Performance Comparison of Probabilistic Methods Based Correction ...

Performance Comparison of Probabilistic Methods Based Correction Algorithms for Localization of Autonomous Guided Vehicle Hyunhak Cho1, Eun Kyeong Kim2, Eunseok Jang2, and Sungshin Kim3(&) 1

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Department of Interdisciplinary Cooperative Course: Robot, Pusan National University, Busan, South Korea [email protected] 2 Department of Electrical and Computer Engineering, Pusan National University, Busan, South Korea {kimeunkyeong,esjang}@pusan.ac.kr School of Electrical and Computer Engineering, Pusan National University, Busan, South Korea [email protected]

Abstract. This paper presents performance comparison of probabilistic methods based correction algorithms for localization of AGV (Autonomous Guided Vehicle). Wireless guidance systems among the various guidance systems guides the AGV using position information from localization sensors. Laser navigation is mostly used to the AGV of a wireless type, however the performance of the laser navigation is influenced by a slow response time, big error of rotation driving and a disturbance with light and reflection. Therefore, the localization error of the laser navigation by the above-mentioned weakness has a great effect on the performance of the AGV. There are many different methods to correct the localization error, such as a method using a fuzzy inference system, a method with probabilistic method and so on. Bayes filter based estimation algorithms (Kalman Filter, Extended Kalman Filter, Unscented Kalman Filter and Particle Filter) are mostly used to correct the localization error of the AGV. This paper analyses performance of estimation algorithms with probabilistic method at localization of the AGV. Algorithms for comparison are Extended Kalman Filter, Unscented Kalman Filter and Particle Filter. Kalman Filter is excluded to the comparison, because Kalman Filter is applied only to a linear system. For the performance comparison, a fork-type AGV is used to the experiments. Variables of algorithms is set experiments based heuristic values, and then variables of same functions on algorithms is set same values. Keywords: Extended Kalman Filter Unscented Kalman Filter Filter Performance comparison Localization

© Springer International Publishing Switzerland 2016 N. Kubota et al. (Eds.): ICIRA 2016, Part I, LNAI 9834, pp. 322–333, 2016. DOI: 10.1007/978-3-319-43506-0_28

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1 Introduction Guidance system technique among various AGV (Autonomous Guided Vehicle) technique is separated to a wire guidance system and a wireless guidance system. The technique guided AGV to destination using the physical properties and information of the logical. AGV of the wire guidance type is guided by underground guide line (magnet, induction line). Wire guidance system has advantages such as high safety, low cost of a sensor, however disadvantages of the system are high expense of laying guidelines and the difficulties of change of work paths [1, 2]. Wireless guidance systems complements the mentioned problems of wire guidance systems using the calculated position by installed landmarks in an environment. Localization technique of the wireless type AGV is comprised of global localization and local localization. The technique of the local localization calculates the relative position from the previous position using acceleration and angular speed. Sensors of the local localization has advantages fast response time, fast calculation time, low cost and so on. However disadvantages are a sensor error, a cumulative error and a bias error [3, 4]. The technique of the global localization calculates the global position in the environment over known landmarks. For global localization, matching methods between measured features and known landmarks are used for the technique of the global localization. However disadvantages the method are long calculation time, a sensor error and inaccurate calculated position over the wrong matching. To complement the above-mentioned problems of the localization, the position of AGV is complementarily calculated by the local localization and the global localization. Correction methods are various, and then probabilistic methods based correction algorithm among various algorithms are used a lot in AGV. Methods are Kalman Filter, Extended Kalman Filter [5, 6], Unscented Kalman Filter [7, 8] and Particle Filter [9, 10]. Extensive research of correction algorithms has been done. Mentioned algorithms are estimated a state of a system (non-linear system or non-Gaussian system) including inputs with much noises, and then there have a high efficiency to the localization. For the performance comparison of algorithms (Extended Kalman Filter, Unscented Kalman Filter and Particle Filter) in this paper, there are implemented using the local localization and the global localization, and then performance of the applied algorithms to AGV are analyzed by experiments. In this paper, Sect. 2 describes the used AGV, and Sect. 3 describes localization method using probabilistic methods. Section 4 explains experiments and results and Sect. 5 describes conclusion.

