'Magnetic Map Building' to the already invented method by Rostyslav Sklyar

Magnetic Map Building for Mobile Robot Localization Purpose Danilo Navarro Universidad de Oriente Departamento de Ingenierı́a Eléctrica Barcelona - Venezuela dnavarro@cantv.net

Abstract

Robotic mapping addresses the problem of modeling environments through mobile robots sensors. The Resulting maps are commonly used for robot localization and navigation. Using a compass in mobile robotics is not frequently considered because it has a signiﬁcant disadvantage: the data it provides can be easily contaminated by surrounding electromagnetic noise or by large ferrous structures. This makes the compass unreliable for heading determination in indoor environments. This paper addresses construction of an environmental magnetic map with a mobile robot, and how to use such map to determine the robots local heading. We present a novel approach that characterize indoor environments as a magnetic ﬁeld function. A mobile robot gathers data from a low cost compass as it moves around. This method models the robots working area by means of a simple representation which is time persistent and does not require specialized sensors. Thus, we propose a methodology based on 2D interpolation aimed at determining the robots heading on the working area. Real test results showed the method is suitable for the partial correction of the robots position.

1. Introduction Mobile robot positioning decomposes into two stage: orientation estimation, followed by localization estimation[7]. Localization is strongly inﬂuenced by wrong heading estimate. Therefore, sensors providing absolute direction are extremely important in robot navigation. A low cost sensor that offers this possibility is the magnetic compass. Using a compass in mobile robotics is considered by some investigators[3, 4, 6, 9]. Suksakulchai et al[8] propose a method that extracts landmarks from compass data and uses it for mobile robot localization. Their method consists in exploring a corridor while collecting and storing the information about the changes observed by the compass. Afterwards, with the robot moving through the same corridor, data is collected from the compass and its correspondence to the stored data is ana-

Gines Benet Universidad Politécnica de Valencia Informática de Sistemas y Computadoras Valencia - España gbenet@disca.upv.es

lyzed by means of a technique of sequential data adjustment using discreet least squares. Few compass-equipped robot have been reported because the compass use has a significant disadvantage: the data it provides can be easily contaminated by surrounding electromagnetic noise or by large ferrous structures. In practice, this makes the compass unreliable for heading determination in indoor environments. Despite this fact, the electronic compass continues being of interest as a support instrument for highlevel processes in indoor mobile robotics, due to its low cost and very good relative precision. So, this paper addresses the task of constructing an environment magnetic map with a mobile robot, and how to use such map to determine the robots local heading. We present a novel approach, which characterize indoor environments as a magnetic field function. A mobile robot gathers data from a low cost compass as it moves around. The robot starts exploring the surroundings and at the same time gathers data of the magnetic field components, Hx , Hy , registered by the compass at defined locations on the working area. This way, the collected data forms a grid that represents the magnetic field present in the explored environment. Applying the proposed method, the robots working area is modeled by means of a simple representation that is time persistent and does not require of specialized sensors, or specialized processes for modeling or calibration. Finally, we propose a method based on 2D interpolation aimed at determining the robots heading on the working area.

2. Environment magnetic field modeling The Earth’s magnetic field intensity is between 0.5 and 0.6 gauss, and can be modeled like a magnetic dipole whose field lines are originated in a point near the Earth geographical south and finish in a point near the Earth geographical north. The magnetic field direction and intensity are represented by a vector of three components Hx , Hy , Hz . The Earths magnetic field intensity is between 0.5 and 0.6 gauss, and can be modeled as a magnetic dipole whose field lines originate in a point near the Earths geographical south and end in a point near the Earths geographical north. The magnetic field direction

and intensity are represented by a vector of three components Hx , Hy , Hz .

ϕ=

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

π 2 3π 2

H π − arctan Hxy H − arctan Hxy H 2π − arctan Hxy

Hx = 0, Hy < 0 Hx = 0, Hy > 0 Hx < 0

(1)

Hx > 0, Hy < 0 Hx > 0, Hy > 0

3. Magnetic map building The indoor environment that needs to be mapped can always be treated as a 2D region in which the mobile robot can travel. The ﬁgure 2 shows the deﬁnition of the angular variables and how they are related to the global map. If we consider a mobile robot equipped with an odometric localization system, this way like also with an electronic compass, then given approximated estimates of a robot’s position based on Odometry and dead reckoning, we can build a map based only on raw compass data.

