Scholarly article on topic 'Range Finder Models for Mobile Robots'

Range Finder Models for Mobile Robots Academic research paper on "Civil engineering"

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Procedia Engineering
OECD Field of science
{"Mobile robots" / "Grid maps" / "Sensor fusion" / Sonar / "Position Sensitive Detectors"}

Abstract of research paper on Civil engineering, author of scientific article — Jaroslav Hanzel, Marian Kľúčik, Ladislav Jurišica, Anton Vitko

Abstract The paper deals with a problem of modeling of an unknown environment by mobile robot control system. The robot is equipped with sensory system constructed for measuring distances to obstacles in the surrounding environment. The range data is used to compute grid a based model of the environment utilized for navigation tasks. The contribution accentuates the proposal of appropriate sensor models for the range finders. The models are designed on the basis of the sensor identification procedures and they are used to interpret distance measurements by sensory fusion algorithms. Experimental examples of occupancy grids built from real data recorded in the environment are presented.

Academic research paper on topic "Range Finder Models for Mobile Robots"

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Procedía Engineering 48 (2012) 189 - 198 ;

MMaMS 2012

Range finder models for mobile robots

Jaroslav Hanzela*, Marian Kl'ucika, Ladislav Jurisicaa, Anton Vitkoa

aInstitute of control and industrial informatics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovicova

3, Bratislava, 812 19


The paper deals with a problem of modeling of an unknown environment by mobile robot control system. The robot is equipped with sensory system constructed for measuring distances to obstacles in the surrounding environment. The range data is used to compute grid a based model of the environment utilized for navigation tasks. The contribution accentuates the proposal of appropriate sensor models for the range finders. The models are designed on the basis of the sensor identification procedures and they are used to interpret distance measurements by sensory fusion algorithms. Experimental examples of occupancy grids built from real data recorded in the environment are presented.

© 2012 Published by Elsevier Ltd.Selection and/or peer-review under responsibility of the Branch Office of Slovak Metallurgical Society at Faculty of Metallurgyand FacultyofMechanical Engineering,Technical UniversityofKosice

Keywords: mobile robots, grid maps, sensor fusion, sonar, Position Sensitive Detectors

1. Introduction

Autonomous navigation of a mobile robot in the environment requires an ability of the robot to perceive the environment in certain a way. The robot is equipped with a sensor system designed specifically for this purpose. The sensor system provides information about actual configuration of the surrounding environment. Collected sensory information is then processed by the robot control system. The control system consequently evaluates the position and distance of the closest obstacles. Resulting data are used in order to find obstacle free path across the environment to reach a desired goal. Another task of the robot control system is to create a model of the environment, called the map of the environment. The construction of the map is based on the gathered spatial information. It consists of determined empty areas of the environment, which enables a free movement to the robot and sensed obstacles, presenting a potential danger of collision during the motion.

2. Sensory system

The sensor system allows the robot control system to obtain information necessary for autonomous robot navigation. Ultrasonic sensor - sonar, often called an ultrasonic rangefinder, is used for the purpose of sensing obstacles around the robot quite frequently. They are used to measure distances in range of tens of centimeters and meters. Thus they are often used in robot sensor systems [8], [10]. These sensors have a number of advantageous features such as easy processing of

* Corresponding author.

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1877-7058 © 2012 Published by Elsevier Ltd.Selection and/or peer-review under responsibility of the Branch Office of Slovak Metallurgical Society at

Faculty of Metallurgy and Faculty of Mechanical Engineering, Technical University of Kosice


measured data, safety and low cost. On the other hand, the information obtained by ultrasonic sensors is noticeable uncertain. The considerable number of errors of the measurements results from the physical principle of operation of these sensors. Other systems used to measure distances are optical systems. They have much wider area of applications ranging from distances in solar system [2] to distances comparable with wavelength of visible light [15]. In the field of mobile robotics it is possible to measure distances to obstacles by the use of infrared (IR) or laser sensors. Infrared sensors are characterized by simple processing of measurements, high safeness as well as acceptable price. However, the IR distance sensors have a number of unsuitable properties that complicate the measurement. The solution is to equip the robot sensory system with ultrasonic as well as infrared rangefinders. Such measuring system combines the advantages of both types of sensors and simultaneously eliminates their negative qualities. The proposed sensing device obtains information about surrounding environment by performing the distance measurement by using ultrasonic and infrared sensors.

