A relative localisation system of a mobile robot

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<ul><li><p>Journal of Intelligent and Robotic Systems 1 (1988) 243-257. 243 9 1988 by Kluwer Academic Publishers. </p><p>A Relative Localisation System of a Mobile Robot </p><p>M. JULL IERE, H. PLACE, E. BAZIN, andJ . F. RADENAC LA TEA, lnstitut National des Sciences Appliqu~es (INSA), 20, avenue des Buttes Co~smes, 35043 Rennes Cedex, France </p><p>(Received: 31 March 1988) </p><p>Abstract. This paper describes a localisation system applied to vehicle displacements on irregular grounds and at moderate speed (about I m/s). It is composed of a gyrometer and a Doppler sensor, which give, by integration, the attitude and position of the vehicle supporting them, without contact with the ground. The precision of the obtained localisation is about 2% for ranges of about a hundred meters. </p><p>Key words. Mobile robot, localisation, inertial systems, Doppler sensors, contactless measurements. </p><p>I. Introduction </p><p>One of the necessary conditions for the autonomy of vehicles (mobile robots) is their localisation, either with respect to a fixed reference in their environment or by integrating their motion from a known position and orientation: the first is called absolute and the second relative localisation. To obtain absolute localisation, it is necessary to have many marks installed in the environment, along the trajectory which is to be followed. It seems more advisable to use relative localisation and to correct errors caused by this sort of localisation, thanks to an absolute iocalisation carried out from time to time. Such a method has been applied in our laboratory to a wireguided vehicle, which can leave its guiding wire (absolute localisation) on short ranges by following a memorised trajectory with odometry (relative localisation). This relative localisation method is very efficient for motions on flat and smooth grounds, but it is more imprecise in the case of rough grounds: that is the reason why the method described here has been developed. </p><p>2. Basic Principle of the Method </p><p>The localisation in space of an object (plane, satellite, etc.) generally requires the knowledge of six coordinates: three for its position and three for its orienta- tion. Since the question here is to localise ground vehicles moving on terrains assimilable to flat areas, the number of coordinates necessary for their iocalisation is reduced to three: two for position (X, Y) and one for orientation 0, called attitude (Figure 1). </p><p>Contrary to odometry localisation, which requires a contact between the vehicle and the ground, the method proposed here is not dependent on the nature of the ground, since the sensors allowing the determination of position and attitude of the </p></li><li><p>244 </p><p>u </p><p>u </p><p>Fig. 1. </p><p>0 </p><p>Definition of the attitude and linear speed. </p><p>M. JULLIERE ET AL. </p><p>/ </p><p>mobile robot are mounted on the vehicle and have no contact with the ground. This method is based upon </p><p>- instantaneous attitude measurement by integrating the angular speed of the vehicle around an axis normal to the ground, from a gyrometer. </p><p>- instantaneous position measurement by integrating the linear speed of the vehicle, from an ultrasonic emitter-receiver based on the Doppler effect. </p><p>- estimation of the trajectory followed by the robot from an initial position (X0, Y0, 00), by determining from the previous measurements the variations [X(t) - X0], [Y(t) - Y0], [0(t) - 00] for each trajectory sample. First the general organisation of this method (Figure 2) will be detailed. </p><p>3. At t i tude Determinat ion </p><p>The robot attitude is defined (see Figure 1) as the angle between the symmetry axis of this robot and a reference axis related to the environment. The various sensors which are able to estimate internally the attitude 0 can only furnish its variations from an initial value given by an absolute localisation: </p><p>3.1. CHOICE OF MEASUREMENT METHOD OF THE ATTITUDE </p><p>AS previously shown, a