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2001 IEEUASME InternationalConference on Advanced Intelligent Mechatronics Proceedings 6-12 July 2001 Como, Italy An outdoor navigation system using GPS and inertial platform S. Panzierit F. PascucciS G. Ulivit tDipartimento di Informatica e Automazione SDipartimento di Informatica e Sistemistica Universith degli Studi "&ma n e " Universita degli Studi "La Sapienza" v i dell8 vasa Navale 79, 00146 &ma, Italy Via Eudossiana 18, 00184 &ma, Italy {panzieri,ulivi)@uniroma%it pascucciQdiauniroma3.it Abstract-The use of Global Positioning System (GPS) in Outdoors, the Global Position System (GPS) is an in- outdoor localization i a quite common solution i large en- s n teresting possibility to cope with these problems without vironments where no other references are available and p- sitioning requirements are not so pressing. Of course, fine adding special devices as reflectors or targets. Till May motion without the use of an expensive differential device 1st of this year, the available precision was downgraded for is not an easy task even now that available precision has military reasons, so that only differential receivers could been greatly improved as the military encoding has been be used for localization; now the full satellite precision can removed. In this paper we present a localization algorithm be achieved with a simple, cheap unit. It requires very lit, based on Kalman filtering that tries to fuse information corn- ing from an inexpensive single GPS with inertial and, some tle data processing and its error is independent from the times uncertain, map based data. The algorithm Is able traveled distance and from the positions of the obstacles. to produce an estimated configuration for the robot that can be successfully fed back in a navigation system, leading The problem is, therefore, to characterize the performance to a motion whose precision is only related to current in- of this system in different situations and t o adapt the lo- formation quality. Some experiments show di5culties and calization and the navigation systems to get the maximum possible solutions to this sensor fusion problem. benefit from its use. The paper is devoted to analyze the localization system I. INTRODUCTION implemented for an ATRV-Jr unit that has t o move in a parking lot on a paved but rather rugged terrain. After Outdoor navigation is an exciting and quite varied topic; a brief description of the available exteroceptive sensors, there are several types of environment that require differ- the accuracy of the GPS is discussed in some detail on the ent levels of autonomy and different kind of sensors. A basis of some experiments. Indeed, this is the most im- vehicle traveling in a wood shows requirements that are portant sensor for large movements in open spaces, when not needed by one exploring a parking lot; both, however, no other reference is available and its short-term error af- are doing outdoor navigation. In this paper we shall ad- fects the implementation of the entire navigation system. dress the latter situation that seems to be more promising The localization system is based on an Extended Kalman for applications; surveillance, cleaning, moving goods, and Filter, it is described giving emphasis to the peculiarities even searching for a specific item (a car, a container) are arising from characteristics of the used sensors. Finally, operations that can be, in a near future, assigned to out- some guidelines are given to design the planner according door robots. By the way, such units could be freed from the to the EKF achievable performance and the nature of the usual energy shortage, because they can adopt fuel instead environment. The description of an experimental result of batteries as the primary power supply. concludes the paper. Even in this rather simple environment, problems are very different from those encountered in indoor navigation; 11. PERFORMANCE OF A SIMPLE G P S SYSTEM indeed, the required sensors must be different; as an exam- A GPS receiver relies on the signal received from several ple, ultrasonic sensors cannot be used, being them affected satellites that are not geostationary. Therefore, the number by rain and wind and having them, anyway, a too short and the position of the available satellites change in time range. However, the greatest difference is the kind of a ipfluencing the system precision. Several information are priori knowledge that can be used for localization, a skill available on sources of GPS errors; often they refer to long- required also outdoors. Indeed, the