2.1. Ultrasonic sensor

There is a vast range of ultrasonic scanners from various manufacturers suitable for use in mobile robotics. These may be individual sensors or complete solutions ready to use for direct ultrasonic measurement. In robotic sensory systems, there is often used an ultrasonic range finder Polaroid [10]. However such solution is almost useless for use in the sensory system of small mobile robot due to over-sized parameters such as measuring range, sensor size and moreover it is too expensive. For this reason, the ultrasonic sensors made by Nippon Ceramic Company [8] were chosen as an appropriate solution. They are readily available at a reasonable price and provide satisfactory results. Ultrasonic sensor is composed of a separate transmitter (T40-16) and a receiver (R40-16) as shown in Fig. 1(a). Each unit has a cylindrical shape with diameter of 16 mm and height of 12 mm. They work at the resonance frequency of 40 kHz. The measuring range of the sensor is approximately from 10-15 cm to 3-4 m and it is sufficient for navigation of the robot in the working environment.

Fig. 1. Components of the ultrasonic sensor: transmitter T40-16 and receiver R40-16 (a) and disassembled PSD sensor GP2D120 (b).

2.2. Infrared sensor

PSD (Position Sensitive Detectors) are photoelectric sensors that allow remotely detect movement, measure the size or determine the shape of the distant object. In mobile robotics they are used in similar manner as sonars, to measure the distance of the robot from the obstacles. Infrared light is employed for the measurement in the case of the PSD sensors. Sensor transmits a beam of the infrared light in the direction of the measurement and it is sensed after the reflection by the object surface. The receiving element of the sensor is able to precisely determine the position of the incident light beam on its active surface. Output potential of the active sensor surface corresponds to the position of the incident beam of light, which is, at the same time, proportional to the distance of the reflecting surface. In principle, one dimensional PSD sensor is a photo-diode with an active photosensitive area and a shape of a rectangular strip up to tens of mm of length.

The IR sensors used in proposed sensor device were Sharp sensors of the type GP2D120 and GP2Y0A02YK [12]. In Fig. 3 there is displayed a disassembled sensor GP2D120. On the left hand side of the component there is the active element of the sensor (light emitting diode - LED) which emits an infrared light beam. On the right hand side there is the PSD sensor itself that senses the beam reflected from obstacles. These sensors have a voltage output corresponding with the measured distance and the scanning range of the GD2D120 sensor is from 4 cm to 40 cm and of the sensor GP2Y0A02YK from 20 cm to 150 cm [12]. The GD2D120 sensor was used to measure distances ranging from 5 cm to 25 cm and the sensor GP2Y0A02YK was used for the measurement of larger distances.

2.3. Implementation of the scanning system

The combined sensor system is built on microcontroller ATmega16. The microcontroller is used to merge individual attached peripherals consists of ultrasonic and infrared sensing devices together with a rotary platform. It enables to turn the sensors to desired direction during the measurement. The platform is driven by a stepper motor and rotates in the range of angles of 360° with the step size of 0.9°. The ultrasonic measuring system is composed of transmitter and receiver circuits. These circuits are connected to the programmable integrated circuit (ATmega16). The task of the microcontroller is to maintain transmission of ultrasonic signal and to process the received signal. To the microprocessor are also connected both the PSD sensors. It provides the processing of the sensor voltage signal and it decides on the choice of the output value according to the measured distance. The microcontroller controls also the movement of the stepper motor. The integrated circuit also communicates with the main control computer (PC) by means of serial interface RS 232. The PC sends commands to the measuring device and waits for the answer. After processing and executing of the received command, the sensor system device sends the results back to the PC. A simple communication protocol is used for needs of communication. The measurement results include values of the stepper motor position, time of flight of ultrasonic signal (for potential future processing), the distance measured by the ultrasonic sensor, the distance measured by IR sensor as well as a checksum for verification of error-free data transfer. The constructed sensing device is depicted in Fig. 2.

