Evaluation of a Low-cost MEMS Accelerometer for Distance Measurement

Transcription

1 Journal of Intelligent and Robotic Systems 30: , Kluwer Academic Publishers. Printed in the Netherlands. 249 Evaluation of a Low-cost MEMS Accelerometer for Distance Measurement GRANTHAM PANG and HUGH LIU Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong; gpang@eee.hku.hk; hugh@graduate.hku.hk (Received: 22 November 1999; in final form: 26 June 2000) Abstract. This paper gives an evaluation of a low-cost MEMS accelerometer. The accelerometer is intended for the distance measurement of a mobile robot or platform in short duration. The distance traveled is obtained by double integration of the sensor signal with time. Bias offset drift exhibited in the acceleration signal is accumulative and the accuracy of the distance measurement can deteriorate with time due to the integration. This problem can be fixed by periodic recalibration with the help of external measurements on position, velocity and attitude. These external signals can be calculated by an inertial system. A Kalman filter can use the differences between these values to provide an optimum estimate of the system error. The random bias drift of the accelerometer was found by experiment to be 2.5 mg. The bias drift rate due to temperature was µg/s when the accelerometer was placed at room temperature. With proper compensation on gravitation, the accelerometer can be a viable solution as a short duration distance-measuring device for a mobile robot. 1. Introduction The Global Positioning System (GPS) is an absolute positioning system if the current position does not depend on the previous positions. Hence, it does not have any bias drift error. However, GPS has the signal blockage problem and cannot be used indoors. Dead Reckoning (DR) method is a relative positioning system commonly used to find the position. The angle and distance data are used to find the current position. DR system with gyros and accelerometers is called an Inertial Navigation System (INS). It requires no external electromagnetic signals and does not have the signal coverage problem met in GPS. The data output rate of INS is much bigger than that of GPS. However, the disadvantage of INS is the bias drift problem. These errors are accumulated and the accuracy deteriorates with time because of integration. The Kalman filter can be employed to blend the absolute and relative positioning data for better accuracy and robustness. Compared to an odometer, a 3-axis accelerometer can sense 3-dimensional movements while the former can only sense single-axis movements. The data rate of an accelerometer can be much higher than that of an odometer. Moreover, an odometer must be fixed to the shaft of some wheels and it can be inconvenient for some applications. A solid-state accelerometer also has the advantages of being small sized, having low cost and

2 250 G. PANG AND H. LIU being self-contained. Thus, this kind of accelerometer could be a viable solution as a short duration distance-measuring device for a mobile robot or platform SURVEY OF PREVIOUS WORK Verplaetse [23] gives a description of inertial sensors such as solid state gyroscope and accelerometer. A sensitivity analysis of a navigation sensor as well as a quantitative examination of the impact that individual navigation sensor has on the performance of a navigation system is given by Abbott and Powell [1]. An evaluation of the Inertial Navigation System (INS) consisting of a solid-state gyroscope and a solid-state accelerometer for a mobile robot can be found in [5]. Mostov [18] has described systematic and random errors in an accelerometer and in [19] he described the method to find the bias and scale factor errors by using inertial data and absolute position data. Gil et al. [8] describe a low cost GPS/INS car navigation system where GPS is used to compensate errors such as drift rate and offset bias error for two gyroscopes and three accelerometers. Lobo et al. [17] describe a prototype of the inertial navigation system. The results describing a medium accuracy aircraft inertial navigation grade silicon accelerometer is presented by Helsel et al. [9]. Their results show the feasibility of making a navigation grade silicon micro-machined accelerometer. Leonardson and Foote [16] discuss the theories and operations of a silicon micromachined accelerometer using vibrating beam accelerometer technology. They aim to produce an accelerometer which can achieve a navigation grade performance with a reduced size and lower cost. The use of an accelerometer for navigation purpose is given by Lemaire [15]. Barshur and Durrant-Whyte [6] give an evaluation of a low cost, solid-state inertial navigation system which consists of two gyroscopes, one triaxial accelerometer and a tilt sensor. Kourepenis et al. [13] describe recent gyro and accelerometer instrument developments in their research center. Allen et al. [2] describe a 6-axis Inertial Measurement Unit (IMU) consisting of three accelerometers and three gyroscopes. In reference [20], Mostov et al. discuss an accelerometer based on a low cost gyro-free inertial device for automotive. The choice of mathematical error model of the accelerometer system is described. Scheding et al. [21] discuss the results of an experimental program for evaluating sensors and sensing technologies in an underground mining applications. Barbour et al. [4] describe recent advances in micromechanical gyro and accelerometer design and packaging. The application of the MEMS on automobile market is also mentioned. Kelly [11] gives some theoretical knowledge of Inertial Navigation System such as theoretical mechanics, inertial sensor technologies and stable platforms OUTLINE OF THIS PAPER Section 2 of this paper describes the use of the Kalman filter for reducing random noise in the data collected from the accelerometer. The setups of the accelerometer

