Enhanced Mobile Robot Outdoor Localization Using INS/GPS Integration Eric North, Jacques Georgy, Mohammed Tarbouchi, Umar Iqbal, and Aboelmagd Noureldin
Index Terms— Mobile Robot Localization, Inertial Sensors, GPS, Kalman Filter
Abstract — An unprecedented surge of developments in mobile robot outdoor navigation was witnessed after the US government removed selective availability of the global positioning system (GPS). However, in certain situations GPS becomes unreliable or unavailable due to obstructions such as buildings and trees. During GPS outages, a positioning solution with a minimum cost is preferred for small wheeled robots. A low-cost inertial measurement unit (IMU) is a good choice to provide such a solution; however, low-cost MEMS-based inertial sensors suffer from several errors that are stochastic in nature. These errors accumulate and cause a rapid deterioration in the quality of position estimate. The purpose of this paper is to describe an enhanced low-cost 3-D navigation system using a Kalman filter (KF) that integrates odometry from wheel encoders, low cost MEMS-based inertial sensors, and GPS. The proposed technique uses reduced inertial sensor system (RISS). The RISS used here includes three accelerometers and one gyroscope aligned with the vertical axis of the body frame of the robot. The benefits of eliminating the two other gyroscopes normally used are decreasing the cost further, and improving the performance by having less inertial sensors and thus less contribution of these sensors errors towards positional errors. These two eliminated gyroscopes were used to calculate pitch and roll which are now calculated using the two horizontal accelerometers. The experimental results show that, during GPS outages, this KF with velocity update derived from the forward speed from wheel encoders is a good technique for greatly reducing localization errors. Real localization data from one trajectory is presented. This data is post-processed and some simulated GPS outages are introduced to assess the effectiveness of the proposed technique.
I.
A
Manuscript received July 31, 2009; accepted October 1, 2009. This research was supported in part by research grants from Natural Sciences and Engineering Research Council (NSERC), Geomatics for Informed Decision (GEOIDE) Network Centers of Excellence, and Defense Research and Development Canada (DRDC) Ottawa. The equipment was acquired by research funds from Canada Foundation for Innovation, Ontario Innovation Trust and the Royal Military College of Canada. E. North is with the Canadian Forces Aerospace and Telecommunications Engineering Support Squadron, Trenton, ON K0K 3W0 Canada (
[email protected]). J. Georgy is with the Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON K7L 3N6 Canada (corresponding author, phone: 613-449-5090; fax: 613-544-8107; e-mail: J.Georgy@queensu ca). M. Tarbouchi, is with the Department of Electrical and Computer Engineering, Royal Military College of Canada, Kingston, ON K7K 7B4 Canada (e-mail:
[email protected]). U. Iqbal is with the Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON K7L 3N6 Canada (e-mail:
[email protected]). A. Noureldin, is with the Department of Electrical and Computer Engineering, Royal Military College of Canada and Queen’s University, Kingston, ON K7K 7B4 Canada (e-mail:
[email protected]).