Figure 1. Earth’s magnetic ﬁeld vector representation.

Instruments sensible to the magnetic field are known as Magnetometers. Mobile robotics interests on those able to measure the Earths magnetic field and express it through an electrical signal. This type of instrument is known as the electronic compass. One type of electronic compass is based on magneto-resistive transducers, whose electrical resistance varies with the changes on the applied magnetic field. This type of sensors present sensitivities below 0.1 milligauss, with response times below 1 sec, allowing its reliable use in vehicles moving at high speeds[2].

Figure 2. Global map and its relation with the angular variables. Here, θ is the heading angle of the robot, θC is the angle measured by the compass at robot’s localization, and θM is the apparent magnetic north direction. The robot starts exploring the surroundings at the same time it gathering data of the magnetic azimuth θC registered by the compass at deﬁned locations on the working area. The estimated robot position x, y, θ is supplied by the odometric dead reckoning system. Since the compass is vertically aligned with the center of rotation of the robot and it is oriented in direction of 0 degrees with respect to its longitudinal moving axis, the direction of the apparent magnetic north of any location (x, y) in the map, viewed in the global plane, is indicated by,

A simple electronic compass is made up of two magneto-resistive transducers, vertically aligned, and with a 90 degrees phase shift. These transducers present their maximum signal value when its respective axis is aligned with the Earths North Pole. This way, if the compass is in an open, clear and sufficiently flat zone, the field components Hx , Hy , Hz can be modeled by cos ϕ and sin ϕ respectively, where ϕ represents the azimuth angle. Since Hy ϕ = arctan Hx , then in the simplest case, the direction of a compass can be determined by measuring the parallel components of field to the earth. In this model, we must take into account that the tangent above calculated is valid only for −90 < ϕ < 90, and also that the division by Hx = 0 is not allowed. Equation 1 shows a set of equations that can be used to determine the direction of this compass type.

θM = θ + θC

(2)

thus, the ﬁeld components that describe the direction of the magnetic north in any point of the map are, Hx = cos θM (3) Hy = sin θM 2

5. Experimental implementation and results

6. Conclusions and further work We have proposed a new system to model the environment based on the magnetic field present on it. Since the constructed map does not change with time, the model serves as suitable absolute reference for the correction of the orientation angle of a robot that moves on it and knows its location (x, y). As this representation is based on a continuous field, it is possible to apply single-hypothesis methods for position correction or tracking - e.g. Kalman filter localization. The proposed angle correction method is also based in the 2D bilinear interpolation. The validity of the proposed method was verified by means of simulation. As further work, we will run the proposed correction method on the real scene and in addition we will try out higher order interpolation methods that can deal with scattered 2D data.

Experiments have been carried out in a structured indoor environment with a differential-drive robot called YAIR (Yet Another Intelligent Robot). YAIR has a multisensorial architecture conformed by a rotating SONAR, an infrared based distance sensor, an electronic compass, an odometric system based on optical encoders rotating synchronously with the drive wheels, as well as an odometry system based on a pair of unloaded independent encoder wheels made as sharp-edged as possible to reduce wheelbase uncertainty[1]. During tests, all localization data was supplied by the robot odometric system, whereas an electronic compass Honeywell HMR300[5] supplied the magnetic field data. The robot was placed in a scene divided in 50x50 cm grids, and then programmed to explore the surroundings, taking measurements from the magnetic field in the vertices of each one of the grids. The apparent direction of the magnetic north in each point was obtained from the compass measurements and the direction registered by the robot odometric system. From these angles, we extracted the magnetic field components Hx , Hy , which are necessary to carry out the interpolation process that allows to correction of the robot heading in any point of the explored scene. The figure 7 shows the environment magnetic model obtained with this approach. Six month later, we ran the test again and we obtained similar results for the magnetic model. On the other hand, the heading angle correction was demonstrated only on simulation, since a first condition that arised was the magnetic map’s data not lying on a regular grid, instead the data points are scattered. In this case, there are still a number of interpolation options we can use. A straightforward option is to connect the points in a triangulation using the Delaunay triangulation. This way is possible to use a regular algorithm as piecewise linear over the set of triangles.