3 LOW-COST MEMS ACCELEROMETER FOR DISTANCE MEASUREMENT 251 and the evaluation experiment are described in Section 3. The evaluation methods and experimental results are explained in Section 4. Section 5 gives a discussion on the results and the paper is concluded in Section The Kalman Filter This section describes the use of the Kalman filter for reducing random noise found in the accelerometer data. The statistical characteristics of a measurement model are used to recursively estimate the required data. The Kalman filter is basically a statistical method that combines a knowledge of the statistical nature of system errors with a knowledge of system dynamics, as represented by a state space model, to provide an estimate of the state of a system. Any number of unknowns can be included in the states. In the navigation system, we are usually concerned with position and velocity. The state estimate is obtained by using a weighting function called the Kalman gain, which is optimized to produce a minimum error variance [10]. The Kalman filter can be used to combine measurements from multiple sensors and provide both an estimate of the current state of a system and a prediction of the future state of the system. The algorithm of the Kalman filter is shown in Figure 1 [7, p. 219] and the notation of the algorithm are presented below: Notation: x k is the system state, z k is the measurement, w k is the plant noise with its covariance Q k, v k is the measurement noise with its covariance R k, ( ) indicates the a priori values of the variables (before the information in the measurement is used), (+) indicates the a posteriori values of the variables (after the information in the measurement is used), K is the Kalman gain, k is the transition matrix at time t k, P k is the error covariance matrix, is the measurement matrix, H k where k = t 2 1 t t 0 0 1

4 252 G. PANG AND H. LIU Figure 1. The Kalman filter algorithm. Figure 2. The process model of the accelerometer data for the Kalman filter. and Q k = W W W 20 t5 8 t4 6 t3 W W W 8 t4 3 t3 2 t2. W W 6 t3 2 t2 W t Figure 2 shows how the accelerometer bias is modeled as a random walk process. The bias is modeled as an integrated white noise with a power spectral density (PSD) being W. The complete process is modeled by three integrators in cascade [8, p. 232]. From this model, the exact expressions for k and Q k can be worked out to the form as shown above. The power spectral density of the input white noise W is 1 (m/s 2 ) 2 /(rad/s), and the sampling time t equals 1/206.6 s.the value of W was obtained after performing some experiments aimed to provide better results.

5 LOW-COST MEMS ACCELEROMETER FOR DISTANCE MEASUREMENT 253 Figure 3. The accelerometer interface board. 3. Experimental Setups of the Accelerometer Evaluation 3.1. THE ACCELEROMETER The accelerometer that has been evaluated is called ADXL202 and is produced by Analog Device. Figure 3 shows the interface circuit. It is a low cost, low power 2-axis micromachined accelerometer with a measurement range of ±2 g (19.6 m/s 2 ). It can measure both dynamic and static accelerations. The outputs are digital signals whose duty cycles are proportional to the acceleration in each of the two axes [3]. The output can be measured directly with a MCU timer system. This accelerometer was chosen to measure the distance because of its small size, low cost and acceptable performance. The sampling rate of the accelerometer depends on the dynamics of the robot. If a high-speed robot is used, the accelerometer should be set to a higher bandwidth, which requires a faster sampling rate. The bandwidth of our accelerometer is from 0.01 Hz to 5 khz. In our case, a bandwidth of 50 Hz and a sampling rate of 200 Hz were used. However, wider bandwidth would cause a higher white noise in the signal THE MICROCONTROLLER AND DATA ACQUISITION BOARD The microcontroller used in the data acquisition board is Motorola 68HC11F1. It has 512 bytes of EEPROM, 1024 bytes of RAM, an enhanced 16-Bit timer system, three Input Capture (IC) channels, an enhanced NRZ Serial Communications Interface (SCI) [22]. The data acquisition circuit board is shown in Figure 4. The accelerometer data output is a 200 Hz square wave whose duty cycle depends on the acceleration. Input Capture 1 (IC1) pin of the MCU was used to detect

