Development of a MEMs-Based IMU Unit

Transcription

1 Development of a MEMs-Based IMU Unit Başaran Bahadır Koçer, Vasfi Emre Ömürlü, Erhan Akdoğan, Celâl Sami Tüfekçi Department of Mechatronics Engineering Yildiz Technical University Turkey, Istanbul Abstract In this study, gyroscope-free inertial measurement unit interface is developed to simulate new system configurations called YILDIZ using known calculation methods and implementation of MEMs accelerometers based on cubic arrangement. Additionally significant effect of different sensing directions and sensor allocations are taken into consideration. Throughout the project, simulation studies, realization of sample gyro-free MEMs-based INS systems, and collection of data through data acquisition systems are performed in given order. Using simulation of the system, parameter-dependent errors are aimed to be minimized on the system output. Then, near-ideal geometry and the sensor configurations can be reached and the system can be realized. Prototype outputs are processed and efficient algorithms are developed using Matlab-Simulink environment. Keywords Inertial Measurement Unit; MEMs; GF-INS I. INTRODUCTION Although, gyro-based inertial navigation systems (INS) are extensively used on air vehicles in order to obtain flight information, MEMs-based INS (GF-INS) has been studied exponentially to reduce the costs of these devices in recent years. Resulting cost-effective and small designs of INS sensors would lead to extended usage of the sensors covering land vehicles. In this research, design parameters of the INS systems, specifically, the ones that are related to the MEMs sensors, their location and directions, are aimed to be optimized so that several near-ideal systems can be realized and the system trials can be performed. Simulation studies aim to minimize the effects of the MEMs locational, directional and internal errors on the overall INS system. Since components related to aerospace industry is costly, integrated system designs and realizations in our country is only reachable through a vast knowledgebase about this very important topic. This research aims to increase the availability of the knowledge about this area and also to produce a very expensive component of INS systems using MEMs sensors instead of gyroscopes so that the usage of these equipment are also available to all vehicles including land, naval and aerial ones. INS is an electromechanical measurement unit that determines the location and speed of any vehicle without using any external reference. They are used in air/space vehicles, ballistic missiles, automatic agricultural vehicles and robotic systems, etc[1]. Although conventional inertial measurement units include three accelerometers and three gyroscopes, GF-INS, gyroscope free INS systems which uses only accelerometers of certain number, have been put into some applications, recently. Since gyroscope units are quite expensive comparing to MEMs-based accelerometers, GF-INS units which only employ MEMsbased accelerometers, would be smaller and less expensive [- 4]. One disadvantage of GF-INS units would be counted as the shift in calculated locations for long-term use. That is the reason of GPS (Global Positioning System) usage as a side-tool to calibrate/update the location information of any GF-INS units for certain time intervals [, 5]. First research works about GF-INS for industrial applications is in late XX. century about automotive applications aiming to obtain navigational information by cordially using various accelerometers[6]. Following, detailed analysis about GF-INS, location of the sensors and their directions, geometrical defects because of the fusion of the sensors and sensor-based errors have been investigated [4, 7]. Various GF-INS types have been manufactured changing the number of sensors and their locations, yet the minimum number of sensors to be employed has been reported to be six. However, keeping the number of sensors at minimum elevates the possible errors at the output of the GF-INS system. These errors are originated from sensor locations and placement defects and can be corrected to some certain degree [6-8]. Researches on GF-INS are focused on using these devices with supporting GPS, calibration against geometrical and internal errors, general system efficiency and general configuration design. GPS, magnetometer or similar navigation devices are used in the GF-INS systems as well as gyro-based inertial navigation systems for the purpose of resetting cumulative sensor errors periodically [9]. Also, in terms of total output quality, sensing quality and evaluation of environment factors, researches are available [10]. After GF- INS design implementation, calibration is an essential stage for positioning and orientation errors to be minimized [, 3, 5, 10]. The number of accelerometers can be used[4, 7], their positions, orientations and the number of axis to be sensed[8, 11] and sensor properties are design criteria and numerous studies are available[6, 9, 1, 13]. User defined cubic configuration for to simulate GF-INS system before implementation has been performed in [14]. Recently researches have been proposed to enhance system efficiency, to determine the minimum and maximum accelerometers and for filtering convenience GFINS.[15, 16] This work is supported by Yildiz Technical Univercity Grant KAP /13/$ IEEE 389

