Precise Indoor Localization System For a Mobile Robot Using Auto Calibration Algorithm

Transcription

1 Precise Indoor Localization Syste For a Mobile Robot Using Auto Calibration Algorith Sung-Bu Ki, JangMyung Lee, and I.O. Lee : Pusan National University, : Ninety syste Abstract: Recently, with the developent of service robots and with the new concept of ubiquitous world, the position estiation of obile objects has been raised to an iportant proble. As pre-liinary research results, soe of the localization schees are introduced, which provide the absolute location of the oving objects subjected to large errors. To ipleent a precise and convenient localization syste, a new absolute position estiation ethod for a obile robot in indoor environent is proposed in this paper. Design and ipleentation of the localization syste coes fro the usage of active beacon systes (based upon RFID technology. The active beacon syste is coposed of an RFID receiver and an ultra-sonic transitter:. The RFID receiver gets the synchronization signal fro the obile robot and. The ultra-sonic transitter sends out the traveling signal to be used for easuring the distance. Position of a obile robot in a three diensional space can be calculated basically fro the distance inforation fro three beacons and the absolute position inforation of the beacons theselves. Since it is not easy to install the beacons at a specific position precisely, there exists a large localization error and the installation tie taes long. To overcoe these probles, and provide a precise and convenient localization syste, a new auto calibration algorith is developed in this paper. Also the extended Kalan filter has been adopted for iproving the localization accuracy during the obile robot navigation. The localization accuracy iproveent through the proposed auto calibration algorith and the extended Kalan filter has been deonstrated by the real experients. Keywords: localization, RFID, active beacon syste, auto calibration, obile robot I. Introduction In a near future, ubiquitous coputing and ubiquitous networ ay generate various new services. Especially, recognition of huan beings and objects at any place at anytie will becoe basic and fundaental technology for the obile robot localization which is perforing the various ubiquitous services to huan beings []. As exaples, for the hoe and service robots, the localization is a ajor issue for the robust operation in different environents. Manufacturing robots have been used for the tas anipulation in a fixed worspace. However a obile robot is perforing various services while it is oving, it can be applied for the industrial applications as well as hoe applications. One of the specialties of the obile robot is that it can replace the huan fro a dangerous woring environent. Therefore to give coands to the obile robot, the current position of the obile robot in a certain environent is essential. The localization schee can be classified into either indoor and outdoor schees or relative and absolute positioning schees depending on the position easureent ethodology. The relative position recognition is based on the representative dead reconing schee which estiates the position of obile robot using the increental value of wheels. This ethod has several advantages: it is siple, cheap and it can be ipleented in real tie. However depending on the floor states, slippage and sensor errors ay occur and ore hoarsely the error is accuulated without reset []. Therefore to copensate for the accuulated error, a gyro or an acceleration sensor should be added to the precise localization syste. *Acnowledgent This wor was partly supported by the IT R&D progra of MIC/IITA. [005-s--0, intelligent robot sensor] and Ninety Syste co., Ltd The absolute positioning syste ostly relies on the navigation beacons, active or passive landars, ap atching or satellite based navigation signals. GPS (Global Positioning Syste [] is atypical positioning syste which is free fro the accuulated errors of the relative position recognition syste. However, GPS can be used for the outdoor navigation, and it has too big error to be used for the obile robot navigation. Ultrasonic sensors are widely used for the indoor navigations to recognize the position of the obile robot and to avoid obstacles around the obile robot..to easure the position and orientation of the obile robot, ultrasonic sensors have been used [4]. To localize the obile robot woring the indoor environent, an ABS (Active Beacon Sensor syste is proposed, which is a cobination of an ultrasonic senor as a transitter and an RF (Radio Frequency odule as an ID receiver. In the syste, four ultrasonic transitters with RF receiver odules are attached at four different corners of ceiling, which can be identified by the ID code. The obile robot carries a localizer to call a specific ultrasonic transitter whose location is pre-recorded in the robot syste. The tie of freight easured fro the oent of calling to the instance of the ultrasonic signal arrival to the localizer is the basic inforation to easure the distance between the obile robot and the ultrasonic transitter whose position is nown a priori. If there are three distance data fro three different sensors, the location of the obile robot in three diensional spaces can be calculated by the triangulation ethod. Since the obile robot is oving in a public space where huans and other objects are scattered around, soe tie three distance data cannot be obtained for a credence instance even though there are at least four beacons (which is a cobination of the ultrasonic