6 254 G. PANG AND H. LIU Figure 4. The data acquisition board with the microcontroller. Figure 5. The accelerometer evaluation experiment hardware setup. the signal from the accelerometer. The MCU would transmit the data to the PC via the Serial Communication Interface (SCI). A Visual Basic program was used at the PC to receive and save the data to the hard disk. A C program was written to process large amounts of accelerometer data. The recorded data is downsampled by averaging the acceleration data within each downsampling period. The down-

7 LOW-COST MEMS ACCELEROMETER FOR DISTANCE MEASUREMENT 255 sampled data was then stored in a file which could be plotted using MATLAB. For the results obtained, the data was averaged every twenty-five seconds to give a downsampled data THE SONY ROBOT ARM The robot arm used to move the accelerometer is a Sony SRX-410 high speed assembly robot. It was designed for high assembling speed and high performance industrial applications. The system consists of a robot arm, a controller, a panel and a PC for programming the robot arm. Figure 5 shows a photograph of the accelerometer evaluation hardware setup. Figure 6 gives the block diagram of the experimental setup. 4. Evaluation and Results 4.1. EXPERIMENTS ON THE ACCELEROMETER The Sony Robot Arm was used for the accelerometer evaluation in this experiment. The robot was commanded to travel at different velocity and acceleration and Figure 6. Accelerometer data acquisition block diagram. Figure 7. Results for acceleration of 10 m s 2 and velocity of 1 m s 1 without Kalman filter processing.

8 256 G. PANG AND H. LIU Figure 8. Acceleration results for acceleration of 10 m s 2 and velocity of 1 m s 1 with Kalman filter processing. Figure 9. Velocity results for acceleration of 10 m s 2 and velocity of 1 m s 1. twenty three sets of experiment were carried out. The velocities range from 0 to 1m/s and the accelerations range from 0 to 10 m/s 2. In this section, three different sets of results with low, moderately high and high acceleration is presented High Acceleration (a = 10 m/s 2 ) Figures 7 10 show the experimental results with a relatively high acceleration of 10 m/s 2 and a velocity equal to 1 m/s. The accelerometer was moved from left to right and vice versa for a distance of 40 cm. Such motions were repeated for eight times. The acceleration was calibrated with a constant bias to reduce the

9 LOW-COST MEMS ACCELEROMETER FOR DISTANCE MEASUREMENT 257 Figure 10. Distance results for acceleration of 10 m s 2 and velocity of 1 m s 1. Figure 11. Results for acceleration of 8 m/s 2 and velocity of 0.8 m/s without Kalman filter processing. zero offsets. Figures 7 and 8 show the acceleration processed without and with the Kalman filter, respectively. The velocity and the distance are shown in Figures 9 and 10, respectively. The final distance was found to be cm Moderately High Acceleration (a = 8 m/s 2 ) Figures show the results of the experiment with acceleration of 8 m/s 2 and with velocity of 0.8 m/s. Again, the accelerometer was moved from left to right and vice versa for a distance of 40 cm. Such motions were repeated three times. The acceleration was calibrated with a constant bias to reduce the zero offsets. Figure 11 shows the acceleration data without the Kalman filter processing. This

10 258 G. PANG AND H. LIU Figure 12. Results for acceleration of 8 m s 2 and velocity of 0.8 m s 1 with Kalman filter processing. Figure 13. Integrated velocity results for acceleration of 8 m s 2 and velocity of 0.8 m s 1. has resulted in a signal disturbed with random noises. A clearer shape of the signal obtained by using the Kalman filter is shown in Figure 12. The integrated velocity is shown in Figure 13 and the integrated distance is shown in Figure 14. The final distance was found to be 1.08 cm while the actual final distance should be zero Low Acceleration (a = 3 m/s 2 ) Figures show the results of the experiment with acceleration of 3 m/s 2 (which is quite low) and with velocity of 0.3 m/s. The accelerometer was moved from left to right and vice versa for a distance of 40 cm. Such motions were repeated three times. Figures 15 and 16 show the acceleration data without and

11 LOW-COST MEMS ACCELEROMETER FOR DISTANCE MEASUREMENT 259 Figure 14. Integrated position results for acceleration of 8 m s 2 and velocity of 0.8 m s 1. Figure 15. Data of acceleration at 3 m/s 2 without Kalman filtering. with the Kalman filtering. Due to the random bias drift, the acceleration data were divided into regions for different bias reductions. The biases in the first seven regions were manually tuned to optimize the accuracy. The last six regions were not calibrated for comparison purpose. These calibrations also helped to estimate the random bias drift of the accelerometer. The values of the manually tuned biases are plotted in Figure 19. Figure 17 shows the velocity that was calculated by integrating the acceleration data in time. Only the first two velocity cycles are calibrated with manually tuned acceleration biases. Figure 18 shows the distance which was calculated by integrating the velocity data in time. Only the first two distance cycles are calibrated with manually tuned acceleration biases. This graph shows