typical environment term averages and/or to high quality receivers that cannot features used indoors for this purpose are quite scarce out- be employed on a mobile robot. doors, moreover, large, stationary obstacles can appear and To understand the level of precision and the error be- disappear: consider, e.g., the effect of some cars parked in haviour when using an inexpensive receiver (we used the front of a wall. When perceived by the exteroceptive sen- Garmin GPS35-HVS), some experiments have been con- sors, they can either be interpreted as the wall itself (and ducted in the parking lot of our department. We chose two therefore produce an erroneous localization) or cause the places, say points A and B; the first was far from obstacles distance measures to be discarded (so reducing the amount affecting the wave propagation, the other was in a sort of of available information). corridor, delimited by two buildings. The robot was placed 0-7803-6736-7/01/$10.000 2001 IEEE 1346 still in the two points where it acquired data in different hours of the day. All the acquisitions lasted 15 minutes, during which measures were collected with a sampling p e Satellite Firat Second Third riod of 1 second, resulting in 900 measures per acquisition. number muisition acquisition acquisition The first two tables refer the satellite availability in the two points. As it can be seen, the number of available satel- TABLE I SATELLITE AVAILABILITY AT POINT A I Total I 3.0 I 7.9 I 2.4 I 0.9 I 10.8 I 9.2 I number acquisition acquisition percentage 6 1 197 I 127 1 18.0 7 1 685 I 282 I 53.7 a 1 18 I 427 I 24.7 Satellite is Frt Second Thud Overall number acquisition acquisition acquisition percentage 3 180 0 0 6.6 4 401 298 121 30.3 5 319 602 697 59.9 I I 6 0 0 82 3.0 - 4 - 2 0 2 4 6 8 m Fig. 1. First acquisition at point A. Number of satellite: dot 4, lites is quite different in the two points, being the most plus 5, circle 6 probable value 7 in the open location and 5 in the partially covered one. Note that 4 satellites is the minimum number for a complete 3D localization. plotted with different symbols according to the number of The next two tables relate the Standard Deviation of the satellites. measures for each acquisition, computed according to the As it can be seen, there is a lack of resolution in one number of satellites and for all the measures. direction, because the available satellites are aligned. Only Observing these tables, it easy to understand that the the addition of the 6-th satellite, which probably was not number of satellites provides just a very rough indication of aligned, allows a remarkable increase of precision, as it can the accuracy of the measure (look, in particular, at row 5 of be shown by the positions of the circles. Tab. 11). Indeed, a different indicator should be available, Another important point is the way the error changes in the Dilution of Precision (DOP), which is based on the time, i.e., if it is white or colored. A fast changing error can satellite geometry in sky, but the installed driver we have be better filtered, but its residue adds some random motion does not return this information. This is shown by the to the one desired for the robot. On the contrary, a slow Fig. 1 and Fig. 2 , where the two acquisition in point A are varying one cannot be removed in short time, but allows for a smoother movement; moreover it should be considered TABLE 1 11 that we are interested in the relative position accuracy, as STANDARD DEVIATION (M) AT POINT A here and there the robot finds some environment feature to improve its localization. satellite I First 1 Second I An easy way to look at the phenomenon is to plot the number acquisition acquisition “path” of the measured position for a given number of satel- EWIS-N EWIS-N lites. Looking at Fig. 3 (obtained for 5 satellites), it is easily 4 I - 1.0 I 3.5 understood that successive errors are tightly related, and 5 I 1.2 I 3.6 I therefore the error is strongly colored, in particular when 6 2.3 1.1 1.9 4.2 the errors are large. A better characterization is shown by 7 2.1 1.7 2.6 4.1 the auto-correlation function that is not reported here for 8 0.4 0.0 1.0 2.3 sake of space. Moreover, in this case, there is also a strong Total I 2.2 I 1.7 I 2.3 I 4.2 correlation between E W errors and N-S errors. jFrom these considerations we can conclude that changing the c& 1347 sensory system prediction prediction matching 5 -20 -15 -10 -5 0 5 10 15 g-yfjyJ-J‘ Z -l m Fig. 2. Second acquisition at point A. Number of satellite plus 4, Fig. 4. - Structure of the localization system (2-l