Fig. 2. The proposed experimental sensory system. 3. Modelling of the robot environment

The autonomous robotic system must be able to react automatically and intelligently during the execution of the given tasks. The intelligent behavior is impossible without a suitable representation of the working environment often called a map of the environment.

In the mobile robotics there are two basic environment modelling approaches: the metric and the topological maps. These maps are quite different in the point of view of the stored qualitative and quantitative information. The spatial structure of the environment is represented in metric maps by basic geometric elements, which can be rigid or adaptive. Metric maps comprise of large amount relatively accurate data about the environment. Therefore these methods are suitable for construction of small local maps. The topological maps express the spatial structure of the environment by more abstract form by means of relatively small amount of information. They allow an effective representation of large-scale environments. Hence, they are suitable for global maps of the environment.

The sensor system of mobile robots often consists of various types of sensors. Moreover, the obtained measurement from the sensor is always more or less inaccurate or uncertain. These facts considerably complicate the process of sensing of the working environment and construction of its model. The solution of this problem is to combine information from various sources. The combination of multiple sensory data is referred as sensor fusion or data fusion [6], [13]. It means that measurements of several sensors of various types or multiple measurements of one sensor are integrated into unified internal representation.

The representation of the environment by occupancy grid introduced by Moravec and Elfes, [7], [3] provides an effective framework for the data fusion from multiple sensors and sensing positions. The environment is represented by rigid geometric elements acquired by discretization of modelled space into the regular tessellation. The basic elements of

occupancy grid are called cells and they usually have rectangular shape. Each cell of the grid represents some area and contains some value which indicates the state of the environment. From the point of view of robot navigation tasks the represented piece of space can occur in one of the two states: it is empty and thus useful for robot motion, or it is occupied and therefore inadequate for robot motion. The grid is actualized with the new sensor reading by the so called sensor model. The sensor model is overlaid on the grid after acquisition of a new measurement and each cell of the grid is updated. The shape of the sensor model is given by a type of sensor. The sensor models should be defined in a uniform statistical framework. The most often grid map construction algorithms utilize the theory of fuzzy sets, Dempster-Shafer theory of evidence and the theory of probability [4], [9], [11].

The most common data fusion method use Bayesian estimation [7], [3]. In the probabilistic grids each cell stores a probabilistic estimate of the occupancy of that cell in the form of a discrete random state variable s(cj). In principle the cells of grid contain the probability to be occupied by the obstacle. The sensor models are defined as probability density functions and so they can be combined in the same grid. Occupancy grid is representing a two-dimensional environment as a discrete structure of finite number of square elements - cells with the size of the edge SxS. The grid is defined as set U which can be formally written as U = {c1, ..., cM} for j = 1, ..., M. Next, set of range readings R = {r1, ..., rn} collected at known locations L = {l1, ..., lk} is assumed. To each cell cj from U is assigned a real number P(s(cj) = O\r1, ..., rn), which indicates the information on cj gathered from R. Because the sensor data is uncertain, this value represents an estimate of the cell state. Consequently it is possible, on the basis of calculated value, to determine the classification of each cell to a set O of cells occupied by obstacles (even partially), or to a set E of empty cells. The cell states are exclusive and exhaustive and they satisfy the condition

The incremental updating of sensory information is accomplished by application of a sequential formulation of Bayes' theorem. Current estimate P(s(cj) = O\r1, ..., rn-1) of the state of a cell cj is based on ob servations R = { r1 , . . . , rn1 } . Cell state estimate improved by new observation rn is given by followed equation:

where P(s(cj) = X\r1, ..., rn-1) is the prior estimate of the cell state on the basis of measurements r1, ..., rn-1, P(r\s(cj) = X) is determined from sensor model and Xe{E,O}. The initial states of the cells are given by prior probability estimates. Usually the grid is initialized with maximum entropy value P(s(cj) = E) = P(s(cj) = O) = 0.5 [3]. This prior estimate sets the state of cell to "unknown".

