Download - A relative localisation system of a mobile robot

Journal of Intelligent and Robotic Systems 1 (1988) 243-257. 243 �9 1988 by Kluwer Academic Publishers.

A Relative Localisation System of a Mobile Robot

M. J U L L I E R E , H. P L A C E , E. B A Z I N , andJ . F. R A D E N A C LA TEA, lnstitut National des Sciences Appliqu~es (INSA), 20, avenue des Buttes Co~smes, 35043 Rennes Cedex, France

(Received: 31 March 1988)

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.

Key words. Mobile robot, localisation, inertial systems, Doppler sensors, contactless measurements.

I. Introduction

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.

2. Basic Principle of the Method

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 orientation. 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).

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

244

u

u

Fig. 1.

0

Definition of the attitude and linear speed.

M. JULLIERE ET AL.

/ •

mobile robot are mounted on the vehicle and have no contact with the ground. This

method is based upon - instantaneous attitude measurement by integrating the angular speed of the

vehicle around an axis normal to the ground, from a gyrometer. - instantaneous position measurement by integrating the linear speed of the

vehicle, from an ultrasonic emitter-receiver based on the Doppler effect. - 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.

3 . A t t i t u d e D e t e r m i n a t i o n

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:

3.1. CHOICE OF MEASUREMENT METHOD OF THE ATTITUDE

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. 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:

RELATIVE LOCALISATION SYSTEM OF A MOBILE ROBOT 245

> 4800 bds Serial Link

vPI

<

I, Coordinate Computing and Filtering

0

I Integrator and [ A/D Converter ]

Coordinates X, Y and 0

Covered Distance

I , ,[

< ) AnaloE Filters

Doppler Sensor

I

Filterin~ and

Countin~

Temperature Measurement

Temperature Control

1 fe fr

Ultrasonic Emitter

and Receiver

Fig. 2. General organisation of the localisation system.

246 M. JULLIERE ET AL.

- the full scale range, i.e. maximal value of l0 I, above which the 0 measurement becomes unreliable.

- the resolution, i.e. minimal value ofl 0 I, below which the 0 measurement is of the order of its drift.

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. l 0 -3

FS). On account of cost and overall dimensions, a sensor of the piezo-electric 'tuning-

fork' type has been selected.

3.2. ANGULAR RATE SENSOR

As for mechanical gyrometers, the effect of the Coriolis force F, = - 2 m f ~ ^ 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.

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.

0 M

V r

>

Fig. 3. Basic principle of the piezoelectric tuning fork gyrometer.


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.

3.3. I N T E G R A T I O N OF T HE SENSOR O U T P U T

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:

k T (V0 - V~) dt = 0 (T: clock period, k: integer >> 1).

It follows that

~ r Vodt = ~r~O dt = ~[O(kT) - 0(0)]

= f2r ~ d t = [ N ( k T ) - N(0)] gerZ,

Gyrometer

Clock

Integrator

ontrol Logic I

I

? ! -

~ o .

Fig. 4. Acquisition of attitude.

UD/down Counter

+

V ref

> f


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

V~aT O ( k T ) - 0(0) = [ N ( k T ) - N ( 0 ) ] - -

The quantity VrefTis chosen so that the counter working with 12 bits (0 ~< N ~< 4095)

goes back to its initial value after a variation of 360 ~ From the former expression, one deduces

V~r T 360 I - - "~ 0.0879 ~

4096

I is the angular equivalent of a counter increment. Analog circuits of the device (Figure 4) have been chosen so that their defects

(drifts, offsets, etc.) have only a very weak effect on the measurement, compared with the sensor resolution.

4 . L i n e a r S p e e d D e t e r m i n a t i o n

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.

4.1. CHOICE OF A SPEED M E A S U R E M E N T M E T H O D

Several solutions can be considered for speed measurements:

- accelerometers, found in air navigation, are not convenient for vehicles whose acceleration is very low ( < 0.1 g), such as industrial trucks.

- odometers, as already mentioned, give inaccurate measurements for rough grounds.

- correlation methods give good results, but are complex to implement, both for their implantation and for their signal processing.

- 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.

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

2 cos ~o fD = - - V (fo = f - f e ) "

2

RELATIVE LOCALISATION SYSTEM OF A MOBILE ROBOT

Fig. 5. Measurement principle of speed by Doppler effect.

249

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

i ,, 2 cos q~

fD d t = N ~ i - N~,g _ - - A u g .

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.

4.2. THE DOPPLER EFFECT ULTRASONIC SENSOR

This sensor consists of a separate emitter and receiver (piezoelectric ceramics), working 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.

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).

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


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.

It can also be shown [4] that, in order to minimise the spectrum width, an aperture angle of the emitted beam near to

~/2 cos q~

Crad = 4Z

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.

In fact, a compromise has to be found between several causes of spectrum enlarge-

ment:

- 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. - if the angle is small, only some irregularities of the ground surface participate in

the Doppler signal, leading to an important amplitude modulation.