method of differential odometry for 0 determination is excluded in the case of irregular grounds. Another method, based on searching for the magnetic north, is not suitable for environments including metallic objects, for instance, in industry. </p><p>Then, only inertial systems remain, such as gyrometers, which give measurements proportional to the attitude derivative 0 [2]. The choice of a type of gyrometer depends on two parameters: </p></li><li><p>RELATIVE LOCALISATION SYSTEM OF A MOBILE ROBOT 245 </p><p>&gt; 4800 bds Serial Link </p><p>vPI </p><p>&lt; </p><p>I, Coordinate Computing </p><p>and Filtering </p><p>0 </p><p>I Integrator and [ A/D Converter ] </p><p>Coordinates X, Y and 0 </p><p>Covered Distance </p><p>I , ,[ </p><p>&lt; ) AnaloE Filters </p><p>Doppler Sensor </p><p>I </p><p>Filterin~ and </p><p>Countin~ </p><p>Temperature Measurement </p><p>Temperature Control </p><p>1 fe fr </p><p>Ultrasonic Emitter </p><p>and Receiver </p><p>Fig. 2. General organisation of the localisation system. </p></li><li><p>246 M. JULLIERE ET AL. </p><p>- the full scale range, i.e. maximal value of l0 I, above which the 0 measurement becomes unreliable. </p><p>- the resolution, i.e. minimal value ofl 0 I, below which the 0 measurement is of the order of its drift. </p><p>The full scale (FS) range to be chosen depends on the dynamics of the robot (e.g. 90~ while the resolution is generally proportional to the full scale range (e.g. l0 -3 FS). </p><p>On account of cost and overall dimensions, a sensor of the piezo-electric 'tuning- fork' type has been selected. </p><p>3.2. ANGULAR RATE SENSOR </p><p>As for mechanical gyrometers, the effect of the Coriolis force F, = -2mf~ ^ Vr upon material elements in motion is detected, except that relative speed V, is not created by rotation, but by vibrating an elastic thin plate. A more simple and less expensive device is thus obtained. </p><p>Figure 3 shows its principle: a material point M of mass m is driven in vibrations of frequency ~o along an axis Y, itself turning with angular speed ~ around an axis normal to O Y. The alternative motion Y = Y0 sin o)t is obtained by a primary oscillator and a secondary oscillator is excited by the Coriolis force F,., inducing vibrations the amplitude of which is proportional to 1~. Finally, the measurement of the angular rate is a signal proportional to this last amplitude. </p><p>0 M </p><p>V r </p><p>&gt; </p><p>Fig. 3. Basic principle of the piezoelectric tuning fork gyrometer. </p></li><li><p>RELATIVE LOCALISATION SYSTEM OF A MOBILE ROBOT 247 </p><p>The measurement of f~ is hampered by errors and drifts which vary, according to the model, from 1 degree per second at short-term to 10 4 degree per hour at long-term for pilot gyrometers. The piezoelectric angular rate sensor used here has a full scale range of 100 ~ per second and a resolution lower than 2 x 10 -3 rd/s. Its zero drifts strongly with the temperature, constraining it to be used in a temperature- controlled enclosure. </p><p>3.3. INTEGRATION OF THE SENSOR OUTPUT </p><p>This analog signal, varying between - 10 and + i 0 V, must be carefully integrated to avoid additional drifts, then converted into digital data. The assembly of Figure 4 carries out the two simultaneous processes of analog-to-digital conversion and integration by means of an up/down counter. Its basic principle lies in balancing the sensor output V 0 with exactly calibrated pulses, so that the mean value of the integrator output is zero: </p><p>kT (V0 - V~) dt = 0 (T: clock period, k: integer &gt;&gt; 1). </p><p>It follows that </p><p>~r Vodt = ~r~O dt = ~[O(kT) - 0(0)] </p><p>= f2r ~dt = [N(kT) - N(0)] gerZ, </p><p>Gyrometer </p><p>Clock Integrator </p><p>ontrol Logic I </p><p>I </p><p>? ! - </p><p>~o. </p><p>Fig. 4. Acquisition of attitude. </p><p>UD/down Counter </p><p>+ V ref </p><p>&gt; f </p></li><li><p>248 M. JULLIERE ET AL. </p><p>where ~ = V0/0 is the sensitivity of the sensor, N(t ) the state of the counter at time t and V~ef T the voltage increment due to the positive pulse. Finally </p><p>V~aT O(kT) - 0(0) = [N(kT) - N(0) ] - - </p><p>The