2 transitter and the RFID receiver within a reachable space. To overcoe this proble instantaneously, a flat floor algorith and linear increental algorith have been proposed [5]. With the proposed algorith, the localizer becae robust against the obstacles and noises in the roo. The extended Kalan filter is helpful for soothing the position inforation, which is derived based on the dynaic odel of the obile robot. Basic assuption in the localization schee is the position of the active beacon is precisely recognized a priori. That is, the relative position inforation fro the beacon is the basis for the localization. Practically the installation of the beacon has several difficulties. The installation position should be selected to be safe and clean fro touching of huans and to be isolated fro water. Therefore, the best candidates are soe locations on the ceiling whose positions are not easy to easure. In this research, an auto-calibration algorith has been proposed to overcoe the difficulty in easuring the position of the beacon. That is, an ABS (Active Beacon Sensor syste with an auto-calibration algorith has been proposed to ae the installation of the beacons easy. The paper is coposed as follows: Section illustrates the structure of the ABS (Active Beacon Sensor Syste and the localization schee with the extended Kalan filter, and section explains the proposed auto-calibration algorith. Section 4 deonstrates the experiental data for providing the feasibility of the proposed auto-calibration algorith, and finally section 5 concludes this paper by opening further research issues. II. Active Beacon Sensor (ABS Syste. Syste architecture The proposed position recognition ethod can be extended and used to all oving vehicles indoor environent (hoe robot, service robot, huanoid robot, etc. Indoor environent is fored by corners and walls where soe of dess, tables, and coputers are assued to be located. Figure illustrates the structure of the proposed ABS syste. Fig.. Structure of the ABS syste. Four beacons are installed at each corner of ceiling in Fig.. The obile robot on the floor carries a localizer on the top surface. The localizer calls a specific beacon and receives the ultrasonic signal for the beacon one by one for the localization of the obile robot. For the calling, an RFID is sent to the beacons and the corresponding beacon responses iediately. That is, the beacon has a RF receiver and an ultrasonic transitter, while the localizer has a RF transitter and an ultrasonic receiver.. Distance easureent Fgure illustrates the basic localization algorith with the ABS syste. te. Fig.. Operation algorith of ABS syste. When the localizer sends out the RFID signal, it starts to count and stops the counting when it receives the ultrasonic signal which is sent bac fro a beacon corresponding to the RFID. The counter value represents the freight tie of the ultrasonic signal for the beacon to the localizer, which can be directly transfored to the distance by ultiplying velocity of the ultrasonic signal in the air. r[ ] v[ / sec] s[sec] ( v.5 0.6T[ / sec] ( s n h t d ( where, T is roo teperature, h is counter period, n is tier counter, td is circuit delay in the ultrasonic signal detection, s is the total ultrasonic freight tie, and r is the distance datu. With a distance datu, the possible location of the obile robot can be represented as a circle on the two diensional space. Therefore when the three distance data, r, r and r generate a coon point or a sall region where the robot ay exist. The absolute coordinates for the region can be provided by the position inforation of the beacons, ( X and, Y, Z, ( X, Y, Z, ( X, Y, Z. The coon point or the robot position, ( x, can, y, z be calculated as follows: x X y Y z Z r x X y Y z Z r x X y Y z Z r (4 There are several probles in the localization process. First of all, the arrival tie detection of the ultrasonic signal is highly susceptible to noises. Therefore only a beacon can be called by the localizer at a certain oent,

