Accurate relative localization using odometry - Robotics and ...
Pr0eeedingsofthe2003 IEEE Inlemalional Conference on Roboties & Automation Taipei, Taiwan, Seplember 14-19, 2003
Accurate Relative Localization Using Odometry Nakju Doh*
Howie Choset"
Wan Kyun Chung'
* Robotics & Bio-Mechatronics Lab.,
Mechanical Engineering, Pohang University of Science & Technology(POSTECH), Pohang, KOREA Tel : 82-54-279-2844 ; Fax : 82-54-279-5899; E-mail : {nakji,wkchung}@postech.ac.!u ** Sensor Based Planning Lab., Mechanical Engineering, Camegie Mellon University(CMU), Pittsburgh, USA Tel : 1-412-268-3722 ; Fax : 1-412-268-3348; E-mail : [email protected]
AbsIracf- All mobile robots suffer from odometry error. Relative localization from odometry has both the systematic and the non-systematic errors. However, once a precise system error model and its parameters are given, the accuracy of odometry can be remarkably improved. Most previous works on this effort focused on the differential drive robots with little attention to the other types of mobile bases. In this paper, we analyze sources of odometry error and propose an error model for the synchro drive robot. We then describe a novel procedure to accurately estimate the error parameters of the derived error model and the covariance matrix of the synchro drive robot. However, this procedure is general for all mobile bases, so we also apply our method for the differential drive robots and show experiments. This new process uses the shape of the path, as opposed to just end points, to estimate the error parameters and covariance matrix. We happen to use the generalized Voronoi graph to generate this path. Experimental results validate the error model of the synchro drive robot and precise estimation ability of the proposed method for the synchro and the differential drive robots.
I. INTRODUCTION Relative localization using odometry fails to accurately position mobile robots for many reasons, including wheel slippages. Thus in addition to odomehy, robotics researchers have proposed various solutions which can be classified into three groups: (a) integrate conventional sensors, (b) employ additional hardware, and (c) exploit a priori information. All of these methods also use odometry data for accurate positioning. Thus the accurate relative localization using odometry is necessary for both precise robot positioning by itself and with combined modalities. Our approach to accurate relative localization using odometry has three key steps which are (1) odomeuy error modeling, (2) error parameters estimation and (3) covariance matrix estimation. Here the first and second steps focus on the compensation of the systematic errors [ I ] induced by different wheel radius, wheel misalignment, etc. The third step deals with the non-systematic errors [ I ] caused by wheel slipping, floor cracks and so on. Our first contribution is an error modeling of the synchro drive robot. We analyze the sources of odometry error
0-7803-7736-2/03/$17.00 02003 IEEE
and propose disturbance force and moment equations. Our second contribution is a general error parameters and covariance matrix estimation technique which is named as the "PC(E0STECH CMUJ-method". This approach is general for all odometry models, not limited to synchro drive. We show it precisely estimates the error parameters of the error model and gives a possible way to estimate the covariance matrix. The PC-method has three advantages. Firstly, it can be used for all types of odometry. We applied this method for the synchro and the differential drive robots in this paper. Secondly, it precisely estimates the error parameters and is more accurate than previous method, the UMBmark [I], for the differential drive robot. The reason of accuracy is that the PC-method uses path data for precise error parameters estimation while the UMBmark uses endpoinr errors only. Finally, it gives the possible way of the covarance matrix estimation. The covariance matrix expresses position uncertainty after error correction and can be used for further extension such as Kalman filter. We present some experimental results which validate the derived error model of the synchro drive robot and the performance of the PC-method. We applied the PCmethod for the synchro and the differential drive robots and the accuracy of the odometty is remarkably improved. This paper is organized as follows. The overview of our contribution is given in Section 11. In Section 111, the odomeuy error model of the synchro drive robot is derived. Section IV suggests the PC-method for error parameters and covariance matrix estimation. Then Section V and Section VI show experimental results of the PCmethod for the synchro and the differential drive robots, respectively. Finally, conclusion follows on Section VII. 11. OVERVIEW OF OUR CONTRIBUTION
Our first contribution is developing a new odometry error model for the synchro drive robots. This error model depends on the wheel type of the mobile base. According to Guy [Z], there are five wheel types. Among those five,
1606
Authorized licensed use limited to: IEEE Xplore. Downloaded on January 24, 2009 at 15:28 from IEEE Xplore. Restrictions apply.