4. Sensor models

Practical application of the sensors for measuring of relative distances to the nearest obstacles is accompanied with a variety of problems. These problems are given by physical principle of their operation and the collected data from the sensing process is uncertain. That fact considerably complicates the process of sensing of the working environment. The use of an appropriate and adjusted sensory model represents a successful approach to minimize the amount of uncertainty in processing of measured data for a robot navigational map. Such advanced sensory model can be constructed on the basis of the data obtained by identification of essential parameters.

The exact determination of object position is impossible due to the uncertainty of its relative distance and its direction in respect to the sensor. The measured distance r is always affected by an error. This error is relatively insignificant in the case of ultrasonic sensors and it is caused by physical properties of the air such as temperature, humidity, pressure and turbulence [14]. In the case of infrared sensors the uncertainty of measured distance is greater and it is apparently caused by refractive surface properties of sensed object. On the other hand, the so-called multiple reflections impose great uncertainty on distance measured by ultrasonic sensors. This case occurs when the incidence angle of signal impinged on the obstacle is larger than so-called critical angle. The reflection of signal is mainly specular and the signal is reflected away from the sensor. Consequently it is never captured by the sensor or it may reach the receiver after multiple reflections, what is called long reading. The value of the critical angle strongly depends on the surface characteristics of the object.

The object angular position uncertainty is given by means signal propagation through the space. The ultrasonic signal propagates from the sensor to space in the form of so called radiation cone. The axis of the cone is in scanning direction and angle of the radiation cone is often fairly wide. This fact makes it impossible to determine the exact angular position of

P[s(cj) = O] + P[s(cj) = E] = 1.


object that originates the echo. The sensed object can be situated anywhere along the arc of circumference of the measured distance radius. So the angle of the radiation cone is essential parameter in the uncertainty model of the ultrasonic sensor. On contrary, the infrared light is emitted by PSD sensor in narrow beam and the angular position uncertainty of the object is in principle negligible. In this case, the important sensor model parameter is width of the light beam.

For modelling of the general behavior of the sonar in range and angular resolution, a radial modulation function fd and an angular radiation function fa are introduced [4], [9]. With increase of distance p of cell Cj from the sensor, the confidence for assertion empty/occupied decreases. This fact is modelled by the radial modulation function

fAp)=1_tanh(2(p-pi (3)

The parameter pv is called visibility radius and it defines the distance from the sensor where certainty of assertions occupied/empty proceeds continuously to uncertainty [4], [9]. This function has universal relevance and therefore it was applied also in the model of infrared sensor.

The angular radiation function fa is used for the purpose of modelling of the uncertainty in angular resolution given by the wide radiation cone of the sonar [4], [9]. Since the intensity of the ultrasonic waves decreases to zero at the borders of radiation cone, degree of certainty of each assertion (empty, occupied) is assumed to be higher for points closer to the beam axis. This is realized by the angular modulation funCtion

) = p ) 0 , (4)

fal j | 0 \e>ek

where P(Q) is the radiation directivity function, 0 is angular distance measured with re spect to the radiation c o ne axi s and 0k is so-called limiting angle of the radiation cone of given sensor.