References [1] F. Blanes. Percepción y representación del entorno en robótica móvil. PhD thesis, Universidad Politécnica de Valencia, Valencia.España, 2000. [2] M. Caruso. Applications of magnetic sensors for low cost compass systems. In IEEE 2000 Position Location and Navigation Symposium, pages 177–184., San Diego, CA, USA, March 2000. [3] H. R. Everett. Sensors for Mobile Robots: Theory and Application. A. K. Peters, Ltd, 1995. [4] R. Hogg, A. Rankin, S. Roumeliotis, D. McHenry, D. Helmick, C. Bergh, and L. Matthies. Algorithms and sensors for small robot path following. In Proceedings of the IEEE International Conference on Robotics and Automation, pages 3850–3857, Washington, DC, May 2002. [5] Honeywell. HMR3000 Digital Compass Module User’s Guide. (accessed September 2005: http://www.ssec.honeywell.com/magnetic/datasheets.html). [6] R. Luo, T. Chen, C.-Y. Hu, and Z. Hsiao. Adaptive intelligent assistance control of electrical wheelchairs by greyfuzzy decision-making algorithm. In Proceedings of the IEEE International Conference on Robotics and Automation, pages 2014–2019, Detroit, Michigan, May 1999. [7] S. Roumeliotis, G. Sukhatme, and G. Bekey. Smoother based 3d attitude estimation for mobile robot localization. In Proceedings of the IEEE International Conference on Robotics and Automation, pages 1979–1986, Detroit, Michigan, May 1999. [8] S. Suksakulchai, S. Thongchai, D. Wilkes, and K. Kawamura. Mobile robot localization using an electronic compass for corridor environment. In Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, pages 3354 – 3359, Nashville, Tennessee, USA, October 2000. [9] C. Tsai. A localization system of a mobile robot by fusing dead reckoning and ultrasonic measurements. In Proceedings of the IEEE Instrumentation and Measurement Technology Conference, pages 144–149, Minnesota, USA., May 1998.

Figure 7. Magnetic ﬁeld pattern of the explored scene.

Induction Magnetic Field Sensor as an Organ of Robot Vision Rostyslav SKLYAR Space Sensing Instruments, Verchratskogo st. 15-1, Lviv 79010 Ukraine Tel/Fax: +380-322-762432/769613; r_sklyar@hotmail.com

Abstract. The robotic vision method of the autonomous system based on the orientation of the plane and according to the magnitude and gradient of the natural and industrial magnetic fields (MFs) has been developed. The head sensor(s) of an ambient temperature or superconducting further electronic circuit placed on the robot limb(s) without modifying them. Sensitivity of the robotic vision makes it possible to recognize the linear translation of 10-2 m and disposal in space of 10-3 m3. I. Introduction. Magnetometers and their robotic applications The measurement of MFs is an important task for the majority of autonomous missions. The distribution of permanent and the value of periodical MFs gives the data about placement of ferromagnetic objects and sources of EM radiation respectively. On the other hand, these signals will z

Fig.1 The w alking robotin M F environm ent. a) x-y plane defines the varying D C natural M F; b) around z axis spreads AC industrial M F interference.