978-1-4244-5844-8/09/$26.00 ©2009 IEEE
INTRODUCTION
s described by Pacis et al [1] from a navigational viewpoint, the control strategy used in a mobile platform range from teleoperated to autonomous. A teleoperated platform is a platform having no onboard intelligence and whose navigation is guided in real-time by a remote human operator. An autonomous platform is one that takes its own decisions using onboard sensors and processor. According to Pacis et al [2], for autonomous mobile robot navigation, the problems that must be dealt with are localization, path planning, obstacle avoidance, and map building. The focus of this work is in the localization problem. Localization is the problem of estimating robot's pose relative to its environment from sensor observations. Localization is a necessity for successful mobile robot systems, it has been referred to as "the most fundamental problem to providing a mobile robot with autonomous capabilities" [3]. Furthermore, as confirmed in [1], to achieve autonomous navigation, the robot must maintain an accurate knowledge of its position and orientation. Successful achievement of all other navigation tasks depends on the robot ability to know its position and orientation accurately. Borenstein et al. [4] presented a review of mobile robot positioning technologies. According to this review, the positioning systems are divided into seven categories falling in two groups. They classified the positioning techniques as: relative position measurements and absolute position measurement. The former includes odometry and inertial navigation, while the latter includes magnetic compass, active beacons, global positioning system (GPS), landmark navigation, map-based positioning. An unprecedented surge of developments in mobile robot outdoor navigation was witnessed after the US government removed selective availability (SA) of GPS. Examples of applications for these robots are autonomous lawnmowers and motorized wheelchairs. These devices are low-cost and are used on terrain that is not flat. GPS can be used to provide three-dimensional (3-D) knowledge of the mobile robot's position. Unfortunately, GPS suffers from outages when lineof-sight is blocked between the robot and GPS satellites. These outages are caused by operating the robot in and around buildings, dense foliage and other obstructions. An inertial measurement unit (IMU), with three accelerometers and three gyroscopes, is a good choice in lieu of GPS during outages for providing a 3-D positioning solution. Since a low-cost
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solution is needed for mobile robots, a low-cost MEMS-based IMU has to be used. However, MEMS-based inertial sensors suffer from several complex errors such as biases; moreover these errors have influential stochastic parts. Since inertial navigation systems (INS) involves integration operations using these sensors readings, these errors will accumulate and cause a rapid degrade in the quality of position estimate. Odometry using wheel encoders is another type of dead reckoning that provides limited localization information mostly two-dimensional (2-D). This information is not subject to the same magnitude of errors as the IMU provided that the vehicle does not encounter excessive skidding or slipping. But these 2-D solutions will not be adequate if the robot often moves outside the horizontal plane. While 2-D and 3-D solutions using sensors in a full-sized vehicle has been done in the work to-date, further research is needed in the area of 3-D localization of small wheeled mobile robots operating in large 3-D terrain. The majority of the previous work using small mobile robots shows that the terrain is flat and the paths of the robots are small (for example[5][6][7][8][9]). This paper attempts to bridge the gap between full-sized vehicle navigation in 3-D, and navigation of small wheeled mobile robots over large paths in uneven terrain. This paper aims at combining the advantages of inertial sensors and odometry while mitigating their disadvantages to provide enhanced low-cost mobile robot 3-D localization capabilities during GPS outages. This will be achieved through the use of a reduced inertial sensor system (RISS) and its integration with GPS using KF in a loosely-coupled approach.
aligned with the vertical axis of the body frame of the robot together with two wheel encoders. Here accelerometers are used to calculate 3-D velocity and position, the vertical gyroscope is used to calculate the azimuth angle (i.e. the heading of the robot). The two eliminated gyroscopes were used to calculate pitch and roll which are now calculated, based on the idea presented in [13][14], using the two horizontal accelerometers and the forward velocity obtained from wheel encoders. This constitutes the RISS mechanization. The benefits of eliminating the two other gyroscopes normally used are: (i) decreasing the cost further, (ii) improving the performance by having less inertial sensors and thus less contribution of these sensors errors towards positional errors especially that the pitch and roll calculations from gyroscopes involves integration while their calculation from accelerometers does not. This last fact decreases the portion of positional error coming from the pitch and roll errors. The details of INS/GPS integration using KF can be found in [15][16][17]. The difference in this work is the use of the previously described RISS instead of a full IMU. The block diagram of the system used is shown in Figure 1. As any INS mechanization, the RISS mechanization, which is a nonlinear operation that involves integration operations, causes accumulation of errors. These mechanization equations are linearized to obtain the predictive RISS error model to be used in KF. The KF role is to estimate the errors in positions, velocities and azimuth angle obtained from RISS mechanization. When GPS is available it provides measurement update for KF. During GPS outages, the KF uses velocity updates computed from forward speed (from wheel encoders) and pitch and azimuth angles from mechanization. The stochastic drift errors of the inertial sensors are modeled in this KF solution as first order Gauss Markov processes. The experimental results, during GPS outages, will show that the developed RISS error model when combined with 3-D measurement updates of velocities using forward speed from encoders in KF is a good technique for greatly reducing localization errors.
