Paper:

# Measurement of a Vehicle Motion Using a New 6-DOF Motion Sensor System – Angular Velocity Estimation with Kalman Filter Using Motion Characteristic of a Vehicle –

## Ryoji Onodera^{*} and Nobuharu Mimura^{**}

^{*}Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-nocho, Nishi-ku, Niigata-shi, Niigata 950-2181, Japan

^{**}Faculty of Engineering, Niigata University

This paper describes a new multi-degrees-of-freedom (DOF) motion sensor system in three-dimensional space. Our sensor system detects the acceleration of moving objects. In general, the moving objects each have 3 DOFs in the translational and rotational directions. Thus, the accurate measurement of all 6 DOFs of motion is essential to control these objects. We have developed a new acceleration sensor that measures 6-DOF motions by resolving multiple acceleration signals and are currently investigating its performance. In the case of multi-axial sensors, a specific problem of cross effect arises, which means the value obtained is different from the actual value, so sensor calibration becomes important. In this work, we achieved relatively stable measurement by inhibiting the cross effect through calibration. Though the only physical value that our sensor system can measure directly is 6-DOF acceleration, we investigated the angular velocity to compare with a conventional highly accurate gyro sensor. In calculations of angular velocity, we combined the motion characteristic with a Kalman filter and estimated angular velocities from detected accelerations. Our method generates a required observational signal in the Kalman filter artificially, using detected translational accelerations with gravity components and non-periodically refers to the observational signal. Finally, we investigated the proposed method in an experiment involving vehicle motion especially likely to have cross effect, and demonstrate that our sensor system (6-DOF accelerometer) performs well.

*J. Robot. Mechatron.*, Vol.20, No.1, pp. 116-124, 2008.

- [1] A. D. King, “Inertial Navigation – Forty Evolution,” General Electric Company Review, Vol.13, No.3, pp. 140-149, 1998.
- [2] J. Fraden, “Handbook of Modern Sensors,” AIP Press, pp. 301-322, 2004.
- [3] A. J. Padgaonkar, K. W. Krieger, and A. I. King, “Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers,” Transaction of the ASME, Journal of Applied Mechanics, Vol.42, pp. 552-556, 1975.
- [4] K. Ohta and K. Kobayashi, “Measurement of Angular Velocity and Angular Acceleration in Sports Using Accelerometers,” Transactions of the Society of Instrument and Control Engineers, Vol.30, No.12, pp. 1442-1448, 1994.
- [5] K. Ohta and K. Kobayashi, “Measurement of Angular Velocity and Angular Acceleration in Sports Using Extended Kalman Filter,” Transactions of the Society of Instrument and Control Engineers, Vol.31, No.9, pp. 1265-1272, 1995.
- [6] T. Masuda and Y. Tanizawa, “Measurement Experiment of the 6 DOF Acceleration Using Multiple Sensors,” Research Report of Industrial Research Division, Mie Pref. Science & Technology Promotion Center, No.26, pp. 117-120, 2002.
- [7] N. Mimura and R. Onodera, “Stability Analysis of 6 DOF Acceleration Sensor System Using Multiple Accelerometers,” Transactions of the Japan Society of Mechanical Engineers Series C, Vol.71, No.707, pp. 2218-2224, 2005.
- [8] R. Onodera and N. Mimura, “Six-Degree-of-Freedom Motion Sensor System Using Multiple Accelerometers,” 36th Int. Symposium on Robotics (ISR2005), TU416, 2005.
- [9] A. Umeda, M. Onoe, K. Sakata, T. Fukushima, K. Kanari, and T. Kobayashi, “Calibration of Three-axis Accelerometers as a Three-Dimensional Accelerometer Using a Three-Dimensional Vibration Generator and Laser Interferometers (Proposal of the New Technique from the Viewpoint that the Acceleration is a Vector Quantity),” Transactions of the Japan Society of Mechanical Engineers Series C, Vol.70, No.697, pp. 2600-2607, 2004.
- [10] A. Umeda, M. Onoe, K. Sakata, T. Fukushima, K. Kanari, H. Iioka, and T. Kobayashi, “Calibration of three-axis accelerometers using a three-dimensional vibration generator and laser Interferometers,” Sensors and Actuators, A, Vol.114, pp. 93-101, 2004.
- [11] N. Mimura and R. Onodera, “Calibration Method for 6 DOF Acceleration Sensor Systems Using Multiple Accelerometers,” Transactions of the Japan Society of Mechanical Engineers Series C, Vol.72, No.724, pp. 3798-3805, 2006.
- [12] R. Onodera and N. Mimura, “A Stability of Six-Degreesof-Freedom Acceleration Sensor System by Integration of Acceleration Signals (Considerations about a Dynamic Influence of Centrifugal Force Term in the Multi-Degree-of-Freedom Motion),” Transactions of the Japan Society of Mechanical Engineers Series C, Vol.72, No.724, pp. 3789-3797, 2006.
- [13] T. Yonezawa and S. Tanaka, “Measurement of Attitude for Ships with Unknown Rolling Axis,” Transactions of the Society of Instrument and Control Engineers, Vol.36, No.11, pp. 901-908, 2001.
- [14] K. Inoue, K. Ohtsuka, M. Sugimoto, N. Murakami, and Wen Li, “Sensor fusion Techniques for Automatic Guidance by the method of Kalman filter using DGPS and Gyrocompass (Part 1),” Journal of the Japanese Society of Agricultural Machinery, Vol.61, No.4, pp. 103-113, 1999.
- [15] L. Wang, G. Libert, and P. Manneback, “Kalman Filter Algorithm based on Singular Value Decomposition,” Proc. 31st IEEE Conf. Decision and Control, pp. 1224-1229, 1992.
- [16] M. C. Berg and K. W. Buffinton, “Extended Kalman Filtering Applied to a Two-Axis Robotic Arm with Flexible Links,” The Int. Journal of Robotics Research, Vol.19, No.3, pp. 254-270, 2000.
- [17] J. S. Bendat and A. G. Piersol, “Random Data: Analysis and Measurement Procedures,” Baifukan Co., Ltd., 1976.
- [18] S. Doi, “Vehicle Dynamics Performance Evaluations Through Human Dynamic Properties,” Toyota Central Labs. R&D Review, Vol.30, No.3, pp. 3-15, 1995.
- [19] E. Ono and S. Doi, “Vehicle Running Stability Analysis and Spin Control,” Toyota Central Labs. R&D Review, Vol.32, No.1, pp. 13-22, 1997.

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