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 ~ Lastly, the variation with temperature of the acoustic wave propagation velocity

(c = 2f) must be taken into account:

c = co (co" velocity at ~

which reacts upon the Doppler frequency measurement. On the other hand, effects of humidity and wind speed variations can be neglected,

since they give a second-order error due to the fact that the wave travels both forwards and backwards.

4.3. DOPPLER FREQUENCY MEASUREMENT

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.

fe

Emi s s io

n

>

Reception

/

.,

, .>

Lo

w-p

ass

Filters

~,1

.5

KHz

Comparators

F D

~PI

_1l_

40

m

m

I_

>

Fig

. 6.

D

oppl

er f

requ

ency

mea

sure

men

t an

d pr

oces

sing

.

Thres-

holding

uP2 t

7=

> -q

C~

�9

>

>

-t

Z

r~

< M

m

�9

> �9

0 �9

-t

to

L~

m


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.

There are two analog filters:

- a band-pass filter, centered on the Doppler frequency estimated by the microprocessor, 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.

- 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 value' of the signal, which is used for thresholding before counting.

A digital filtering of the same type is implemented by two microprocessors (see Figure 6):

- the first (#Pj) estimates, from the conditioned Doppler signal, its half-period and generates a squared signal of a 50 times higher frequency, a signal which drives the analog filters. - the second (#P:) repeats this filtering applied to the analog filter output, whose

spectrum is reduced.

The digital filtering algorithm allowing the Doppler frequency estimation is the same for both microprocessors. It can be summarized as follows.

From the microprocessor clock (frequency: 10 MHz), a frequency ~0j2 = 833 kHz is obtained by dividing by 12 and the period number Ni of ~0j2 is counted during the ith half-period of the Doppler signal:

tP12

The four last acquired values of N,. are memorized and also the last calculated mean value N, _ ~, and every N~ is compared to ~ _ ~. Any value N, having a difference with N,. ~ of at least 50% is replaced by N~ ~ ___ 1 (depending on the margin sign) and a new mean value N, is calculated before acquiring a new sample.

The microprocessor PPz corrects this value to take into account variations of the sound velocity with temperature by means of the acquisition of a voltage arising from a thermistor and the use of a table listing the correction factor to be applied to N,.


This corrected value N,, represents the half-period of the Dopp le r signal and gives the

required value of the Dopp le r frequency.

~12

2N,

N,. is also used to generate a signal o f frequency ~ using a counter driven by a

frequencyf~x~ selected so that the vehicle covers a distance of 40 m m during a period

l/f~:

fext fext 4 cos q~ fext Z - - 2 f D - v,

N, (]912 2 (PI2

I'+r~ 4c~ t 4 c~ q~ fext AU" J~i dt = 1 - 2 qh2 - 2 ~ol2

To obta in Au = 4 0 m m with 2 -- 1 .508mm (c = 330m/s a n d f e = (3.5/16) M H z )

and 1/~p~2 = 1.2ps, one finds

Jext COS ~ : 7 . 8 5 4 k H z .

By choosing

3.5 .f~xt - M H z = 10.938kHz,

32

cos ~p is given by

c o s r = 0.718 or ~ = 44 ~ .

An interrupt signal is generated every t ime a distance of 40 m m has been covered by

the robot�9

5. Mobile Robot Path Estimation

5.1. PRINCIPLE OF THIS ESTIMATION

The p rob lem is to est imate the coordinates X(t) and Y(t) of the robot , knowing its initial coordinates X(0) and Y(0), and also the longitudinal speed V(ti) and the

at t i tude O(ti) for every sampling time (0 < ti < t). It is possible to write [5]

X(t) = f~i V(r) cos 0 (r) dr, Y(t) = f~ V(r) sin O(z) dr

or, in discrete form

x, = x, , + E ( t i - t , , ) co sg ,

Y, = Yi , + ~ ( t i - ti l ) s inO, .


-~ and ~ are mean values in the interval [ti_l, t~]:

g : �89 + o,_,),

I4 (ti - t~_ ~) = Au~, distance covered during this interval.

The more the sampling step is small, the more these relations are exact. But, as was previously shown, a small interval [t~ 1, t,] involves significant errors in the estimation of the Doppler frequencyfD and, according to the covered distance, Au, Therefore, it was preferred to sample, not at (ti - ti ~) constant, but at the covered distance Au constant [1]: the former value Au = 40 mm has been chosen as a sampling step. This value agrees with t~ - t~ j = 40 ms for a speed of I m/s.

5.2. IMPLEMENTATION

In the case of industrial trucks, the former time interval can be considered as a minimum. So, during 40 ms, it is necessary to acquire the attitude 0i given by the gyrometer, calculate new values of X, and Y~, and deal with the result out- puts. To avoid angle conversions and trigonometric functions calculation, sin 0 and cos 0 are tabulated between 0 and 90 ~ the table input being expressed as gyrometric sensor units (0 ~< N ~< 4095). The integer values of 2 ~~ Au sin (2rcN/4096) are stored in this table, allowing further calculations on integers. With these pre- cautions, the microprocessor has sufficient time to calculate the coordinates X,, Yi and 0i, and express them in usual units (for example, ~ and Y~ in cm, and 0i in degrees).

