IEEE Robotics & Automation Magazine - June 2013 - 56

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Figure 5. IR calibration curves obtained from different sensors:
(a) original data and (b) curves after unbiasing. Y axis are analog
to digital (AD) units, and on the X axis distance is reported.

determine whether a measure can be considered reliable or
not, e.g., in the case of an image captured from a camera.
Infrared Sensors
Each infrared sensor, a GP2Y0A02YK from Sharp, is composed
of an emitter and a separate detector. The analog range measurement is obtained by a triangulation of the spot projected on
the obstacle. Intensity is discarded; thus, the sensor is insensitive
to obstacle reflectance. However, different from the other sensors mounted on the robot, the relation between the output
voltage of the sensor and distance is not monotonic and shows
a maximum near 20 cm. Therefore, the same reading can refer
to two different distances [see Figure 5(a)], and this ambiguity
is located in a range that can be dangerous with respect to the
safety of the robot (e.g., collision avoidance). Therefore, a dangerous and safe zone must be considered in the IR curve. One
way to overcome this problem is to consider subsequent

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Figure 6. Gyroscope calibration curve: red asterisks represent the
measured data, and the blue line is the calibration curve achieved
by least-square estimation.

IEEE ROBOTICS & AUTOMATION MAGAZINE

june 2013

readings to disambiguate the two zones. The calibration was
effected for each unit using a standard polynomial fitting, considering a separate subset of data for each zone. As shown in
Figure 5(a), a small difference results between the tested units;
however, it can be reduced to acceptable values by a simple vertical translation of the calibration curve: the result of this operation can be viewed in Figure 5(b). The operative range can be
considered to be from 7 to 120 cm: in our implementation, out
of this range, the measures are useless due to the noise and discretization of the converter. Errors are particularly important
for distances greater than 80 cm: the standard deviation of the
measure, even averaging 64 samples, is near 10 cm and affects,
in particular, localization and mapping tasks. Instead, for distances between 25 and 50 cm, the repeatability is about 1 cm.
Along this range, the mean error is below 2 cm.
Rotation Sensors
This section briefly describes the behavior of both gyro and
magnetometer sensors. The gyro is a two-axes ADXRS150
sensor from Analog Devices, oriented along the roll and yaw
axes of the robot. At the moment, only the yaw axis, which
measures the rotational speed of the robot, is considered.
The magnetometer is a HMC1043 sensor from Honeywell. It is used to sense the direction of the magnetic field
along the moving plane of the robot by a couple of orthogonal axes that span such a plane. Both the gyro and magnetometer require calibrations that are performed by
self-rotations of the platform. The gyro revealed a linear
behavior with respect to the rotational velocity of the robot
(see Figure 6), and the magnetometer axes showed the
expected sinusoidal profiles, although particular care about
the biases of such signals has to be taken. In fact, these
biases assume different values at each power on: this
requires that, whenever the robot is turned on, a selfcalibration has to be done. Two remarks are in order: first,
the currents flowing in the circuits of the robot have a negligible effect on the readings of the magnetometer; second,
the temperature affects the gyro bias, and this makes its
removal difficult, and, thus, velocity integration is unreliable
over long time intervals. During navigation, the gyro error
maintained the aforementioned characteristics while the
magnetometer showed important distortions in some areas.
Such distortions were induced by large iron beams under
the floor. One typical situation is depicted in Figure 7: in this
test, SAETTA traveled two straight paths inter-leaved by a
90° rotation. During self-rotation, the field direction was
constant, and the angle was correctly measured (the sensor
returned 88.8°); on the contrary, during the straight paths,
the reading exhibited large errors because they passed over a
beam under the floor that modified the magnetic field.
Obviously, any large ferromagnetic mass induces the same
problems. When no disturbing mass is present, the compass
is highly reliable as can be seen in Figure 8. In this test, the
magnetometer measures are compared with the odometry
ones that can be considered reliable due to the slow velocity
imposed to actuators.

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - June 2013