Rostyslav SKLYAR

be a reference point and guiding line for a walking robot (Fig. 1). Detection of some magnetic anomalies of the Earth MF and their variations is provided by fluxgate sensors [1]. When the spectrum of EM signals in the environment lies in a wide frequency range (10Hz-500kHz), the application of highly-sensitive induction sensors is necessary. The application of a low-Tc SQUID device is able to embrace both of the said frequency ranges with maximum sensitivity. It is made of non-magnetic material and the principle of operation is to detect two magnetic signals at different distances from the source and arrange for these to be in opposition around a local supercooled circuit. This ‘gradiometer’ approach eliminates most of the noise—caused by spurious MFs originating from, for example, electrical devices or natural (geomagnetic (GM) sources. A typical unshielded laboratory has a noise level in the 0—10 Hz frequency region of about 10-7 T and GM noise in the same frequency range is of the order of 10-10 T. Any small field changes the direction of the MF vector in the space and this produces a distortion in the waveform of the signal in the detection coils. The very expensive use of the SQUID magnetometer up until now has produced many advances in the understanding of MFs from weak sources. The advance of much cheaper room—temperature sensor technologies offers the prospect of much greater use of MF monitoring [2]. As a general rule, scientific instrumentation should impact mass constraints as little as possible; however, robot-mounted instruments in particular must be lightweight to survive deployment under high- stress conditions when used in connection with spacecraft or underwater. This weight constraint can limit both the size of the sensor and its placement on the moving part. Also, autonomous systems require the minimal consumption power. Both factors translate into severe constraints on the capability of the instrument to measure weak EMFs encountered in the environment. In addition, the outer space and underwater conditions require endurance against variations in the wide range of temperature, humidity, and atmospheric pressure. II. Induction (superconducting) sensor as the organ of vision Taking into account the said restrictions, it is undesirable to use in robot a fluxgate sensor due to its active type of action. Also is impossible exploiting SQUID device since it needs the liquid helium container. SQUID systems being almost ideal for the detection of very small amounts of flux from small samples, but less well-suited to the detection of low flux densities (i.e. where very low MFs are encountered). The high coil induc-

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ωlimb

ω limb

Fig. 2 Placement of PC on the limb. a)a winding of PC; b) a ferromagnetic core of PC as a part of the limb(s); c) a wire which connects PC with an electronic circuit in the body.

tance of the induction system, on the other hand, can couple to a large quantity of flux [3]. It appears that these difficulties frequently reduce, in principle, the performance of SQUID magnetometers to a level below that demonstrated in this article using an ambient-temperature induction system. This induction sensor is also compact, robust, operates at room temperature, exhibits a wide dynamic range, and may be easily integrated into differential or multiple sensor gradiometric configurations which are feasible in a multi-limb walking robot. 1. Placing of the PCs on the limbs

A PC of walking robot is connected in parallel with the drain of a SuFET cryogenic device or an ordinary OA which are placed in the body (Fig. 2). A PC realizing the oscillatory-forward movement along both AC industrial interferences and quasi-DC natural (Earth) environmental MFs. These fields are distributed on a surface and in space roughly according to Fig. 1. The movement in quasi-DC MF HDC with the defined speed υ and oscillating frequency ω with a magnitude ∆α gives e.m.f. from PC: (1) EPC=SNωµeffµ0HDCsinα⋅∆α , where S=µeffπd2N/4 with µ0 -the permeability of free space, µ0=4π⋅10-7 henry/meter; µeff -the effective relative permeability of a high-µ metal core; d-the average diameter of a PC; N-total turn number of solenoid; α- an angle between PC's magnetic axis and the vector of HDC. Further amplifying/processing circuit depends on the measuring conditions and can vary from the simplest of the ordinary induction sensor modifications to the superconducting one [4].

Rostyslav SKLYAR

2. The design of the MF transducer

Some combined device, that includes all the best features of the said MF sensors/transducers seems to be the preferable trend for further development as a vision organ [4]. The SuFET is implemented into a wideband induction sensor device in order to acquire the sensitivity threshold below 1fT/√Hz in the frequency range from small values of Hertz to tens of MHz (0.1Hz-107 Hz). The proposed magnetometer (SIM) circuit consists of both room-temperature or cooled (up to superconductive) pickup coil (PC) and a SuFET. Moreover, it gives the possibility of repudiating both windings and electronics of feedback loops that are used in the known magnetometers. Magnetic induction BPC of AC MF with the frequency ωlimb of limbs' oscillations produce an e.m.f. in PC: (2) EPC=BPCωlimbSN, where S- a cross-section of PC, N- its number of turns. All AC MFs with the frequencies ω, high than ωlimb can be rejected by the passive HF filter [5].On the other hand, the value of EPC can be determined from the output voltage Uout of the specific kind of the induction transducer [4] with known its transfer function G according to the formula: (3) Uout=GEPC. As a result, an output signal receiving spontaneously, during twodimensional travel of a walking robot in a quasi-DC MF. Moreover, by picking up the signals from both horizontal and vertical parts of the limbs, the robot derives its' directional information from the axial course of the field lines and their inclination (defined as the angle between the direction of the field lines and the horizontal) in space. Executing the oscillations of PC with parameters (number of turns N=2⋅104 and a cross-section area S=π⋅10-4 m2) [4] in the earth MF B0=50 mkT [6] with the frequency 2 Hz and α=30°, ∆α=30° arouse e.m.f. with a magnitude 50 mV according to Eq. 1. This e.m.f. will be on average equal to 5 mkV for the possible variations of the said MF with magnitude 1÷10 nT [6]. Hence these data it is possible to calculate the value of Uout for all five known of the induction transducer [4] with given parameters of their electrical circuit. Thus so then: a) for the basic transducer's variant with PC's resistance R=2.4 kOhm, inductance L=30 H and capacitance C=50 pF the values of Uout shown in the second column of the table; b) the voltage feedback resistance Rfb=27 kOhm is introduced into the circuit; c) the magnetic flux feedback turns Nfb=1000 is introduced into the device; d) for SuFET the constant partial of gate voltage equal to 0.1 V and ωT, which closely relates to the small signal transconductance, are defined [4].