2 System Configuration 2.1

Automatic Guided Vehicle – Fork Type

For experiments of this paper, Fork-type AGV is used to analysis. The used fork-type AGV was remodeled the manual fork-lift production, and then that has an axle drive unit with a full-electric power steering.

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Fig. 1. Autonomous Guided Vehicle; (a) Fork-type AGV, (b) System configuration

Encoders and a gyro for a linear velocity and an angular velocity for local localization are installed to AGV, and then a laser navigation is used to global localization of AGV. The laser navigation is installed to the top of AGV for minimizing effect of disturbance by surroundings objects, and then encoders are installed to road wheels (auxiliary wheels) under forks of AGV. The gyro is installed above of the axle drive of AGV. System of the used AGV consists of a localization part, a control part and a driving part. To calculate positions of AGV, information (x, y, t of the laser navigation, linear velocities of encoders and an angular velocity of the gyro) of a localization part are transmitted to the control part over a micro controller unit every 100 ms. The control part calculates AGV’s position and controls the driving part using the calculated position. Figure 1 shows the system configuration of AGV.

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Used sensors are relative localization sensors (encoders and a gyro) and global localization sensor (laser navigation). To local localization, the used encoder is E40H-12-1000-3-V-5 (1000 pulse resolution), and then the gyro is myGyro300-SPI (±300º/s sensitivity). Tables 1 and 2 show the specification of sensors. To global localization, the used sensor is NAV200 (laser navigation). Table 1. Specification of encoder (E40-H12-1000-3-V-5)


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Table 2. Specification of gyro (myGyro300-SPI)

That calculates a position over comparison of positions between measured reflector and known reflectors, therefore NAV200 system needs to know positions of reflectors in an environment. More specifically, the header of NAV200 transmits infrared light over 360 rotation and receives reflected infrared light from installed reflections in the environment. NAV200 calculates distances and angles over measured information between the header and reflectos, and then the system calculates now position and now angle using a matching method. Table 3 shows the specification of NAV200. Table 3. Specification of laser navigation (NAV200)

3 Localization Method Localization of AGV is composed local localization and global localiztion. To local localization, this paper used kinematics of AGV with the axle-drive type and used sensors are 2 encoders and 1 gyro. Global localization uses bayes filter based correction method such as EKF (Extended Kalaman Filter), UKF (Unscented Kalman Filter) and PF (Particle Filter). The prediction step of above-mentioned filters uses kinematics of AGV and the estimation step uses the correction method of each filters. Subsection 3.1 explains the kinematics for local localization and Subsect. 3.2 explains correction localization method using probabilistic method with global localization and local localization.

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Fig. 2. Kinematics

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The used AGV has the axle-drive model, and kinematics of the used system is same Fig. 2. In Fig. 2, OICR is the central axis of rotation in the axle-drive system. Angular velocities (wl and wr)of road wheels are measured by encoders, linear velocities are calculated by Eq. (1). In Eq. (1) rl and rr are radiuses of each road wheels. vl ¼ wl 2rl vr ¼ wr 2rr

ð1Þ

The linear velocity (v) of AGV and the angular velocity (w) of AGV are calculated by Eq. (2), and then l of Eq. (2) is the length between road wheels. vr þ vl 2 vr vl w ¼ tan1 l v¼

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The angular velocity using the gyro is calculated by Eq. (3), in Eq. (3) GyroCenter is the mean value of 1000 data on the stop state and GyroADC is the output value of the gyro. Sensitivity in Eq. (3) is the value of the specification. w ¼ ðGyroCenter GyroADC ÞSensitivity

ð3Þ

The angular velocity of AGV is the mean value (angular velocity using encoders and angular velocity using the gyro). The local localization is calculated by 3 method (Euler Integration – Eq. (4), 2nd order Runge-Kutta Integration – Eq. (5) and Exact Integration – Eq. (6)). Used localization method is exact integration because of the most efficient performance based on experiments.