denotes the unit dot 5, circle 6 delay operator) the Cartesian coordinates of the vehicle center and 4 is the mobile platform orientation with respect to the x-axis. The on-board sensory system includes two incremental encoders measuring the rotation of each motor, a inertial navigation system that provides measures of the robot lin- ear accelerations and angular velocities, a laser scanner E which measures the distances between a fixed point on the robot body and obstacle surfaces in the environment, and a GPS antenna measuring absolute position in the geodetic coordinates. The structure of our localization system, shown in Fig. 4, proceeds directly from the EKF equations [2]. At the k-th step, the kinematic model of the robot is used to compute -15 -10 -5 0 5 10 15 an inertial prediction 5 k l k - l and an associated covariance m matrix P k l k - 1 ; an observation prediction &k is formed and Fig. 3. Second acquisition at point A. Error path for 5 satellites compared with the measure z k provided by the sensory system. The results are the innovation term Vk and its variance matrix of the GPS according to the number of covariance matrix s k , that are used by the EKF to produce satellites is of little or no help in improving the overall p r e the state estimate 2 k and the new associated covariance P k . cision, whilst this could be done if the satellite geometry were available. A . Inertial prediction Moreover, a the error is slow varying, approaching once s in a while some known environment feature can reset the Define the state vector as x = (P2,pY,~$,w,b) where v overall error and keep it bounded at a d u e lower than the is the linear velocity of the vehicle and b denotes the ac- expected one. celerometer bias [5]. The rate gyro bias is constant, so we estimate it only at the beginning of the navigation (see [8] 111. THELOCALIZATION SYSTEM for an algorithm estimating gyro bias). The inputs of the inertid model are ?Lk = (az,wf where a: is the mean We consider a mobile robot with differential drive kine robot acceleration along the motion direction and w i is the matics [6],described by the following equation: mean angular velocity during the k-th sampling interval. (i) (H).. (1) The inertial prediction is then The motion is generated by four tires, actuated by two independent motors. The robot location (i.e. robot con- figuration [3]) is given by z = (pz,pu, q5), where p”,pu are 1348 TY P" where & = &1+ (1/2)w+,Atk is the average vehicle ori- entation during the sampling interval Atk. The covariance matrix associated with the prediction error is written as Fig. 5. Holonomic and nonholonomic velocities The measurement noise depends on the interaction be- tween the sensor system and the environment, which is + J,f (uk)c (J,f( U k ) ) T Q* (3) not invariant in space and time. For example some sur- Here, J l ( . ) and ,Ti(.) the Jacobian matrices off(-) with faces (glass or hedges) are more difficult t o detect for laser are respect to 5k-1 and U k , Pk-1 is the covariance matrix at sensor. To model this fact, we have chosen to label each time instant t k - 1 , C = diag{u,2,,o&) is the covariance segment of the map with a value representing the relia- matrix of the gaussian white noise which corrupts the in- bility of the laser measure provided by that segment, and put measure and Q = diag{og,, U&, .&U:, ,} ." is the CO- to modify the corrispondent rows of the covariance matrix variance matrix of the gaussian whte-noise which directly R accordingly [ ] Also the GPS rows of R are modified 7. affects the state in the kinematic model. by the number of satellite that the antenna uses at the is tant time t k , because the sensor accuracy depend on their B. Observation prediction and matching number and position. The observation prediction consists of subvectors 2; (pre- Moreover to avoid the inclusion of outliers in the cor- dicted encoder velocity), 2: (predicted laser readings), 2' ; rection phase, we need to set up for the laser measure a (predicted robot position by GPS). For the observationpre- validation gate as follows [I]. Suppose that vk,j is the in- diction a;, we simply let novation term for a laser ray; it will be passed t o the EKF only if 4 = he(Xk/k-l) = &/k-l. (4) (9) The observation prediction of the laser mearmre is com- puted over a given environment map M and the inertial where sj is the j-th diagonal term of S and parameter 7 prediction should be tuned by experimental trials. In the same way GPS measure obtained using less than four satellite are = h'(%k/k-i, M ) . ( 5 ) discharged. We shall not detail here the above