12 260 G. PANG AND H. LIU Figure 16. Acceleration at 3 m/s 2 after Kalman filtering with bias calibration. Figure 17. Velocity with and without manually tuned acceleration biases reduction (only the first two velocity cycles are calibrated). the effect of the random bias drift on the distance data after double integration of the accelerometer data THERMAL BIAS DRIFT In the second part of the experiment, fourteen hours of stationary accelerometer data were taken in order to study the effect of temperature on the bias drift. The recorded data occupied 81.3 Mbytes of hard disk space. The data was processed to give the acceleration readings and then plotted using MATLAB. The duty cycle of the accelerometer output is proportional to the acceleration. The microcontroller

13 LOW-COST MEMS ACCELEROMETER FOR DISTANCE MEASUREMENT 261 Figure 18. Distance traveled with and without manually tuned acceleration biases reduction (only the first two distance cycles are calibrated). Figure 19. Manually tuned biases for the first seven regions of the acceleration data. was used to measure the duty cycle using the timer system. The timer counts were converted to ASCII and then sent to the PC for recording. The difference between consecutive timer counter values is combined to obtain the duty cycle. The acceleration value can be found from the duty cycle according to the proportional relationship. Figures 20 and 21 show the 14-hour of stationary acceleration data without and with the Kalman filter processing, respectively. The thermal bias drift rate of the accelerometer placed at room temperature was found by this experiment to be µg/s.

14 262 G. PANG AND H. LIU Figure 20. Acceleration data in 14 h without Kalman filter processing. Figure 21. Acceleration data in 14 h with Kalman filter processing.

15 LOW-COST MEMS ACCELEROMETER FOR DISTANCE MEASUREMENT Discussions 5.1. EXPERIMENTS CARRIED OUT USING SONY ROBOT ARM Random Bias Drift Here, the effects of the random bias drift on the velocity and position error on the accelerometer are described. From the graph of manually tuned biases (Figure 19), the range of the biase deviations is about 2 3 mg, which is fairly large. Better navigational grade accelerometers have about 0.1 mg random bias drift. The velocity error and the position error built up can be calculated by the equations below [14]: Velocity error = m/spermgpermin, Position error = m per mg per min 2. Thus, for a bias error of 2 mg, the velocity errors built up in one minute is m/s. Moreover, the position error built up in one minute for a bias error of 2 mg is m. Thus, if the random bias could be modeled properly, the accuracy in distance measurement can be greatly improved. The system can also be recalibrated periodically by the use of external measurements on position, velocity and attitude. The external measurements can be compared with the corresponding quantities calculated by the inertial system and the Kalman filter would use the differences between these values to provide an optimum estimate of the system error Relation Between Magnitude of Acceleration and Accuracy in Distance Measurement From the distance graphs of Figures 10 and 14, distortions are observed which were due to the random biases of the accelerometer. The bending shape of the curve in Figure 14 is due to the doubly integrated error of the acceleration bias drift. The polarity of the drift error can be positive or negative. In the first 2200 samples, there was a negative bias error in the acceleration data. This caused the position plot to be shifted downward. However, for the next 2000 samples, the position plot was shifted upward which is due to a positive acceleration drift error. The random bias drift error is one of the major sources of the positioning error. When the acceleration is higher, the errors caused by the random bias are less significant. The integrated final distance was found to be 1.08 cm and cm when the accelerations were 8 m/s 2 and10m/s 2 while the actual final distances should both be zero. Thus, the results are quite close to the ideal ones. These good results were due to the relatively large acceleration imposed on the accelerometer. As the accelerometer can measure up to 2 g which is m/s 2 of acceleration, the applied acceleration which are 8 m/s 2 and 10 m/s 2 are relatively large. When compared with Figure 18, the distortions in distance measurement for higher accelerations are less. This means that when the acceleration is higher, the errors caused by the random biases are less significant.