The important value of the sonar limiting angle can be computed from certain intrinsic parameters of the sonar. Generally, the size of the limiting angle of radiation cone depends on the ultrasound wavelength and dimension of the sensor active element [1]. In order to analyze sonar radiation characteristics, the transducer can be treated as a plane circular piston. The radiation characteristics is then given by the radiation directivity function [1], [10]

P(d) = 2 J1(kasin(^.), (5) ka sin(#)

where J1 is the Bessel function of the first order, k = 2n / l is the wave number dep endent on the w avelength l, a is the piston radius and 0 is the azimuthal angle measured with respect to the radiation cone axis. For used sensor the valid values are a = 0.01921 m and l = c /f, where c is the sound speed in air and f = 49.410 kHz [10].

The shape of the function intended to model lateral uncertainty of the measurement obtained by infrared sensor is quite different from that of sonar. The PSD sensor emites a beam of infrared light and the optical signal propagates through space in the form of relatively narrow belt. This belt has generally constant width over entire measuring range. So the sensor has radiation characteristics of shape of narrow rectangle and can be called radiation belt. Hence the position uncertainty of object in respect of belt axis is independent from the measured distance. Uncertainty function is therefore defined as function of lateral distance of the grid cell from axis of the measurement. This function is called lateral modulation function and is similar to angular radiation function, however in lateral domain. The proposed definition of the function is given by following equation:

where P(s) is function analogous to the radiation directivity function, s is lateral di stanc e me a sured with respect to the radiation belt axis and sk is so-called limiting width of the radiation belt of given sensor.

The formulation of radiation directivity function of the ultrasonic sensor infers from theory of mechanical waves and it is defined by sensor parameters. In contrast of sonar, the infrared sensor is emitting light and so this formulation is not appropriate to model the sensor lateral uncertainty. Hence the polynomial function of second order was chosen as radiation

directivity function for infrared sensor. Consequently the following function P(£ was proposed to formulate decrease of object position certainty with increase of lateral distance from measurement axis:

p£) = £_Z££_, (7)

where £ is lateral distance of computed grid cell measured with resp ect to the radiation belt axis an d £ is limiting width of the radiation belt.

The key element in the process of interpretation of sensory measurements to the grid based environment representation is the sensor model. Role of the sensor model is conversion of the distance value obtained from the sensor to the probability of occupancy of given cell by an obstacle. On the basis of work [11] the following probabilistic sensor model intended to interpret range data measured by sonar was proposed:

p[r\s(cj )=o] = p [r|s(p, e )=o]+ P2 |(p, e ) = o] ,

p|, m) = o] =

(1 -¿)(0.5 - Pe ),

0 < p < r - 2Ar,

(0.5 - Pe)

^ OA \2

r - 2Ar - p

r - 2Ar < p< r - Ar,

x(p0 - 0.5)

r - Ar < p< r + Ar 0, p > r + Ar,

P2 [rls(p, {e,£})=o]=

pE, 0 < p< r -Ar, 0.5, p> r-Ar.

The constant factors pE and pO are the minimum and maximum values of sensor model function and they sati sfy the condition pE + pO = 1, r is a given range reading, 2Ar is the width of the area in the vicinity to the arc of radius r, p is distance cj from the sensor, 9 (£) represents the angular (lateral) distance between the axis of radiation cone (belt) and cell cj and k= fa(9).fd(p).

The proposed sensor model is after minor modification directly applicable to interpret the measured distances by PSD sensor. The measurement uncertainty is in this case function of lateral distance, unlike in the case of sonar, where it is a function of angular distance. Therefore the infrared sensor model is given by following equation:

p[r\s(c]) = O] = pl[r|s(p,£) = o]+ p2[r|s(p,£) = O], (11)

where p is distance of cell cj from the sensor and £is the lateral distance between the axis of radiation belt and cell cj and *= fl(£).fd(p).