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Table. The dependence of signal's value Uout from the varying MF BPC. a b c d BPC(Uout 50 mkT 10 V 70 mV 1.4 V 3 mkV+0.1 V 5 nT 1 mV 7 mkV 0.14 mV 0.3 pV+0.1 V (0.1 mkT) III. Using an ambient DC and AC MFs for robot's walking An output signal of the sensor will be involved into differencial (gradiometric) operation between the robot’s limbs. After envelope detection of the quantity Uout, can be presented by changing the corresponding quasiDC MF by the robot’s movement as defined in Fig. 3. In the similar manner, way an AC MF partial can be shown.

HDC, HAC, Vout

1 2

oscillations of a PC modulated by variations of external natural MF;

an envelope of sensor's output voltage UDC as the appropriate quasiDC MF along the walking way;

changing of an AC industrial MF interference into the travel space;

the integral output voltage UAC which determines changing of the interference's power by a distance.

Fig. 3 The variations of measured MF strength HDC, HAC.

4 3

The linear travel of the robot can be derived from the known distance between any two limbs and measured during the movement gradient of MF ∆H, which is presumed constant. Otherwise, the robot can be walking in the direction of minimal or maximal MF strength H according to the said gradient (Fig. 4). In both cases the precision of movement will be defined by the sensors’ sensitivity, which lies in a range of the orders from pT/√Hz to fT/√Hz . 1. Determination of the earth's MF gradient

A portable single axis magnetic gradiometer, which is a relative instrument because it measures the spatial variation of the MF, has been described [7]. The finite distance between the magnetic sensors d for detecting the field difference is used to get an expression for the estimate of the exact magnetic gradient, adjusted by a function of the field distance, ∆Bz=Bz(z+(1/2)d)-Bz(z-(1/2)d), as follows:

Rostyslav SKLYAR

∇B z z

∆Bz µ0 md 2 ≅ +5 d 4πz 6

(4)

where µ0=4π10-7 H/m, z is the distance from the dipole to the center of the gradiometer probe and m the magnetic moment of the dipole. In the case to be treated in the following, the oscillations of the limbs are taking place according to the law closer to harmonical. Then the magnitude value of magnetic induction, which produced by oscillations of PC in the ambient DC MF Bz is: (5) BPC=Bz·sinα·∆α , where α is an angle between PC's direction of detection and vector of B, ∆α is a range (of a value) of this angle variation. Having substituted Eqs. 1, 3, 5 into Eq. 4, we have the dependence between signals from PCs of any two limbs and the relevant magnetic gradient occurs:

∇B z z ≅

U out [(z + (1/2)) - (z - (1/2))] µ md 2 +5 0 6 Gω limbSNsinα∆α 4πz

(6)