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xk þ 1 ¼ xk þ v cos hk yk þ 1 ¼ yk þ vsinhk hk þ 1 ¼ hk þ w

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w xk þ 1 ¼ xk þ v cos hk þ 2 w yk þ 1 ¼ yk þ vsin hk þ 2 hk þ 1 ¼ hk þ w

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v ðsinðhk þ 1 Þ sinðhk ÞÞ w v ¼ yk þ ðcosðhk þ 1 Þ cosðhk ÞÞ w ¼ hk þ w

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xk þ 1 ¼ xk þ yk þ 1 hk þ 1

3.2

Correction of Localization Method Using Probabilistic Algorithm

Probabilistic based correction methods of the localization of AGV are EKF, UKF and PF. Above-mentioned filters has high effectiveness to a dynamic system, non-linear system and non-gaussian system including noise inputs. Base algorithm of above-mentioned filters is bayes filter, and that recursively estimates the state of a system using measurement values of sensors. Figure 3 shows the estimation process of the bayes filter.

Fig. 3. Bayes filter

In Fig. 3, x−t is the prediction state of the time t, xt is the estimation state of the time t. u is the input of system model, z is the measurement value. Bayes filter based EKF is consisted like Fig. 4. EKF is the designed algorithm to apply Kalman Filter at a non-linear system, and that used linearlization over partial differential of the system model and the

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Fig. 4. Extended Kalman Filter

measurement model in the estimation model system. Prediction step of EKF predicts the system state and the P covariance. The system state and the P covariance are corrected by Kalman Gain in the estimation step. Covariances (Q of predtion step and R of estimation step) are selected by a user over experiments. In Fig. 4, x is the position of AGV, u is values of sensors for the local localization and e is noise values of sensors. P is covariance of the system, A and B are model using partial differential. zk is measurement values.

Fig. 5. Unscented Transform

UKF (Unscented Kaman Filter) used sigma points, weights and UT (Unscented Transform) instead of partial differential in EKF. The system state and error covariance in UKF are predicted by the UT using sigma points and the model. UT calculates a mean value and a covariance, that used a gaussian distribution instead of partial differential using jacobian. Figure 5 shows the UT process and Fig. 6 shows the process of UKF. PF (Particle Filter) is non-parametric filter that has not parameters unlike EKF and UKF. The method repeatedly estimates optimal states using particles. Particles has the system state each differently. PF estimates the system state using information particles over properly proposed probability distributions based randomly particles. However, initial state of particles, resampling step and so on are selected by a user on experiments. Figure 7 shows the process of PF.


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Fig. 6. Unscented Kalman Filter

Fig. 7. Particle Filter

In this paper, setting variables (covariance, function) by the user are selected the most effective value by experiments.

4 Experiments and Results For analysis of localization performance, the experiment environment is 8400 × 2100 mm. Reflectors cylindrical for the laser navigation were installed to the surface of a wall, and the length and the radius are 600 mm and 60 mm.

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H. Cho et al. Table 4. Experiment results of straight driving (unit:mm) Mean error Max error Non 88.76 264.65 Extended Kalman Filter 17.68 39.11 Unscented Kalman Filter 7.32 29.66 Particle Filter 20.06 36.64

Std 80.82 13.83 6.91 12.81

Table 5. Experiment results of rotation driving (unit:mm) Mean error Non 121.04 Extended Kalman Filter 94.82 Unscented Kalman Filter 71.67 Particle Filter 119.07

Max error 146.83 126.06 184.04 135.60

Std 23.21 12.73 30.86 3.70

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Fig. 8. Experiment result of rotation driving; (a) Non Filter, (b) Extended Kalman Filter, (c) Unscented Kalman Filter, (d) Particle Filter