II. METHODOLOGY The concept of RISS was used in full-sized vehicle navigation [9] in order to further lower the cost of the positioning solution. The RISS used in [9] involves a singleaxis gyroscope and two-axis accelerometers together with a full-sized vehicle built-in speed sensor to provide 2-D navigation solution in denied GPS environments. With the assumption that the vehicle mostly stay in the horizontal plane, the vehicle speed obtained from the speed sensor are used together with the heading information obtained from the vertically aligned gyroscope to determine the velocities along the East and North directions. Consequently, the vehicles longitude and latitude are determined. If the pitch and roll angles are needed, the two accelerometers pointing towards the forward and transverse directions are used together with odometer-derived speed and a reliable gravity model to determine these angles independently of the integration filter. Several 2-D RISS/GPS integration were presented using Kalman filter (KF) [10], augmented KF/neural networks [11], and particle filter [12]. All these solutions were tested using a full-sized vehicle. In this paper a low-cost navigation system using a KF to integrate MEMS-based RISS with GPS in a loosely-coupled scheme is described. The RISS used here is a 2-D one that includes three-axis accelerometers and single-axis gyroscope
Figure 1: An overview of the system used for outdoor mobile robot localization.
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III. EXPERIMENTAL SETUP
Table 2: Bias, scale factor error and random walk for the Honeywell HG1700 IMU used in Novatel Span [19][20] Honeywell IMU (HG1700) Gyroscopes Accelerometers Bias, deg/hr 1.000 Bias, mg 1.000 Scale Factor, ppm 150.000 Scale Factor, ppm 300.000 Random Walk, 0.125 deg/¥KU
The performance of the developed navigation solution is examined with outdoor trajectory test experiments using the mobile robot shown in Figure 2. The robot was developed in NavINST research group. A block diagram of the electronics on-board the mobile robot appears in Figure 3. The inertial sensors used in this work are from the MEMSgrade IMU made by Crossbow, model IMU300CC-100. The specifications of this IMU are in Table 1, and the detailed specifications can be found in [18]. The forward speed used to get velocity updates is derived from wheel encoders. The results of the presented navigation solution are evaluated with respect to a reference solution made by NovAtel, where Honeywell HG1700 high-end tactical grade IMU is integrated with the NovAtel OEM4 GPS receiver. Together the NovAtel and Honeywell systems are integrated with an off-the-shelf unit developed by NovAtel, the G2 Pro-Pack SPAN unit. The details of this system are described in [19]. See Table 2 for the biases and scale factors for the HG1700 IMU, and the detailed specification can be found in [20]. The high-cost NovAtel SPAN system provided the reference solution to validate the proposed method which uses the low-cost MEMS-based sensors and to examine the overall performance during some GPS outages intentionally introduced in post processing.
IV. RESULTS AND DISCUSSIONS Trajectories were carried out using the mobile robot with the previous setup. Sensors data were collected to test the developed solution in post processing. To show the benefit of using the RISS instead of a full IMU and the benefit of using velocity updates from wheel encoders during GPS outages, four navigation solutions are compared. The KF using RISS and velocity updates during GPS outages is compared to KF using RISS without any updates during outages, KF using full IMU with velocity updates during outages, and KF using full IMU without any updates during outages. The errors in all the estimated solutions are calculated with respect to the NovAtel reference solution.