The coordinates X and Y are available on 16 bits, with centimeters as the unit. Consequently, - 327 m < X, Y < 327 m. They can be transmitted to an upper level computer, at its request, in the form of a 12-character ASCII message:

X3 X2 Xl -S'0 Y3Y2Yi Y0 020, 00CR

the X,, Y, and 0~ representing the ASCII codes of hexadecimal numbers of 16 ~ weight.

5.3. TRAJECTORY ACHIEVEMENT FROM INITIALISATION

To calculate 0i, X~ and Y,., the system must know their initial values given by the former computer. Since the data transmission is time expensive, all the calculations are made in reference axes Moxy bound to the initial position (00, X0, Y0) (Figure 7).

The absolute position (0a, X, Y) is obtained, from the relative position (0, x, y) by

0, = 0 + 0 0 ,

X = X0 + x c o s 0 0 - y s in00 ,

Y = Y0 + x s in00 + y c o s 0 0 .


Y(t)

Yo M0 t

I

I X o X (t)

Fig. 7. Estimation of the trajectory.

>X

The interest in this method lies in that sin 00 and cos 00 are computed only once between two initialisations.

5.4. RESULTS

The relative localisation system described here has been tested on a wireguided truck which runs along a closed loop of about 50 m, at a speed of 0.5 m/s. Figure 8 compares the trajectories determined by this system with those actually followed by the truck, in the two subsequent cases:

- the trajectory of Figure 8(a) has been obtained with an initial balancing of gyrometer offset (electronic balancing) but without its drift being removed.

- the trajectory of Figure 8(b) has been obtained after estimation of that drift and its correction by computing throughout the run (logic balancing). This figure shows a localisation of _+ 0.5 cm, on a covered distance of 50 m, giving a precision of about 2%.

This precision must be considered as optimum, because

- it diminishes for the extreme values (small or high) of motion speed because of the difficulty of estimating the Doppler frequency;

- it is better on high ranges, since the over-estimates and the under-estimates are balanced out and the starting and stopping periods yield weaker relative errors;

256 M. J U L L I E R E E T A L .

S.~ ....................... "~176

i ~ .." ...,."

i ,...,. .................. . ...." i. { (a)

i~ ............................ "~--, \\~ ............................... \ ::::::::::::::::::::::::::::::::::::: .....................................................

�9 i

................ ~ ........ :_

~....... .. ...." "". . ....... .,,..'"""'"

.r

' ;) : .."

i .. .......................... "'~

i" (b)

~,?..~ \-.~ k,~'222222 .-'::'::':::::::::::::::::.'.'-.'.'::.'-'-'~.'.'":""""":-""::&?,. ?:: :--:~ 7:"::.'::::::

i# I

'.,'\

d ....!

~'_:. .................................. i.~ -.. .1"/

".. ........................ ..-'""

Fig. 8. Two estimations of a same closed trajectory: without (a) and with (b) correction of gyrometer offset drift.


- it is a function of the attitude measurement, itself function of the gyrometer offset drift. Even when stopped or running in a straight line, the gyrometer delivers a

signal not zero and time variable.

The localisation measurement of a mobile robot is thus greatly dependent on the attitude measurement and its precision would be highly increased by use of a gyrometer introducing a weaker offset drift. On the other hand, the Doppler sensor gives range measurement with a precision of within about 1%.

6. Conclusion

The interest in the localisation system of a mobile robot presented in this paper, is that it can be applied to any evolution universe, without preliminary preparation (beacons,

marks, etc.), since this localisation needs no contact with the ground. It appears most efficient and precise for motion speeds of about 1 m/s and on ranges of about 100 m. The defect found in the attitude measurement depends only on the choice of the gyrometer type and can be reduced by use of a gyrometer with less drift, but which is more expensive.

This localisation system can be used in various environments (car parks, greens, fields, ocean beds, etc) and can induce many applications (cleaning, lawnmowing, farm work, nodule gathering, etc.).

References

1. Julli6re, M., Marc& L., and Perrichot, H., A guidance system for a vehicle which has to follow a memorized path, Proc. 2nd Intern. Conf. on AGVS, Stuttgart (1983) pp. 211-221.

2. Radix, J.C., Gyroscopes et gyromktres, C6padu6s Editions, Toulouse (1978). 3. Richardson, N.A., Lanning, R.L., Kopp, K.P., and Carnegie, E.P., True ground speed measurement

technique, Intern. Off-Highway Meeting and Exposition (ed. SAE), Millwaukee, 821058 (1982), pp. 1-10. 4. Th6venin, A., Etude et r6alisation d'un capteur fi ultrasons permettant de mesurer la vitesse d'un

tracteur agricole par effet Doppler, Th+se de Doctorat d'Ing6nieur, Universit6 de Bordeaux I (1983). 5. Tsumura, T. and Fujiwara, N., An experimental system for processing movement information of

vehicle, Proc. 28th IEEE Vehicular Technology Conf. (1978), pp. 163-168.

Download - A relative localisation system of a mobile robot

Top Related