2 II. THEORETICAL BACKGROUND A. GF-INS Model Although the feasibility of gyroscope-free inertial navigation system for cubic arrangement and error analysis is demonstrated by PATH researchers [17, 18], a different selection of sensing directions and locations of sensors are experimented in this research. It is called as YILDIZ alignment. There are six accelerometers at the center of each face of a cube with median sensing directions. The location of sensors and the sensing directions are shown in Figure-1. These are expressed by the vectors u and θ, respectively. U=[ u1,..., u 6] is location matrix and each column of matrix consist of three projections of related sensor direction relative to the INS coordinate system (I). Same is valid for sensing direction matrix, J =[ θ 1,..., θ 6]. Subscripts indicate the accelerometers number U= J = () J 1 is the dot product of U (locations) and J (sensing directions) members relative to origin of YILDIZ coordinate system; J = [ u θ,..., u θ ] (3) The output of accelerometers; θωu 1 1 ω = QA Q... P θnω un 1 In equation (4), Q= [ J T J T ] and 1 0 ω3 ω = ω3 0 ω1 ω ω1 0 (1) (4) Ω (5) ω is angular and P is translational accelerations of YILDIZ, Ω is skew symmetric matrix which is composed of angular rate and inferred from accelerometer outputs relative to sensing directions. Because of the configuration matrix T T [ J1 J ] is invertible, YILDIZ is feasible in consideration of Q. Fig. 1. YILDIZ cubic arrangement III. IMPLEMENTATION OF THE SYSTEM Experimental set-up has three main units which is given in Fig as a computer, data acquisition card (DAQ) and acceleration sensors. The DAQ card is used to convert MEMs analog output data to digital data. To this regard, Quanser Q-8 hardware in the loop DAQ system was used with ms sampling time with 16 bit resolution. On the other hand, it has 8 analog and digital outputs, PWM and encoder modules. Acceleration measurement process was realized using Analog Device ADXL03 dual axis Mems accelerometer evaluation board system. The control software of the system was generated through MATLAB Simulink with Quanser real-time processing toolbox. The general real time working algorithm is shown in Fig 3. In scheme, configuration equation consists of equation 4 last terms which is specified in matrix. This algorithm is carried out only for attitude information from YILDIZ. Angular acceleration, angular rate and angular position may be obtained using this information at each Euler axes. Additionally, translational information may be determined from YILDIZ but it is not implemented in this work. IV. EXPERIMENTAL RESULTS Experimental setup is shown in Fig. 4. The validation is carried out for yaw channel and some results are shown below for some random maneuvers. YILDIZ is tested on rate table(fig. 5) and outputs are compared with encoder output which has angular position output. The output of encoder is differentiated and filtered out in order to get velocity information. The filter is butterworth low pass filter. Fig

3 shows yaw acceleration and yaw rate (rpm) of YILDIZ which are reasonable for considered systems in the sense that our references. Fig. 7 shows the outputs of YILDIZ and encoder and according to this results encoder output has a delay because of filtering. However YILDIZ output has a steady state error in velocity channel. Particularly, first loop of iteration may be responsible of state error in acceleration integration. Configuration (U, J and Q) determination has significant effect on the performance. considered which is originated from integration and sensor errors. To tackle this inherent disadvantage, wind up integrator is used but errors of position information can not be prevented which contains double integral from acceleration. To overcome sensor and general GFINS errors, an external navigation device can be employed with a feasible filter and sensor fusion algorithm. Also, configuration matrices should be determined as precise as possible and general algorithm should contain error process. Therefore, a user defined GF- INS interface is proposed (VI-Appeddix) which is useful and cost effective for preliminary results. Fig.. Experimental setup units Fig. 3. General GFINS algorithm Fig. 5. Yaw channel experimental setup 6 4 Yaw Acceleration Yaw Rate Fig. 4. Experimental setup V. CONCLUSION In this research, an original configuration of GF-INS system with six MEMs accelerometers is investigated. Each accelerometer has vectorial projection on every x,y,z axes because of the placement of new configuration. The calibration process is the first case which is considered, particularly roll and pitch motion which includes the gravitational effect. Quadratic terms which come from skew symmetric matrix output of (4) causes the direction of sensing problem and, for this reason, a feasible and simple filter of butterworth type is employed without any estimation process. Additionally, steady state and drift error problems are Fig. 6. Yaw acceleration and yaw rate Yildiz Angular Rate Output Encoder Angular Rate Output Fig. 7. Yaw rate output of YILDIZ and rate table output 391