3 which delays the distance easuring tie. To synchronize the transitter and receiver of the ultrasonic signal, RFID has been used to identify a specific beacon as well as to ae the start to transit coand to the ultrasonic transitter. For the triangulation technique, iniu three beacons are necessary. In this syste, total four beacons are installed to provide the redundancy considering obstacles which blocs the ultrasonic transission. When there is no obstacle, the four distance data can iprove the position estiation accuracy. Practically, the accuracy is decreasing with the distance. Therefore, three sallest data are used to estiate the position. Through the pre-filtering process, the localization accuracy based on the tri-angulation technique can be iproved and becoe ready to be used for the post-filtering process by extended Kalan filter.. Extended Kalan Filter When there are noises in a easured signal, a Kalan filter is a general tool for estiating the true value of a signal [6]. Notice that there is a nonlinear relation between the easured distance and Cartesian coordinates of a obile robot in this ABS syste. Therefore, an extended Kalan filter for the nonlinear syste is applied for this syste to iprove the estiation accuracy [7,8], using the partial derivatives of the process and easureent functions to copute estiates even in the face of non-linear relationships. To apply for the extended Kalan filter, it is necessary to odel the easureent syste and the obile robot. It is assued that the obile robot has a state vector n r. The process, which is defined by the state vector, r, can be described by the nonlinear stochastic difference equations as follows: r f ( r, u, w (5 where x represents the position, is the input of u the obile robot, and w is disturbances in the process at tie -. n The easured values of the states, z, can be described as z h( r, n (6 where the rando variables, n, represent the easureent noise. In this case the non-linear function, f, in the difference equation (5 relates the states at the previous tie step to the states at the current tie step. It includes the paraeters of any driving function, u, and the zero-ean process noise,. w The non-linear function in the easureent equation (6 relates the states, r, to the easureent vectors, z. In practice, of course, it not possible to estiate the individual values of the noises at each tie step. However, the states and easureent vectors can be odeled assuing that they are negligible or copensated a priori as follows: ~ r f (ˆ r, u,0 (7 ~ z ( ~ h r,0 (8 where is a posteriori estiate of the state (fro a rˆ previous tie step. To estiate a process with non-linear difference and easureent relationships, new governing linear equations can be derived based on the nonlinear equations (7 and (8 as follows: r ~ ˆ r A( r r Ww (9 z ~ z H ( r ~ r Vn (0 where r and are the actual states and z easureent vectors, respectively, r~ and z~ are the approxiated states and easureent vectors fro (7 and (8, rˆ is a posteriori estiate of the states at step, the rando variables w and n represent the process and easureent noises, respectively. A is the Jacobian atrix that is defined by the partial derivatives of f with respect to r, that is, f [ i ] A ( ˆ [ i, r, u,0, W is the Jacobian atrix r[ defined by the partial derivatives of f with respect to w f, [ i ] W ( ˆ [ i, r, u,0, H is the Jacobian w[ atrix defined by the partial derivatives of h with h[ i ] respect to r, H ( ~ [ i, r,0, and V is the r[ Jacobian atrix defined by the partial derivatives of h h[ i ] with respect to v, V ( ~ [ i, r,0. v[ Note that for the siplicity in notation, the tie step subscript is sipped for the Jacobians A, W, H, and V, even though they are in fact different at each tie step. The Kalan filter iniizes the estiation errors by odifying the state transition odel based on the error between the estiated vectors and the easured vectors, with an appropriate filer gain. The state vector, which consists of the position on the x-y plane, linear/angular velocities, and linear/angular accelerations, can be estiated using the obile robot controller. The covariance atrix of estiated error ust be calculated to deterine the filter gain. The projected estiate of the covariance atrix of estiated error is represented as t P A P A Q ( P where is a zero-ean covariance atrix representing the prediction error, A represents the state transition atrix, P is an error covariance atrix for the previous step, and represents the process noise that coes fro the odeling error and other easureent or coputational errors. The optial filter gain K that iniizes the errors associated with the updated estiate is t Q t H P H G K P H ( where H is the observation atrix and G is the zero-ean covariance atrix representing the easureent noises. The estiate of the state vector rˆ

4 fro the easureent z is expressed as r ˆ rˆ K z h rˆ, n ( Therefore, rˆ is updated based on the new easured values represented as z. The error covariance atrix that will be used for the prediction, P, can be updated as follows: P I K H P. (4 After the current tie is updated to +, a new estiation can be provided using the equations ( to (4. III. Auto Calibration Algorith In the previous researches [9,0], the precise coordinates of the beacons are prerequisite for the localization of the obile robot in the roo as shown in Fig.. Therefore if the position of the beacon is shifted in soe reason, the localization error cannot be reduced by any ethod. With the auto calibration algorith, the positions of the beacons are calculated by the localizer within in the ABS syste. Figure 5illustrates the auto calibration algorith. Fig. 4. Mobile robot position. Figure 4 illustrates the auto calibration environent. After the four beacons are installed at the desired positions, the obile robot with the localizer is oved to the location A ( x, y, z which is nown and ared a priori. At the location, the localizer gathers all the distance data to the four beacons. And then, the obile robot is oved to A ( x, y, z and A ( x sequentially and gathers the distance, y, z data as in location A. Using the distance data, the beacon coordinates can be estiated. As an exaple, the location of beacon, ( X, Y, Z, can be calculated as x X y Y z Z d x X y Y z Z d x X y Y z Z d (5 where d, d and d are the distance to beacon when the obile robot is at A, A and A, respectively. By the sae procedure, the locations of other beacons also can be calculated. Fig.. Flowchart of Auto Calibration Algorith. IV. Experients and results Active Beacon Syste The localizer which sends out the RFID and easures the distance to the beacons, is designed in the intelligent robot laboratory using DSP TMS0C406. Four ultrasonic transitters are designed by using MSP40. For the syste developent, C++ has been used to support the object-oriented structural design.