quantity VrefTis chosen so that the counter working with 12 bits (0 ~&lt; N ~&lt; 4095) goes back to its initial value after a variation of 360 ~ From the former expression, one deduces </p><p>V~r T 360 I - - "~ 0.0879 ~ </p><p>4096 </p><p>I is the angular equivalent of a counter increment. Analog circuits of the device (Figure 4) have been chosen so that their defects </p><p>(drifts, offsets, etc.) have only a very weak effect on the measurement, compared with the sensor resolution. </p><p>4. L inear Speed Determinat ion </p><p>The problem is to determine the speed V of the robot along its axis (see Figure 1), then, by integration, to deduce from this the variations of the coordinates of M, the attitude 0 being known from the previous sensor. </p><p>4.1. CHOICE OF A SPEED MEASUREMENT METHOD </p><p>Several solutions can be considered for speed measurements: </p><p>- accelerometers, found in air navigation, are not convenient for vehicles whose acceleration is very low ( &lt; 0.1 g), such as industrial trucks. </p><p>- odometers, as already mentioned, give inaccurate measurements for rough grounds. </p><p>- correlation methods give good results, but are complex to implement, both for their implantation and for their signal processing. </p><p>- Doppler sensors are relatively simple, in both their basic principle and their implementation, and permit speed measurement on any surface, provided that the type and frequency of the emitted wave are suitable: such a type of sensor has been chosen. </p><p>In this method, the vehicle speed is obtained by measuring the frequency difference between the waves emitted (fe) and received ( f ) by the on-board sensor after retrodiffusion on the ground (Figure 5). If V is the vehicle speed, 2 the wavelength of the emitted wave, and ~p the angle between the direction of V and the direction of the emitted wave, the frequency difference is written as </p><p>2 cos ~o fD = - - V (fo =f - fe ) " </p><p>2 </p></li><li><p>RELATIVE LOCALISATION SYSTEM OF A MOBILE ROBOT </p><p>Fig. 5. Measurement principle of speed by Doppler effect. </p><p>249 </p><p>By integrating fo over a sampling period Ts = t i - tg ~ and by counting the number of periods of emitted N,,, and received Nri signals during T~, the distance Aug covered by the sensor during the same time is given by </p><p>i ,, 2 cos q~ </p><p>fD dt = N~i - N~,g _ - - Aug . </p><p>This expression shows that a Doppler sensor theoretically allows the estimation of the covered distance, with a resolution of the order of 2 [3]. For obtaining a precise measurement from an available received signal, a low wavelength must be chosen because the wave diffusion will be better. Lastly, there is a choice between acoustic and electromagnetic millimetric waves (ultrasonic and microwaves): ultrasonic waves have been chosen because the corresponding frequencies (of about a hundred kHz) easily permit simple electronic processing. </p><p>4.2. THE DOPPLER EFFECT ULTRASONIC SENSOR </p><p>This sensor consists of a separate emitter and receiver (piezoelectric ceramics), work- ing at 218.75 kHz, inclined at 45 ~ with respect to the ground and mounted on a single support with their emitting and receiving axis converging on the ground. </p><p>The emitted signal is a square of 24 V peak-to-peak, whose frequency is obtained by dividing a quartz frequency (3.5 MHz/16 = 218.75 kHz). </p><p>The received signal is of very weak amplitude (a few tens of pV), depending on the nature of the ground, and has a very wide frequency spectrum. Indeed, it can be shown that this signal depends on the diffusion coefficient of the ground area element irradiated by the emitted signal. This coefficient varies with the beam width, the </p></li><li><p>250 M. JULLIERE ET AL. </p><p>irregular nature of the ground and the sensor height and velocity relative to the ground. Consequently, the received signal has a very wide spectrum, especially due to an amplitude modulation of this signal, and an amplitude varying with the diffusion coefficient and the receiver sensitivity. </p><p>It can also be shown [4] that, in order to minimise