4.1. Identification of sensor parameters

Mathematical model of the angular/lateral uncertainty of the measurement requires knowledge of angular/lateral range in which the sensor is able to detect an obstacle. Although the theoretical value of limiting angle for the ultrasonic sensor can be calculated, if the sensor parameters are unknown or a more precise value is needed for the sensory model, the identification of the limiting angle is the only way of determining its real value. The limiting width cannot be computed because of non-existence of the theoretical model of light diffusion of the PSD sensor. Thus its real value is possible to obtain only by its identification. Therefore a simple universal procedure for identification of width of radiation cone and radiation belt was proposed. The sensor is positioned in a manner, that it directs to open space and in certain distance is positioned a reflecting surface which emulates obstacle. The reflecting surface is moved in direction perpendicular to the

sensor direction. The emitted signal impinges at reflecting surface and it is reflected back to the sensor. As the reflector moves continuously, in certain point of the motion the reflected signal is lost and the coordinates of that point are stored. Processing of the stored values consequently enables to identify the searched parameter of the sensor. Moreover it is possible with a change of the measured distance to determine the dependency of identified parameters with measuring distance. The identification procedure is suited to directly measure limiting width sk of the radiation belt of the infrared sensor. To precisely measure the limiting angle ek of the ultrasonic sensor radiation cone, it is more appropriate to rotate the sonar against the static reflector [5]. However the practice showed, that the presented simple procedure is rather adequate also for identification of wide angle of the ultrasonic sensor. The only difference is the conversion of coordinates of stored points of signal lost to corresponding angles.

The measured values of limiting angles of used ultrasonic sensor range from approximately 55° for very short distances to approximately 25° for distances near maximal measuring range. So the value of 40° was chosen as width of the radiation cone. The chosen value corresponds with theoretical calculated value of 40.8° for radius 8 mm of sonar active element and working frequency 40 kHz. The identified width of the radiation belt was approximately 20 mm and it is rather constant along measuring range of the used PSD sensors. The value of parameter Ar was chosen to be a 1.5 greater than grid cell size in regard of relatively small error of measured distance by the ultrasonic sensor. In case of infrared sensor it was chosen to be a 3 times greater than grid cell size, because of greater measurement error of infrared sensor.

5. Experimental results

A small scale artificial environment was used as the experimental environment for testing the constructed sensory system. This environment was put together from large plasterboards and cardboard plates. (Fig. 3 - 7). From the point of view of a small mobile robot, this environment represents indoor office environment very well. The chosen materials of the prepared testing environment have relatively different surface properties. The walls depicted in the figures as upper and lower constraints of the environment were made of smooth bright plasterboard. The used material was intended to model the ordinary indoor walls. The right side and left side was made of cardboard which approximately emulates the common environment details such as furniture and doors. In addition, in the centre and one of the corners of the testing environment rectangular obstacles were placed. The obstacles made the experimental space more cluttered and it resembled fortiori real indoor office environment. Such experimental conditions enable to obtain quite certain informations about operation of the sensing system of the robot in real environments.

The length of the testing space was 200 cm and its width was approximately 120 cm. The data acquisition was made with movable rotary platform equipped with sensor device installed at the top of the platform. The sensor device was able to rotate in full angle of 360°. Experimental data were gathered from 14 selected locations. To obtain a good coverage of the environment, the measuring locations were distributed evenly over the experimental space in the intervals of 0.35 m longwise and 0.3 m broad-wise. At each location two data sets consisted of 400 range readings by rotation of sensor by 0.9° were collected. First data set consisted of the range readings collected by ultrasonic sensor and second data set consisted of the range readings collected by infrared sensor. The set U consisted of 200 x 200 cells of size and 3= 0.03m. For ultrasonic and infrared sensory models, following parameter pO = 0.6 and pv = 0.6 m were used. The parameter Ar had values 0.045 m for ultrasonic and 0.09 m for infrared sensor model.

Algorithms were implemented in C language on Athlon 3500 MHz based PC under OS Linux. Navigation maps are depicted as grey scale images. The color in the map indicates the level of confidence about that area to be empty or occupied by an obstacle. The lighter areas correspond to P(s(cj))—0 represents the empty space and the darker areas where P(s(Cj))—represents occupied cells. The grey background color represents entire ignorance about the state of the cells in the map. The constraints of the experimental space are represented in the pictures with white lines and the measuring locations are depicted like small crosses.