Figure 2: The mobile robot used in the experiments. Table 1: Bias, scale factor error and random walk for the Crossbow IMU300CC IMU [18]. Crossbow IMU (IMU300CC) Gyroscopes Accelerometers Bias, deg/sec < +/- 2.000 Bias, mg < +/- 30.000 Scale Factor, % < 1.000 Scale Factor, % 1.000 Random Walk, Random Walk, deg/¥KU 2.250 m/(s¥KU 0.150
Figure 3: Block diagram for the electronics on-board the mobile robot used for the experiments The trajectory used in this paper, shown in Figure 4, is in The Royal Military College of Canada. It forms a loop with start and end at the same position. It contains two different sections which include hills both at an incline and decline to the robot's trajectory.
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The ultimate check for the proposed system’s accuracy is during GPS signal blockage, which can be intentionally introduced in post processing. Since the presented solution is loosely coupled, the outages used have complete blockage. Seven GPS outages are simulated of duration 60 seconds each. The simulated outages were chosen such that they encompass straight portions, turns, and slopes. Table 3 shows the root mean square (RMS) error in both the estimated 2-D horizontal position and the estimated altitude during the seven GPS outages for the four compared solutions. These errors are calculated with respect to the NovAtel reference solution. Table 4 shows the maximum errors in the estimated 2-D horizontal position and the estimated altitude during these outages. Figure 5 shows a 2-D plot of four tracks, namely: the reference solution, the KF with full IMU and velocity updates during GPS outages, the KF with RISS and without updates during outages, the KF with RISS and velocity updates during outages. The KF with full IMU and without updates during GPS outages is not shown because the position errors are too big that they will change the scale of the plot.
maximum positional error for the seven GPS outages equal to 8.77 meters, while the case without updates has 139.3 meters of error. The second case is for the KF with RISS, when comparing the results once with and once without the velocity updates. With velocity updates, the solution has an average of the maximum positional error for the seven GPS outages equal to 3.35 meters, while the case without updates has 18.67 meters of error. When comparing KF with RISS and velocity updates to KF with full IMU and velocity updates, the advantage of RISS can be noticed. The former has an average of the maximum positional error for the seven GPS outages equal to 3.35 meters, the latter shows an error of 8.77 meters. These results together with the trajectory plots in Figure 5 demonstrate that the proposed 3-D localization solution using KF for RISS/GPS integration and employing velocity updates using wheel encoders outperforms all the other compared solutions. Furthermore, when compared to the MEMS-based INS/GPS integration results in the literature, the proposed solution provides very good results. Table 3: RMS errors for altitude and 2D position for the seven outages. Out. No. Dur (sec) h (m) 2D pos(m)
1
RMS Errors during GPS outages 2 3 4 5 6 60 60 60 60 60 60
7 60
Avg. 60
KF full IMU without updates 6.63 25.56 16.30 7.73 17.86 2.26 11.42 12.54 30.01 26.55 82.14 79.83 37.54 172.5 21.63 64.32
h (m) 2D pos(m)
KF full IMU with velocity updates 1.39 13.91 17.22 18.07 1.46 5.38 5.64 1.61 3.32 3.54 7.28 9.10
6.11 4.53
9.08 5.00
h (m) 2D pos(m)
KF RISS with velocity updates 1.20 4.96 9.21 0.27 1.02 0.66 16.43 6.32 2.47 4.07 10.75 21.49
3.86 7.21
3.03 9.82
h (m) 2D pos(m)
KF RISS with velocity updates 1.43 0.68 3.61 0.44 0.43 1.38 2.48 1.21 2.96 0.76 2.39 3.05
1.86 1.60
1.40 2.06
Table 4: Max errors for altitude and 2D position for the seven outages.