computation. It should be noted that h reflects the way in which the environment C. Extended Kalman Filter map is represented - in our case, a list of segment [4] - The Ektended Kalman Filter is used to correct the in- as well as the model interaction between the environment ertial configuration estimate one the basis of the validated itself and the laser scanner. The subvector 2 is written observations. Particularly, the final configuration estimate ' : as is obtained as In (6),we consider a conversion of the GPS measure from where Kk is the Kalman gain matrix geodetic coordinates to the environment framework. The innovation term and the associated covariance, be- ing & = (4,ak, ~ p "and Z k the measured outputs, are ) The covariance associated with the final configuration e s then computed 8s timate & is given by where J,"(-) is the Jacobian matrix of h = (he,h', h9pS) Iv. PLANNING AND CONTROL respect to xk/k-1. The first term used to compute s k r e p As explained before, the GPS provides the position of resents the uncertainty on the observation due to the un- the robot with a maximum error that can be as high as 20 certainty on the inertial prediction. The second term is the meters, even if generally this is quite lower. If the trajeo observation noise covariance matrix. tory proceeds for a long time far from any reference point, 1349 -I 0 -3 0 0.5 I -I . U o as I Fig. 6. Trajectorieswithout (left) and with (right) forward cut o f f the position error can reach that value. If the range of Fig. 7. The mobile robot ATEN-Jr the other exteroceptive sensors is larger than the actual position error, then this can be corrected when a feature has been set at zero until 11 11 is less than a threshold appears in the robot field of view. Otherwise, as it happens of 1Odeg. In this case trajectories are more linear and, for in our case, there is the possibility that the error cannot be this reason, this strategy has been implemented. The only corrected. This event is uncommon, and its occurrence can point where this control fails is the origin itself where p be avoided by planning a path that passes near some en- is undefined but to avoid also strong discontinuities in the vironment feature before the errors grow too large, even if control law, possibly caused by sudden corrections of the in this way the minimum length property is missed. More estimated position due t o new available laser measures, the over, if the DOP is available, this behaviour can be acti- via-points have been defined as a circular region of radius vated only when needed, perhaps by a real time trajectory 0.5m and the robot has been forced to halt when it steps reconfiguration. into this region. Thereafter, the proposed solution has been the one of specifying the path as a sequence of via-points to be at- Finally, to take into account the presence of obstacles, tained using, for example, a simple static timeinvariant has been added an obstacle avoidance module whose de- feedback control law on each segment. It is well known scription can be found in [9]. ie that, for nonholonomic systems lk unicycle robots, the point tracking problem, i.e., tracking of only Cartesian c e v. EXPERIMENTAL RESULTS ordinates, can be solved using a partial feedback lineariza- The proposed algorithm has been tested on the mo- tion of the dynamic model and a simple P D like control bile robot ATRV-Jr produced by Real World Interface (see law in the new coordinates [lo]. If we suppose that both Fig. 7. The robot has four tires, actuated by two inde- ) exact tracking along each segment and a particular pos- pendent motors, so the kinematic model of the platform is ture at the via-point are not required, the problem can be a differential drive one. The sensory system is composed relaxed to the stabilization of only the first two coordi- by two incremental encoders mounted on the two motors, a nates of system (1). This could be attained with an easy 180 degrees view laser scanner (LMSSick), a GPS (Garmin strategy, obtained by simplifying the one presented in [ll]: GPS35-WS) and the Crossbow 6-axis inertial navigation first of all (see Fig. 5 ) define a suitable holonomic velocity sensor. Each sensor is connected to the ATRV-Jr on-board 'uh, unaware of the nonholonomic constraint, able to per- PC (Pentium II, 350MHz) through a serial port on a Rock- form the stabilizing task, i.e., able to steer the origin of the eport multiserial port card. On the same P C run the low robot frame over the origin 0 of the reference frame; sec- level control software (the RW's ReFlex accepting speed ond, define two control laws