5 The position estiation accuracy with the auto calibration algorith can be copared to the conventional approach without the calibration, and the results are shown in Table. Table. Position estiation results. Fig. 5. Localizer and Beacon. Ipleentation of auto calibration experients The experiental environent is fored and shown in Fig. 6. The position estiation results are copared with the auto calibration algorith and without auto calibration, assuing the width of floor and height of the pole are nown a priori.. The position estiation has been reduced to less than 5% by applying the auto calibration algorith for the localization, which is shown in Fig. 8. Fig. 6. Experiental environent. Indoor environent was prepared on the square floor to put the beacons at each corner of the floor to provide accurate positions of beacons: the width =,000, the depth=,000, and the height =,00. To set the three reference points, A, A, and A, on the floor, the localizer has been placed on the floor directly. To chec the effectiveness of the auto calibration algorith, the localized are directly oved on the floor to several points: E, E, E, E4, and E5. For the reliability of the easureent, the position estiation processes are perfored 00 ties for a specific point, and the estiated values are averaged and displayed in Table. Fig. 7. Estiation of Mobile robot. Fig. 8. Estiation error. The installation tie also can be reduced fro 5 inutes to inutes when the auto calibration algorith is applied. In the conventional approach, the position of each beacon should be checed after installation one by one, which taes a lot of tie for the syste installation. However with the auto calibration algorith, after all the beacons are installed, the locations are checed by the localizer, which shorten the installation process draatically. Also in the conventional syste, the position estiation error caused by the erroneous position inforation of the beacons cannot be recovered. Therefore, within a certain period, the positions should be checed again and again to provide the precise localization of the obile robot.. Localization accuracy iproveent by extended Kalan filter To iprove the location accuracy, the extended Kalan filter hs been applied to estiate the trajectory of the oving object. The initial procedure estiates trace of the obile robot using the auto calibration algorith for ABS syste, which is illustrated in Fig. 9(a. The planned trajectory was a circle. However the real trajectory was never be a circle. Figure 9 (b represents the trace of the obile robot when the extended Kalan filter has been applied for the estiation of the robot.

6 with the application of the extended Kalan filter, the localization error has been reduced einently. Actual path, +++ Estiated path Fig. 9 (a. Localization results. Actual path, +++ Estiated path Fig. 9 (b. Localization results by the extended Kalan filter. Fig. 0 (a. The error between real value and estiate value of a oving object. Fig. 0 (b. The error between real value and estiate value of a oving object. V. Conclusion This paper proposes a new localization schee with the ABS syste to overcoe the difficulty of installing the beacons precisely on the wall and to iprove the localization accuracy. The new localization schee which is based on the auto calibration algorith is experientally verified that it iproves the location accuracy and shortens the beacon installation tie. When the new localization syste is coercialized, it can have price erit since it reduces all the tedious installation process of the beacons. Another contribution of this paper is that the extended Kalan filter has been properly utilized for the trajectory estiation of the obile robot, which iproves the localization accuracy a lot. This localization syste can be applied for the public service robot as well as hoe robot as a part of positioning sensor. As a sensor, it can also contribute to boo up the robot industry since it can provide a tool for ubiquitous and/or networ robot to identify its own location anytie, reliably and conveniently. References [] S. Singh and P. Keller, Obstacle detection for high speed autonoous navigation, Proc. Of IEEE int. Conf. on Robotics and Autoation, pp , 99. [] J. Borenstein and L. Feng, UMBar A Method for Measuring, Coparing, and Correcting Dead-reconing Errors in Mobile Robots, The University of Michigan, Technical Report UM-MEAM-94-, Deceber, 994. [] Iowa State University GPS page. Web site at [4] Soo-Yeong Yi, Jae-Ho Jin, Self-localization of a Mobile Robot using Global Ultrasonic Sensor Syste, Journal of Control, Autoation and systes Engineering, vol. 9, no, pp. 45-5, 00. [5] Sung-Bu Ki, Dong-Hui Lee, and Jang-Myung Lee, Indoor Localization Schee of a Mobile Robot Applying RFID Technology, J. of Control, Autoation, and Systes Engineering, Vol., no., Dec.005. [6] S. M. Bozic, Digital and Kalan Filtering, Edward Arnold, 979. [7] R. Brown and P. Hwang, Introduction to rando signals and applied Kalan filtering, John Wiley and Sons, 99. [8] Greg Welch and Gary Bishop, An Introduction to the Kalan Filter, 004. [9] D. Fox, W. Burgard and S. Thrun, The dynaic window approach to collision avoidance, IEEE Robotics and Autoation Magazine, pp. -, March, 997. [0] Byoung-Suc Choi, Jang-Myung Lee, An Optial Capturing Trajectory Planning for a Moving Object, Proc. International Syposiu on Artificial Life And Robotics, pp. 7-78, Feb.005. Figure 0 (a shows the ABS syste localization error of a oving object with the triangulation technique and Fig. 0 (b shows the localization error after the application of the extended Kalan filter for the trajectory estiation. By the coparison, it is noted that