the spectrum width, an aperture angle of the emitted beam near to </p><p>~/2 cos q~ </p><p>Crad = 4Z </p><p>must be chosen, where z is the sensor height relative to the ground (= 20 cm, in our application) and ~O the half-power angle of the radiation diagram. </p><p>In fact, a compromise has to be found between several causes of spectrum enlarge- ment: </p><p>- if the aperture angle of the emitted beam is large, an important area of the ground participates in the Doppler signal creation: the amplitude modulation is weak, but the variation of the Doppler frequency fD is great, yielding a frequency modulation. </p><p>- if the angle is small, only some irregularities of the ground surface participate in the Doppler signal, leading to an important amplitude modulation. </p><p>Hence, a value of that angle will be chosen so that the spectrum enlargement due to amplitude modulation is of the same order as the one due to frequency modulation. This angle corresponds to 10 ~ </p><p>Lastly, the variation with temperature of the acoustic wave propagation velocity (c = 2f) must be taken into account: </p><p>c = co (co" velocity at ~ </p><p>which reacts upon the Doppler frequency measurement. On the other hand, effects of humidity and wind speed variations can be neglected, </p><p>since they give a second-order error due to the fact that the wave travels both forwards and backwards. </p><p>4.3. DOPPLER FREQUENCY MEASUREMENT </p><p>Figure 6 shows the circuit which gives the Doppler signal and its sign in analog form and in the form of pulses achieved by thresholding. The automatic gain control (AGC) is necessary because of the large variation of the received signal amplitude according to the nature of the ground. The Doppler signal results from multiplication of emitted and received signals and low-pass filtering (rejection of emission frequency at 218.75 kHz). Two channels, which have a phase-difference of 90 ~ to the emitted signal, give the Doppler signal sign and, therefore, the direction of robot motion. </p></li><li><p>fe </p><p>Emi s</p><p> s io</p><p>n </p><p>&gt; </p><p>Rec</p><p>epti</p><p>on </p><p>/ </p><p>., , </p><p>.&gt; </p><p>Lo</p><p>w-p</p><p>ass</p><p> Filt</p><p>ers </p><p>~,1</p><p>.5 K</p><p>Hz </p><p>Com</p><p>para</p><p>tors</p><p>F D </p><p>~PI</p><p> _1</p><p>l_ </p><p>40</p><p> mm</p><p>I_ &gt;</p><p>Fig</p><p>. 6. </p><p>Do</p><p>pp</p><p>ler f</p><p>req</p><p>ue</p><p>ncy</p><p> m</p><p>ea</p><p>sure</p><p>me</p><p>nt </p><p>an</p><p>d p</p><p>roce</p><p>ssin</p><p>g. </p><p>Thre</p><p>s- </p><p>hold</p><p>ing </p><p>uP2 t </p><p>7= </p><p>&gt; </p><p>-q </p><p>C~ </p><p>9 </p><p>&gt; </p><p>&gt; </p><p>-t </p><p>Z </p><p>r~ </p><p>&lt; </p><p>M </p><p>m </p><p>9 </p><p>&gt; </p><p>9 </p><p>0 9 -t </p><p>to </p><p>L~ </p><p>m </p></li><li><p>252 M. JULLIERE ET AL. </p><p>As explained above (see Section 4.2), the Doppler signal is modulated at the same time in amplitude (because of ground irregularities), in frequency (because of the width of the emitted beam:cos ~0 is varying) and in phase (because of variations in distance covered by the ultrasonic wave). In order to determine precisely the speed from counting the signal period, it is necessary to achieve a digital filtering which estimates, on a sufficient sample number, the exact value of this period. But, since the robot speed can vary quickly, it is not possible to average on a great number of periods. Therefore, the analog signal is first improved by switched capacitor filters which are driven by a microprocessor (#Pj) which is also used for digital filtering. </p><p>There are two analog filters: </p><p>- a band-pass filter, centered on the Doppler frequency estimated by the micro- processor, reduces the signal spectrum and makes less random its comparison to a threshold, since the output depends not only on the instantaneous value, but also on the earlier values. </p><p>- and a low-pass filter, with a cut-off frequency four times lower than the former frequency, gives an estimation of the 'short-term mean val...</p></li></ul>


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