objective Robot Wall-Following Control

In this section, the MO-RACACO-based FC design approach
is applied to the multi-objective control problem of a mobile
robot following a wall. This section first describes the robot
used in the experiments and then introduces the learning configuration and the objective functions proposed in the wallfollowing control task.
A. Mobile Robot Description

Fig. 5(a) shows the mobile robot, a PINONEER 3-DX
(http://robots.mobilerobots.com/), that was employed to
implement the multi-objective wall-following control task
in actual environments. The dimensions of the robot body
are 45 # 38 # 25 cm. This robot has two drive wheels, each
driven by independently controlled motor, and a caster.
Unlike in previous studies [27], [32], [33] that used sonar
sensors, this paper uses the SICK LMS-200 laser rangefinder

SN1

SN2
SN3
SN4

Figure 7 Disposition of the sonar sensors for measurement of the
parallelism between the wall and the robot.

IEEE ComputatIonal IntEllIgEnCE magazInE | august 2013

B. Learning Configuration and Multi-Objective Functions

Fig. 6 shows the training environment for the evolutionary
learning of an FC that optimizes the specified objective
functions in the wall-following control task. In the training
stage, an FC controls the steering angle i and the speed v
with a maximum number of time steps Ts ; Ts was set to
200 so that the robot moves along the wall with at least
one cycle. During the control process, the robot stops if it
collides with the wall, and the total number of control time
steps, TC , before the collision is recorded. A penalty term
T p , defined as T p = TS - TC , is included in the objective
functions to favor collision-free control. The penalty term
T p is equal to zero for collision-free control along the wall
in all of the TS time steps.
To evaluate the performance of an FC (an individual in the
colony), the following four objective functions are defined:
❏ Objective 1 ^ f1 h : minimization of the number of fuzzy rules
❏ Objective 2 ^ f2 h : maintaining a proper distance from the
wall being followed
❏ Objective 3 ^ f3 h : making smooth changes in steering angles;
❏ Objective 4 ^ f4 h : moving with a high speed.
The first function f1 is defined as the number of rules M in
an FC. The second function f2 describes the right-side distance
(RD) between the robot and the wall according to the laser

http://robots.mobilerobots.com/

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