A first order radial gradiometer consists of two axially displaced magnetometer loops, wound in opposing sense from a common wire that is connected to the induction sensor. Two radial magnetometers with opposite polarity can be connected together to form planar gradiometers [8]. Such devices detect tangential gradient of the radial field, and two gradiometers are usually used at each site to detect two orthogonal planar gradients. The planar gradiometer behaviour is qualitatively different from that of the radial gradiometer. 2. Measuring of the MF signal (noise) in a triaxial arrangement A flux transformer detects more environmental noise if its baseline is long (or if it is a magnetometer). Thus long baseline gradiometers detect not only stronger signal from deep sources, but also larger environmental noise. The noise parameters for different baselines were measured and are shown graphically [8]. Gradiometers can also be configured to detect radial gradient of the tangential MF. Two orthogonal ‘tangential radial gradiometers’ and one ‘radial gradiometer’ can be combined to form a first-order gradiometer equivalent of the vector magnetometer. The vector of the industrial or household man-made AC MF (noise) ω can be measured during the complete pass of the robot's walking. Placing of the PC's triplets (the three orthogonal components at each location) on the respective limbs dive the necessary data for the triaxial MF determination according to the geomet

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rical summation. In such case, frequency of the limb's oscillations much lower than ambient MF noise. That is why, they do not influence the measured components and, moreover, these oscillations can be additionally suppressed by a passive LF filter [9]. The value of MF induction along a single component will be calculated similarly to Eq. 1 and Eq. 2 by the formula: (7) BPC=ωSNUout/G Some example of the result of the calculations according Eq. 7 shown in Fig. 4. The dependence of volumetric error on the baseline for environmental noise is shown [8].

∆HAC(n)

∆HAC(m) x

∆HDC(m)

∆HDC(n)

grad(∆HDC)

Fig. 4 Orientation of the walking robot in an environmental MF. a) distribution of the detected gradients of DC natural MF over the x-y plane; b) distribution of DC MF interference in the space around z axis as a difference between the limbs. IV. Conclusions

The attempt to solve this problem of simplifying the robotic vision structure and reducing of such performance data as mass, volume and power consumption by the employing of the induction (also superconducting)

Rostyslav SKLYAR

sensor was done. This method allows us to use the oscillations of limbs during robot's walking for receiving the measured signal and make the vision more natural for this machine. The advanced sensor has an unlimited frequency range from DC to HF, and sensitivity to the ambient MF is closer to the theoretical possibility. V. References [1] Cerman A., Ripka P., KaÓpar P., “Precise Magnetic Sensors and Magnetometers for Military and Space Applications”, Sensors & Transducers Magazine, vol. 38, iss. 12, 2003, pp. 54-58; [2] Mapps D. J., “Remote Magnetic Sensing of People”, Sensors and Actuators A, vol. 106, 2003, pp. 321-325; [3] Prance R. J., Clark T. D. and Prance H., “Compact RoomTemperature Induction Magnetometer With Superconducting Quantum Interference Device Level Field Sensitivity”, Rev. Sci. Instrum., vol.74, No. 8, 2003, pp. 3735-3739; [4] Sklyar R., “SIM- A SuFET Based Induction Magnetometer”, Proceedings of 'Recent Advances of Space Technology: RAST-2003', Nov. 20-22, 2003, Istanbul, Turkey, pp.193-199; [5] Zambresky L. F., Watanabe T., “Equivalent Circuit of a Magnetic Sensor Coil and a Simple Filter for Rejection of 60 Hz Man- Made Noise”, J.Geomag. Geoelectr., vol. 32, 1980, pp. 325-331; [6] Ripka P., “Review of Fluxgate Sensors”, Sensors and Actuators A, vol. 33, 1992, pp. 129-141; [7] Merayo J. M. G., Petersen J. R., Nielsen et al., “A Portable Single Axis Magnetic Gradiometer”, Sens. Act. A, vol. 93, 2001, pp. 185-196; [8] Vrba J. and Robinson S E, “SQUID sensor array configurations for magnetoencephalography applications (Topical review)”, Supercond. Sci. Technol., vol. 15, 2002, pp. R51–R89; [9] Sklyar R., “Suppression of Low-Frequency Interferences in the Induction Sensor of Magnetic Field”, has been considering for publication in Measurement (M03/73).