the error models for the differential and the synchro drive robots are suggested. For the differential drive robots, Borenstein [I] analyzed the sources of error and proposed an error model. His and other researchers' results show that his suggested error model is quite accurate. For the synchro drive robot which is widely used, it is said that the odometry error depends on wheel angle [31. However, there seems to be no established model to explain this tendency. Recently, Martinelli [4] proposed an error model of the synchro drive robot and the possible way of error parameters estimation. However, his model is not consistent with the tendency that the odometry emor depends on wheel angle and is not validated by experiments. We presume that the major sources of odometry error are disturbance force and moment from wheel misalignment. These terms drag and rotate the robot. Based on these analyses, we suggest a simple error model for the synchro drive robot. Our error model explains previously reported trend and coincides with the experimental results. For the differential drive robot, Borenstein [ l ] suggested a good estimation method called UMBmark. But the UMBmark just uses end position errors after 4m x 4m square navigations which seem to be not enough for precise error parameters estimation. We propose a general error parameters and covariance matrix estimation method which is named as the PCmethod. The PC-method is based on the philosophy that sensor based navigation through the Generalized Yoroni Graph(GVG) [5] hounds absolute error but odometry does not. Thus if we navigate the GVG twice, we have two different odometry paths which are actually the same GVG in the real world. Then we can find the error parameters which match these two odometry paths. Moreover, we can estimate the trends of error propagation using two odometry paths after correction. The covariance matrix can be approximated from these trends.
Fig. 1. robot
..
Wheel nii\aligniiicnr: A in t i g . I Oil,ct distance k t u c c n center ufrorarion and ulieel: B in big. I Oflwt di%inse hctu.r.cn !he numind1 cenrcr oi uhcelr and th: csntcr of inn,, induced hv uneven ma\* distrihution: C' in Fig. I Dil'icrcnt uhesl radiu.>:I ) in Fig.1. Diiicrent lorces on c:icIi wheel bccauss o i uneven ma\, distribution. Pwition .;hilt duriitp pure rntation. We beltcve rhnt the mdjor \nurcc' oi the >ystemati.' error I \ uheel mirilignnient :tnd the other live sources sre ncgligibls. The rcdron I S thdl rhe wheel riiiraligiiment induw, disturbance force xnd moment which x: majnr wurccs ,it' di.twliun ot (I. For rhc dnal)\i.r. u e detinc wruc notarion3 , h o w in 'ldhle I nntl Fig. 2. 'lhsn rhc di.,iurb~nceforw. AT. and monsnt. W. arc given by.
.
A F - { 3 l . - h , < " > u ,cO\/l--..sin(B+E3). The E I drags the robot toward the j , direction and E2 sin( 0 E3) forcefully rotates the robot. A simulation result for the effects of a = O.Olrad,P = y = 0 is shown in Fig. 3 for different initial wheel angle @in
Accurate Relative Localization Using Odometry Nakju Doh*
Howie Choset"
Wan Kyun Chung'
* Robotics & Bio-Mechatronics Lab.,
Mechanical Engineering, Pohang University of Science & Technology(POSTECH), Pohang, KOREA Tel : 82-54-279-2844 ; Fax : 82-54-279-5899; E-mail : {nakji,wkchung}@postech.ac.!u ** Sensor Based Planning Lab., Mechanical Engineering, Camegie Mellon University(CMU), Pittsburgh, USA Tel : 1-412-268-3722 ; Fax : 1-412-268-3348; E-mail : [email protected]
AbsIracf- All mobile robots suffer from odometry error. Relative localization from odometry has both the systematic and the non-systematic errors. However, once a precise system error model and its parameters are given, the accuracy of odometry can be remarkably improved. Most previous works on this effort focused on the differential drive robots with little attention to the other types of mobile bases. In this paper, we analyze sources of odometry error and propose an error model for the synchro drive robot. We then describe a novel procedure to accurately estimate the error parameters of the derived error model and the covariance matrix of the synchro drive robot. However, this procedure is general for all mobile bases, so we also apply our method for the differential drive robots and show experiments. This new process uses the shape of the path, as opposed to just end points, to estimate the error parameters and covariance matrix. We happen to use the generalized Voronoi graph to generate this path. Experimental results validate the error model of the synchro drive robot and precise estimation ability of the proposed method for the synchro and the differential drive robots.