Final maps of the experimental environment are depicted in the Fig. 3 - 7. It is obvious that in real navigation and mapmaking in the environment, the mobile robot does not collect such huge amount of range data, because the sensing process is somewhat time consuming. The reason for the collection of such big data sets was to reveal the properties of individual sensors and influence of executed number of measurements on the quality of the final maps. The experimental results were obtained by application of mapmaking algorithms on subsets selected from original data sets. The tested scanning system is constituted from two different sensors with opposite properties. This fact clearly shows itself in the processing of the measured data.

The ultrasonic sensor has a wide radiation cone and consequently the appropriate map can be constructed from relative small number of measurements performed at each location. The large number of measurements produces maps in which the obstacles start to disappear as in the map constructed from 100 measurements per location depicted in Fig. 3. The poor results of the map are mainly caused by large number of long readings. They produced vivid virtual obstacles behind the

walls and the walls alone disappeared like the obstacle in the environment. Relatively good results are obtained from 20 measurements per measuring location as can be seen in the Fig. 4. The boundaries of occupied space are detected relatively accurately. The contours of walls in the map continuously copy the real ones and the boundaries are of thickness of about four cells. The obstacle in left upper corner is also detected reliably. The boundaries of the obstacle positioned in middle of the experimental environment are more fuzzy, especially the lower and upper ones. It is caused by the deficient number of measurements directed straightly to them. The nonexistent obstacle in the corridor between obstacle and the upper environment boundary is created due to a wide radiation cone of the sonar. Behind the boundaries in the unknown area there were created nonexistent obstacles too. They exist as a consequence of a large number of long readings.

Fig. 3. Map of the experimental environment constructed from 100 measurements per measuring location collected by the ultrasonic sensor.

Fig. 4. Map of the experimental environment constructed from 20 measurements per measuring location collected by the ultrasonic sensor.

On the other hand the narrow radiation belt of infrared sensor gives after performed measurement information about quite small number of cells. The Fig. 5 shows the map constructed from data set contained 20 measurements per location. It

can bee clearly seen that the map contains enough information for robot navigation only very closely to measurement positions. Rest of map gives almost any useful information about the obstacles in the environment. Therefore in order to obtain a map of good quality, it is necessary to perform a relative large number of measurements in one location. Such map constructed on the basis of 100 measurements per location can be seen in the Fig. 6. The boundaries of occupied space are detected quite accurately. The contours of walls in the map follow the real boundaries and the wall thickness in the map is of about six to seven cells. The greater thickness of the boundaries in comparison with sonar is caused by greater measurement error of the infrared sensor. This property also caused the streaks of a darker color coming up from the walls in the empty area (left and lower wall in the Fig. 6). The obstacles are detected rather reliably.

Fig. 5. Map of the experimental environment constructed from 20 measurements per measuring location collected by the infrared sensor.

Fig. 6. Map of the experimental environment constructed from 100 measurements per measuring location collected by the infrared sensor.

The map constructed on the bases of data fused from ultrasonic and infrared sensor is depicted in the Fig. 7. The map was computed from the data sets consisting of 20 measurements per location in case of the ultrasonic sensor and 100

measurements in case of the infrared sensor. It is obvious that it combines the good properties of each sensor and eliminates the bad ones. In this map there are the obstacles reliable detected and modelled by thin contours and the empty area is modeled also very clearly.

Fig. 7. Map of the experimental environment constructed from fused data sets of 100 measurements per measuring location collected by the infrared sensor and from 20 measurements per measuring location collected by the ultrasonic sensor.

6. Conclusion

The aim of performed experiment was to investigate properties of the constructed sensory system intended for a small mobile robot. Given probabilistic formulation of sensor models permits to combine the information obtained from different sensors and enables successful data fusion. The experimental results show advantages and disadvantages of used sensors as well as they offer topics for future research.


This work was supported by Grant No. APVV-0261-10. The authors are pleased to acknowledge this support.


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