Table. The similar fragments in two said articles. #

R Sklyar “Induction Magnetic Field Sensor as an Organ of Robot Vision”

Danilo Navarro and Gines Benetnse “Magnetic Map Building for Mobile Robot Localization Purpose”

Title- ... Magnetic Field Sensor ... of Robot Vision

Title- Magnetic Map ... for Mobile Robot

abstract- The robotic vision method of the autonomous system based on

abstract- This paper addresses construction of an environmental magnetic

the orientation of the plane and according to the magnitude and gradient of map with a mobile robot, and how to use such map to determine the robots local heading. We present a novel approach that characterize indoor the natural and industrial magnetic fields (MFs) has been developed. The head sensor(s) of an ambient temperature ... placed on the robot limb(s) without modifying them. Sensitivity of the robotic vision makes it possible to recognize the linear translation of 10-2 m and disposal in space of 10-3 m3.

environments as a magnetic feld function. A mobile robot gathers data from a low cost compass as it moves around. This method models the robots working area by means of a simple representation which is time persistent and does not require specialized sensors.

A PC realizing the oscillatory-forward movement along both AC industrial interferences and quasi-DC natural (Earth) environmental MFs. These fields are distributed on a surface and in space roughly according to Fig. 1. The movement in quasi-DC MF H with the defined speed υ and DC oscillating frequency ω with a magnitude ∆α gives e.m.f. from PC: Eq. [p. 3]

The robot starts exploring the surroundings and at the same time gathers data of the magnetic feld components, Hx,Hy, registered by the compass at defned locations on the working area. This way, the collected data forms a grid that represents the magnetic feld present in the explored environment. [p. 1, right]

This e.m.f. will be on average equal to 5 mkV for the possible variations of the said MF with magnitude 1-10 nT. [p. 4]

The Earth’s magnetic feld intensity is between 0.5 and 0.6 gauss [p. 1, right]

The proposed magnetometer (SIM) circuit consists of both roomtemperature or cooled (up to superconductive) pickup coil (PC) and a SuFET. Magnetic induction Bpc of AC MF with the frequency Wlimb of limbs' oscillations produce an e.m.f. in PC: (Eq.) [p. 4]

Instruments sensible to the magnetic feld are known as Magnetometers. Mobile robotics interests on those able to measure the Earths magnetic feld and express it through an electrical signal. This type of instrument is known as the electronic compass. [p. 2, left]

The linear travel of the robot can be derived from the known distance between any two limbs and measured during the movement gradient of MF dH, which is presumed constant. Otherwise, the robot can be walking in the direction of minimal or maximal MF strength H according to the said gradient (Fig. 4). In both cases the precision of movement will be defined by the sensors’ sensitivity, which lies in a range of the orders from pT/√Hz to fT/√Hz . [p. 5]

The indoor environment that needs to be mapped can always be treated as a 2D region in which the mobile robot can travel. The fgure 2 shows the defnition of the angular variables and how they are related to the global map. If we consider a mobile robot equipped with an odometric localization system, this way like also with an electronic compass, then given approximated estimates of a robot’s position based on Odometry and dead reckoning, we can build a map based only on raw compass data. [p. 2, right]

Eqs. (5) & (6) [p. 6]

Eqs. (2) & (3) [p. 2, right]

The finite distance between the magnetic sensors d for detecting the field difference is used to get an expression for the estimate of the exact magnetic gradient, adjusted by a function of the field distance, dBz=Bz(z+(1/2)d)-Bz(z-(1/2)d), as follows: Eq. [p. 5] Having substituted Eqs. 1, 3, 5 into Eq. 4, we have the dependence between signals from PCs of any two limbs and the relevant magnetic gradient occurs:: Eq. [p. 6]

The apparent direction of the magnetic north in each point was obtained from the compass measurements and the direction registered by the robot odometric system. From these angles, we extracted the magnetic feld components #Hx,Hy#, which are necessary to carry out the interpolation process that allows to correction of the robot heading in any point of the explored scene. [p. 4, left]

Conclusions: The attempt to solve this problem of simplifying the robotic

Conclusions: We have proposed a new system to model the environment vision structure ... by the employing of the induction sensor was done. This based on the magnetic feld present on it. Since the constructed map does method allows us to use the oscillations of limbs during robot's walking for not change with time, the model serves as suitable absolute reference for the correction of the orientation angle of a robot that moves on it and knows its receiving the measured signal and make the vision more natural for this machine. The advanced sensor has an unlimited frequency range from DC to location (x, y). [p. 4, right] HF, and sensitivity to the ambient MF is closer to the theoretical possibility. [p. 7-8]