one as projection of V h along commands and returning odometric data) and the CORBA the nonholonomic direction 2),h and the other steering the servers, that distribute the sensor data over the network. nonholonomic axis of the vehicle towards the holonomic The high level control software, written in C++ language, velocity vector (to reduce p) is a client program that runs on a notebook (Pentium I1 at 366MHz) that interacts with the ATRV-Jr using TCP/IP over Ethernet link. The experiment here reported has been conducted in the parking lot of our Department (Fig. 8). V The navigation algorithm described in section l has been The convergence to the origin can be easily proved con- implemented using data coming from the localization filter. sidering that eq. 13b independently steers the angle $ to a I The robot, starting its path in S (see Fig. 8), remains value that will definitively let B = 0. Now, using a Lya- still for 15sec to estimate both the initial bias for the in- + punov candidate V(z, y) =.x2 y2 it is easy to see that its ertial navigation system and the offset for the GPS carte- + derivative is, when = 0, V = -2Ke(z2 y2), and is neg- sian position. In this figure the odometric path (dashed) is ative defined. At the left of Fig. 6 trajectories generated extremely inaccurate and rapidly diverges while the GPS for different starting points are reported. To avoid back estimate (plus) has a limited error. The output of the fll- motion a different strategy has been applied and its results ter (circles) does not coincide with the effective path (not reported at the right of the same figure: the first control reported) but its maximum deviation has been of 0.5m. 1350 25 Laser correction m m Fig. 9. Laser correction on building corner Fig. 8. Robot path in the Department parking lot: the path by the algorithm (circle), GPS (plus) and odometry (dashed line) ment an Extended Kalman Filter for an ATRV Jr robot. The results show that it is very important to have infor- After this initialization step, moving with constant speed mation about the Dilution Of Precision (DOP) or about towards point 1, the robot integrates satellite measures the satellite geometry to estimate its error. This error also with laser readings but, due to unpredictable obstacles affects the strategy of the planning system: if large errors (parked cars) the matching with the map is not always are expected the trajectory must pass near some easily rec- possible. Moreover, in the front direction, walls are too ognizable environment feature, even if this lengthens the far (more than 8 meters) and the estimated position relies path. only on GPS with an error that slowly increases. When the robot approaches point 1, and the laser system starts Acknowledgments to give a reliable measure that can be matched with the This work has been partially supported by Murst funds map, the error is reduced from 0 . b to O.lm. To help the inside RAMSETE project. Kalman filter, an additional stop of a few seconds is used to stabilize the estimate configuration. After that, circumnav- REFERENCES igating the obstacle, the robot moves to via-points 2 and [I]J. J. Leonard and H. F. Durrant-Whyte, "Mobile robot lo& 3. Although the robot, approaching point 3, has no infor- tion by tracking geometric beacons," IEEE n-Om. on Robotics and Automation, vol. 7 , no. 3, pp, 376-382, 1991. mation from the laser system and uses only GPS data, its [2] A. C. Gelb, Applied Optimal Estimation, MI" Preas, Cambridge, position estimate does not appreciably drift towards North: MA, 1994. this could be expected due to the big difference with GPS [3] J. C. Latombe, Robot motion planning, Kluwer Academic Pub- lisher, Boston,MA, 1991. information, but, being the covariance matrix associated [4] J. Gomala,A. Stem, and A. Ollero, "An iconic position estium to the GPS data greater than P l - ,the filter output is kk1 tor for a 2D laser rangefinder," 1992 IEEE Int. Conf. on Robotics not greatly influenced. This dominance, with actual gains, and Automation, San Diego, CA, pp. 2646-2651, 1992. ( 1 B.Barshan and H.F. 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C d i o , G. Indiveri, "On the sta- . Global Positioning System has made outdoor localization bilization of the unicycle model projecting a holonomic solution," Proc. of 8th Int. Symp. on Robot& with Application, Maui, H , I available even using inexpensive receivers. In the present 2000. paper au experimental analysis of its performance is re- . ported and it used, together with other sensors, to impls 1351

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