I. INTRODUCTION Relative localization using odometry fails to accurately position mobile robots for many reasons, including wheel slippages. Thus in addition to odomehy, robotics researchers have proposed various solutions which can be classified into three groups: (a) integrate conventional sensors, (b) employ additional hardware, and (c) exploit a priori information. All of these methods also use odometry data for accurate positioning. Thus the accurate relative localization using odometry is necessary for both precise robot positioning by itself and with combined modalities. Our approach to accurate relative localization using odometry has three key steps which are (1) odomeuy error modeling, (2) error parameters estimation and (3) covariance matrix estimation. Here the first and second steps focus on the compensation of the systematic errors [ I ] induced by different wheel radius, wheel misalignment, etc. The third step deals with the non-systematic errors [ I ] caused by wheel slipping, floor cracks and so on. Our first contribution is an error modeling of the synchro drive robot. We analyze the sources of odometry error
0-7803-7736-2/03/$17.00 02003 IEEE
and propose disturbance force and moment equations. Our second contribution is a general error parameters and covariance matrix estimation technique which is named as the "PC(E0STECH CMUJ-method". This approach is general for all odometry models, not limited to synchro drive. We show it precisely estimates the error parameters of the error model and gives a possible way to estimate the covariance matrix. The PC-method has three advantages. Firstly, it can be used for all types of odometry. We applied this method for the synchro and the differential drive robots in this paper. Secondly, it precisely estimates the error parameters and is more accurate than previous method, the UMBmark [I], for the differential drive robot. The reason of accuracy is that the PC-method uses path data for precise error parameters estimation while the UMBmark uses endpoinr errors only. Finally, it gives the possible way of the covarance matrix estimation. The covariance matrix expresses position uncertainty after error correction and can be used for further extension such as Kalman filter. We present some experimental results which validate the derived error model of the synchro drive robot and the performance of the PC-method. We applied the PCmethod for the synchro and the differential drive robots and the accuracy of the odometty is remarkably improved. This paper is organized as follows. The overview of our contribution is given in Section 11. In Section 111, the odomeuy error model of the synchro drive robot is derived. Section IV suggests the PC-method for error parameters and covariance matrix estimation. Then Section V and Section VI show experimental results of the PCmethod for the synchro and the differential drive robots, respectively. Finally, conclusion follows on Section VII. 11. OVERVIEW OF OUR CONTRIBUTION
Our first contribution is developing a new odometry error model for the synchro drive robots. This error model depends on the wheel type of the mobile base. According to Guy [Z], there are five wheel types. Among those five,
1606
Authorized licensed use limited to: IEEE Xplore. Downloaded on January 24, 2009 at 15:28 from IEEE Xplore. Restrictions apply.
the error models for the differential and the synchro drive robots are suggested. For the differential drive robots, Borenstein [I] analyzed the sources of error and proposed an error model. His and other researchers' results show that his suggested error model is quite accurate. For the synchro drive robot which is widely used, it is said that the odometry error depends on wheel angle [31. However, there seems to be no established model to explain this tendency. Recently, Martinelli [4] proposed an error model of the synchro drive robot and the possible way of error parameters estimation. However, his model is not consistent with the tendency that the odometry emor depends on wheel angle and is not validated by experiments. We presume that the major sources of odometry error are disturbance force and moment from wheel misalignment. These terms drag and rotate the robot. Based on these analyses, we suggest a simple error model for the synchro drive robot. Our error model explains previously reported trend and coincides with the experimental results. For the differential drive robot, Borenstein [ l ] suggested a good estimation method called UMBmark. But the UMBmark just uses end position errors after 4m x 4m square navigations which seem to be not enough for precise error parameters estimation. We propose a general error parameters and covariance matrix estimation method which is named as the PCmethod. The PC-method is based on the philosophy that sensor based navigation through the Generalized Yoroni Graph(GVG) [5] hounds absolute error but odometry does not. Thus if we navigate the GVG twice, we have two different odometry paths which are actually the same GVG in the real world. Then we can find the error parameters which match these two odometry paths. Moreover, we can estimate the trends of error propagation using two odometry paths after correction. The covariance matrix can be approximated from these trends.
Fig. 1. robot
..
Wheel nii\aligniiicnr: A in t i g . I Oil,ct distance k t u c c n center ufrorarion and ulieel: B in big. I Oflwt di%inse hctu.r.cn !he numind1 cenrcr oi uhcelr and th: csntcr of inn,, induced hv uneven ma\* distrihution: C' in Fig. I Dil'icrcnt uhesl radiu.>:I ) in Fig.1. Diiicrent lorces on c:icIi wheel bccauss o i uneven ma\, distribution. Pwition .;hilt duriitp pure rntation. We beltcve rhnt the mdjor \nurcc' oi the >ystemati.' error I \ uheel mirilignnient :tnd the other live sources sre ncgligibls. The rcdron I S thdl rhe wheel riiiraligiiment induw, disturbance force xnd moment which x: majnr wurccs ,it' di.twliun ot (I. For rhc dnal)\i.r. u e detinc wruc notarion3 , h o w in 'ldhle I nntl Fig. 2. 'lhsn rhc di.,iurb~nceforw. AT. and monsnt. W. arc given by.
.
A F - { 3 l . - h , < " > u ,cO\/l--..sin(B+E3). The E I drags the robot toward the j , direction and E2 sin( 0 E3) forcefully rotates the robot. A simulation result for the effects of a = O.Olrad,P = y = 0 is shown in Fig. 3 for different initial wheel angle @in