Figure 4: Trajectory for assessing the compared solutions. The results in Table 3 and Table 4 clearly show the advantage of RISS over a full IMU. Comparing the results of KF with full IMU without updates during GPS outages with the results of KF with RISS without updates during outages, one can see the big difference in 2-D positional errors. While the former has an average of the maximum positional error for the seven GPS outages equal to 139.3 meters, the latter shows an error of 18.67 meters. The reason for this difference is the elimination of the two gyroscopes used to get pitch and roll from the RISS and using accelerometers instead. The benefit of using the wheel encoders to provide velocity updates during GPS outages can be seen by two comparisons. The first case is for the KF with full IMU, when comparing the results once with and once without these velocity updates. With velocity updates, the solution has an average of the
Out. No. Dur (sec) h (m) 2D pos(m) h (m) 2D pos(m) h (m) 2D pos(m) h (m) 2D pos(m)
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1
Max Errors during GPS outages 2 3 4 5 6 60 60 60 60 60 60
7 60
Avg. 60
KF full IMU without updates 9.76 46.81 27.02 11.91 34.49 5.02 21.24 22.32 64.22 55.19 183.1 163.2 96.39 366.1 46.85 139.3 KF full IMU with velocity updates 4.96 24.31 29.16 28.15 1.69 8.97 8.98 2.00 5.62 7.44 13.23 17.00
9.46 15.24 7.15 8.77
KF RISS with velocity updates 4.97 9.46 13.36 0.61 2.17 1.84 4.72 5.30 34.42 12.40 4.83 9.26 17.88 38.39 13.51 18.67 KF RISS with velocity updates 3.51 2.83 3.75 0.58 0.82 1.71 3.36 1.99 5.91 1.23 3.21 4.79
2.04 2.97
2.18 3.35
V.
CONCLUSION
This study presented an outdoor 3-D localization solution for mobile robots using low-cost MEMS-based sensors, wheel encoders and GPS. A reduced inertial sensor system was used for both decreasing the cost and improving the performance. The integration was achieved using KF, and a loosely coupled approach was used. This positioning solution was tested with a real trajectory with seven simulated 60 seconds GPS outages and compared to three other solutions. Considering the maximum error in horizontal positioning, the KF with RISS and velocity updates during GPS outages achieved an average improvement of approximately 97.6% over KF with full IMU without any updates during outages, of approximately 61.8% over KF with full IMU with velocity updates during outages, and of approximately 82% over KF with RISS without any updates during outages. These results show the superiority of the proposed localization solution.
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[10] U. Iqbal, A. F. Okou, and A. Noureldin, “An Integrated Reduced Inertial Sensor System - RISS/GPS for Land Vehicle”, in Proceedings of IEEE/ION Position, Location and Navigation Symposium (PLANS) 2008, pp.912-922, Monterey, California, USA, May 2008. [11] J. Perreault, U. Iqbal, A. Okou, and A. Noureldin, “RISS/GPS Integration Utilizing an Augmented KF/NN Module,” European Journal of Navigation, vol. 6, no. 3, pp. 15–21, November 2008. [12] J. Georgy, U. Iqbal, M. Bayoumi, and A. Noureldin, “Reduced Inertial Sensor System (RISS)/GPS Integration Using Particle Filtering for Land Vehicles”, in Proceedings of the 21st International Technical Meeting of the Satellite Division of the Institute of Navigation, (ION GNSS 2008), pp. 30-37, Savannah, Georgia, USA , September 2008. [13] A. Noureldin, D. Irvine-Halliday and M.P. Mintchev, “MeasurementWhile- Drilling Surveying of Highly-Inclined and Horizontal Well Sections Utilizing Single-Axis Gyro Sensing System,” Measurement Science and Technology, IoP, vol. 15, no. 12, pp. 2426 – 2434, December 2004. [14] A. Noureldin, D. Irvine-Halliday and M.P. Mintchev, “Accuracy Limitations of FOG-based Continuous Measurement-While-Drilling Surveying Instruments for Horizontal Wells,” IEEE Transactions on Instrumentation and Measurement, vol. 51, no. 6, pp. 1177 – 1191, December 2002. [15] J. A. Farrell and M. Barth, “The Global Positioning System & Inertial Navigation”, McGraw Hill, 1998.
Figure 5: Three solutions and reference: Red for reference, Yellow for KF using full IMU with velocity updates, Green for KF using RISS without updates, Blue for KF using RISS with velocity updates.