4 REFERENCES [1] D. H. Titterton, J. L. Weston, and I. o. E. Engineers, Strapdown Inertial Navigation Technology, nd Edition: Institution of Engineering and Technology, 004. [] L. Qin, W. Zhang, H. Zhang, and W. Xu, "Attitude measurement system based on micro-silicon accelerometer array," Chaos, Solitons & Fractals, vol. 9, pp , 7// 006. [3] A. Buhmann, C. Peters, M. Cornils, and Y. Manoli, "A GPS aided Full Linear Accelerometer Based Gyroscope-free Navigation System," in Position, Location, And Navigation Symposium, 006 IEEE/ION, 006, pp [4] N. Xiaoji, C. Goodall, S. Nassar, and N. El-Sheimy, "An Efficient Method for Evaluating the Performance of MEMS IMUs," in Position, Location, And Navigation Symposium, 006 IEEE/ION, 006, pp [5] X. Baoping, "An Application of MEMS Sensors in Inertial Navigation System," in Intelligent Information Systems, IASTED International Conference on, 009, pp [6] E. Akeila, Z. Salcic, and A. Swain, "Implementation, calibration and testing of GFINS models based on six-accelerometer cube," in TENCON IEEE Region 10 Conference, 008, pp [7] T. J. S. Kumar, "Estimation of attitudes from a low-cost miniaturized inertial platform using Kalman Filter-based sensor fusion algorithm," Sadhana - Academy Proceedings in Engineering Series, vol. 9, pp , 004. [8] S.-z. Mu, x.-z. Bu, and y.-x. Li, "Optimization Design and Calibration of Installation Error Coefficients for Gyroscope-Free Strapdown Inertial Measurement Unit," in Mechatronics and Automation, Proceedings of the 006 IEEE International Conference on, 006, pp [9] Q. FangJun, X. Jiangning, and J. Sai, "A New Scheme of Gyroscope Free Inertial navigation System Using 9 Accelerometers," in Intelligent Systems and Applications, 009. ISA 009. International Workshop on, 009, pp [10] L. An, Q. FangJun, X. Jiangning, and J. Sai, "Gyroscope Free Strapdown Inertial Navigation System Using rotation modulation," in Intelligent Computation Technology and Automation, 009. ICICTA '09. Second International Conference on, 009, pp [11] X. Jin, Z. Mao, F. Wei, and Y. Wang, "Research on Gyroscope Free Strapdown Inertial Navigation System Based on 3-axis accelerometer," in Electronic Measurement and Instruments, 007. ICEMI '07. 8th International Conference on, 007, pp [1] J. A. Philippe Cardou, "A Comparative Study of All- Accelerometer Strapdowns for UAV INS," in Meeting Proceedings RTO-MP-SET-09, France, 005, pp [13] S. Nakamura, "MEMS inertial sensor toward higher accuracy & multi-axis sensing," in Sensors, 005 IEEE, 005, p. 4 pp. [14] D. Aydeniz, "MEMs İvme Sensörlü Ataletsel Seyrüsefer Sistemi İçin Arayüz Tasarımı," Msc, Mechanical Engineering, Yildiz Teknik Universitesi, Istanbul, 011. [15] S. Park and S. K. Hong, "Angular Rate Estimation Using a Distributed Set of Accelerometers," Sensors, vol. 11, pp , Nov 011. [16] E. Edwan, S. Knedlik, and O. Loffeld, "Constrained Angular Motion Estimation in a Gyro-Free IMU," Ieee Transactions on Aerospace and Electronic Systems, vol. 47, pp , Jan 011. [17] C.-W. Tan, K. Mostov, and P. Varaiya, "Feasibility of a Gyroscope-free Inertial Navigation System for Tracking Rigid Body Motion," PATH Research Report 000. [18] C.-W. Tan and S. Park, "Design and Error Analysis of Accelerometer-based Inertial Navigation Systems," PATH Research Report 00. VI. APPENDIX GFINS GUI In this research, design parameters of the GFINS systems, specifically, the ones that are related to the MEMs sensors, their location and directions on a GFINS, are aimed to be optimized so that several near-ideal systems can be realized and the system trials can be performed. Simulation studies aim to minimize the effects of the MEMs locational, directional and internal errors on the overall INS system. Main menu of user defined GFINS, which consists of number of sensors, its locations and sensing directions, accelerometer outputs and measurement errors, is shown below; Fig. 8. GFINS main menu 39

5 After selecting number of sensors, sensor location definitions displayed; User defined configuration values may be displayed in main menu(see Fig. 1). This example is carried out for conventional configuration which consist of six accelerometer and diagonal sensing directions. Fig. 9. Sensor location definition Last stage for GFINS configuration definition is sensing direction values which is shown in Fig.10. Fig. 11. A selected configuration on main menu Output graph selection tabs shown in Fig. 1 and this menu provide convenience of selected configuration according to input trajectory. Fig. 1. Output graph selection Fig. 10. Sensor sensing direction definitions 393