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Straight driving and rotation driving are used to performance test for performance analysis of filter algorithms. The speed of straight driving is 24 cm/s, and then the speed and the angle are 24 cm/s and 30˚. Number of experiments are each 10 times. For comparison of algorithms performance, results of filters were compared to the driving line of the simulation using kinematics without noise. In experiments, the used kinematics model among 3 type is Exact Integration because of high efficiency at experiments. EKF, UKF and PF are implemented by experiments based setting variables of algorithms. Table 4 shows the result value of straight driving and Table 5 shows the result value of rotation driving. Figure 8 shows results of the rotation driving. Figure 9 shows errors of driving experiments, and then there expressed one of all experiments. System covariance (Q) of EKF changes every time by outputs of encoders, and measurement covariance (R) of EKF and covariance (Q and R) of UKF are the fixed constant matrix. Number of particles to PF is 200, and then Weighted Mean Method is used to the estimation of the system state at PF. In resampling step at PF, high rank 20 % reuses for the next estimation step, and then the others are redistributed to the arbitrary positions (±100 mm and ±10˚) of the estimated position. To experiments, UKF performance versus the others are more efficient. However, the position may not be predicted to UKF model, because kalman gain of UKF is greatly influenced by noise. That only can apply to the system model of the Gaussian distribution. Parameters of correction algorithms are important that the properly selected, and then performance of algorithms is determined by the parameters.

5 Conclusion This paper presented the performance comparison of the probabilistic method based correction algorithms (Extended Kalman Filter, Unscented Kalman Filter and Particle Filter) of the localization method of AGV. The algorithms apply to AGV, and the performance are compared by straight driving and rotation driving. For localization method in this paper, the local position is calculated by kinematics method (Exact Integration) with over encoders and the gyro. The used kinematics model among 3 type is Exact Integration because of high efficiency at experiments. The global localization is measured by laser navigation. Setting variables from a user are selected to the highest performance value by experiments. To comparison of performance, the designed fork-type AGV is used to experiments (each straight driving and rotation driving 10 times). UKF among algorithms are the most efficient to the correction of localization method. However, the position may not be predicted to UKF model, because kalman gain of UKF is greatly influenced by noise. That only can apply to the system model of the Gaussian distribution. Therefore, future work is optimization of parameters in algorithms. Acknowledgments. This work was supported by BK21PLUS, Creative Human Resource Development Program for IT Convergence and was supported by the MOTIE (Ministry of Trade, Industry & Energy), Korea, under the Industry Convergence Liaison Robotics Creative Graduates Education Program supervised by the KIAT (N0001126).


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References 1. Vis, I.F.A.: Survey of research in the design and control of automated guided vehicle systems. Eur. J. Oper. Res. 170(3), 677–709 (2006) 2. Xiang, G., Tao, Z.: Robust RGB-D simultaneous localization and mapping using planar point feature. Robot. Auton. Syst. 72, 1–14 (2015) 3. Spandan, R., Sambhunath, N., Ranjit, R., Sankar, N.S.: Robust path tracking control of nonholonomic wheeled mobile robot experimental validation. Int. J. Control Autom. Syst. 13, 897–905 (2015) 4. Christof, R., Daniel, H., Christopher, K., Frank, K.: Localization of an omnidirectional transport robot using IEEE 802.15.4a ranging and laser range finder. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3798–3803 (2010) 5. Miguel, P., Antonio, P.M., Anibal, M.: Localization of mobile robots using an Extended Kalman Filter in a LEGO NXT. IEEE Trans. Educ. 55(1), 135–144 (2012) 6. Jakub, S., Michal, R., Vladimir, K.: Evaluation of the EKF-based estimation architectures for data fusion in mobile robots. IEEE/ASME Trans. Mechatron. 20(2), 985–990 (2015) 7. Maral, P., Guangjun, L.: An adaptive unscented Kalman filtering approach for online estimation of model parameters and state-of-charge of lithium-ion batteries for autonomous mobile robots. IEEE Trans. Control Syst. Technol. 23(1), 357–363 (2015) 8. Ramazan, H., Hamid, D.T., Mohammad, A.N., Mohammad, T.: A square root unscented fast SLAM with improved proposal distribution and resampling. IEEE Trans. Ind. Electron. 61 (5), 2334–2345 (2014) 9. Bin, Y., Yongsheng, D., Yaochu, J., Kuangrong, H.: Self-organized swarm robot for target search and trapping inspired by bacterial chemotaxis. Robot. Auton. Syst. 71, 83–92 (2015) 10. Gerasimous, G.R.: Nonlinear Kalman filters and particle filters for integrated navigation of unmanned aerial vehicles. Robot. Auton. Syst. 60, 978–995 (2012)