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[18] IMU300 – 6DOF Inertial Measurement Unit: Crossbow Technology Inc. www.xbow.com/Products/Product pdf files/Inertial pdf/IMU300CC D atasheet.pdf [Accessed: May 21, 2009]. [19] SPAN Technology System User Manual OM-20000062: NovAtel Inc. [Accessed: www.novatel.com/Documents/Manuals/om-20000062.pdf May 21, 2009]. [20] HG1700 Inertial Measurement Unit: Honeywell. http://www51.honeywell.com/aero/common/documents/myaerospacecat alog-documents/MissilesMunitions/HG1700 Inertial Measurement Unit.pdf [Accessed: May 21, 2009].
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automotive industry. After completing his B.Sc. in Electrical Engineering at University of Engineering and Technology, Lahore, in 1993, he joined the Pakistan Air Force where he gained practical experience of navigation and guidance systems. In 2004, he obtained his M.Sc. of Electronics Engineering from GIK Institute of Engineering Sciences and Technology, Pakistan, where he served as a faculty member afterward. In 2008, he completed his Masters of Electrical Engineering in integrated positioning and navigation systems from Royal Military College of Canada.
Captain Eric North is an aerospace engineer who enrolled in the Canadian Forces in 1998. He graduated from the Royal Military College of Canada (RMC) in 2002 with a degree of Bachelor of Engineering in Computer Engineering. In 2009, he graduated from RMC with a degree of Master of Applied Science in Electrical Engineering. During his Masters he was a member of the Navigation and Instrumentation group (NavINST) headed by Dr Aboelmagd Noureldin. He currently works in avionics design at the Aerospace and Telecommunications Engineering Support Squadron in Trenton, Ontario Canada."
Dr. Aboelmagd Noureldin (M’98–SM’08) is Cross-Appointment Associate Professor at the Departments of Electrical and Computer Engineering of Both Queen’s University and the Royal Military College (RMC) of Canada. He is also the founder and the leader of the Navigation and Instrumentation research group at RMC. His research is related to artificial intelligence, digital signal processing, spectral estimation and de-noising, wavelet multi-resolution analysis and adaptive filtering with emphasis on their applications in mobile multi-sensor system integration for navigation and positioning technologies. Dr. Noureldin holds B.Sc. degree in Electrical Engineering (1993) and M.Sc. degree in Engineering Physics (1997) from Cairo University, Giza, Egypt. In addition, he holds Ph.D. degree in Electrical and Computer Engineering (2002) from The University of Calgary, Alberta, Canada. Dr. Noureldin is a Senior member of IEEE and is the chair of the Alternative Integration Methods research group at the International Association of Geodesy (IAG – SC 4.1). http://www.ece.queensu.ca/directory/crossappointed/noureldin.html
Mr. Jacques Georgy is a Ph.D. candidate at the Department of Electrical and Computer Engineering, Queen’s University, Canada, and an assistant lecturer at the Computer and Systems Engineering Department, Ain Shams University, Egypt. He obtained his B.Sc. and M.Sc. degrees in 2001 and 2007, respectively, from the Department of Computer and Systems Engineering at Ain Shams University, Cairo, Egypt. His research interests include linear and nonlinear state estimation, vehicular navigation by INS/GPS integration, autonomous mobile robot navigation, and under-water target tracking. He is a member of the Navigation and Instrumentation research group at the Royal Military College, Kingston, Ontario, Canada. Dr. Mohammed Tarbouchi received his M.Sc. and Ph.D. from Laval University, Quebec, Canada in 1993 and 1997, respectively. In September 1997 he joined the Department of Electrical and Computer Engineering at the Royal Military College of Canada where he is currently Associate Professor. His current research interests include analysis and design of electrical machines, variable speed drives and fault diagnosis of electric machines. Mr. Umar Iqbal is a doctoral candidate at Queen's University, Canada. His research focuses on the development of enhanced performance navigation and guidance systems that can be used in several applications including
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