16 264 G. PANG AND H. LIU 5.2. BEHAVIOR OF THE 14-HOUR STATIONARY ACCELEROMETER DATA From the results shown in Figure 21, it can be observed that the bias or zero offset of the accelerometer generally increased after powering up. After about seven hours, the bias settled down to fairly stable values. The results are due to the thermal bias drift of the accelerometer. The internal temperature of the sensor increases when it is warming up. The thermal bias drift rate when the accelerometer is placed at room temperature was found to be µg/s. If these bias drifts due to the temperature are not compensated, the results would be affected after operating for long duration. Compensation can be done by using the low cost temperature sensing IC and crystal oven [12]. 6. Conclusions A low-cost, solid-state MEMS accelerometer has been evaluated. The performance of the accelerometer is shown to be acceptable as a short duration distance-measuring device for a mobile platform or robot. With 2 mg of random bias drift, the low-cost accelerometer can be considered as acceptable for a highly dynamic robot operation with a suitable periodical recalibration from external measurements on position, velocity and attitude. Such an accelerometer can be a low-cost and small-sized distance-measuring device for a mobile robot, platform or vehicle. It can be combined with gyroscope and odometer to form a dead reckoning positioning system for a mobile robot or platform. In a real world application of the MEMS accelerometer, the gravitational component needs to be compensated due to a change of orientations of sensor sensitive axes [20]. For example, the pitch, roll and yaw of the robot can be found by a 3-axis gyroscope. For low cost application, six MEMS accelerometers can be used to resolve for both the gravitational and translational accelerations. Further research would be on the proper modeling of the accelerometer in order to reduce the effect of random bias drift. References 1. Abbott, E. and Powell, D.: Land-vehicle navigation using GPS, Proc. IEEE 87 (1) (1999). 2. Allen, J. J., Kinney, R. D., Sarsfield, J., Daily, M. R., Ellis, J. R., Smith, J. H., Montague, S.,Howe,R.T.,Boser,B.E.,Horowitz,R.,Pisano,A.P.,Lemkin,M.A.,Clark,W.A.,and Juneau, T.: Integrated micro-electro-mechanical sensor development for inertial applications, in: IEEE Position Location and Navigation Symposium, 1998, pp Analog Devices, ADXL202 data sheet, Barbour, N., Brown, E., Connelly, J., Dowdle, J., Brand, G., Nelson, J., and O Bannon, J.: Micromachined inertial sensors for vehicle, in: IEEE Conf. on Intelligent Transportation System, 1997, pp Barshan, B. and Durrant-Whyte, H. F.: An inertial navigation system for a mobile robot, in: Proc. Internat. Conf. on Intelligent Robots and Systems, Yokohama, Japan, Barshur, B. and Durrant-Whyte, H. F.: Inertial navigation systems for mobile robots, IEEE Trans. Robotics Automat. 11 (3) (1995),

17 LOW-COST MEMS ACCELEROMETER FOR DISTANCE MEASUREMENT Brown, R. G. and Hwang, P. Y. C.: Introduction to Random Signals and Applied Kalman Filtering, Wiley, New York, 1997, p Gil, J.-S., Cho, Y.-D., and Kim, S.-H.: Design of a low-cost inertial navigation system with GPS for car navigation system, in: Proc. of the 5th World Congress on ITS, Helsel, M., Gassner, G., Robinson, M., and Woodruff, J.: A navigation grade micro-machined silicon accelerometer, in: Proc. of IEEE Position Location and Navigation Symposium, 1994, pp Kaplan, E. D.: Understanding GPS: Principle and Applications, Artech House, Boston, 1996, p Kelly, A.: Modern Inertial and Satellite Navigation System, Carnegie Mellon University, Kitchin, C.: Understanding accelerometer scale factor and offset adjustments, Analog Devices. 13. Kourepenis, A., Borenstein, J., Connelly, J., Elliott, R., Ward, P., and Weinberg, M.: Performance of MEMS inertial sensors, in: IEEE Position Location and Navigation Symposium, Lawrence, A.: Modern Inertial Technology, Springer, Berlin, 1993, p Lemaire, C.: surface micromachined sensors for vehicle and personal navigation system, in: IEEE Conf. on Intelligent Transportation System ITSC 97, 1997, pp Leonardson, R. and Foote, S.: SiMMA accelerometer for inertial guidance and navigation, in: IEEE Position Location and Navigation Symposium, 1998, pp Lobo, J., Lucas, P., Dias, J., and Traca de Almeida, A.: Inertial navigation system for mobile land vehicles, in: Proc. of IEEE Internat. Symposium on Industrial Electronics, Vol. 2, 1995, pp Mostov, K.: Inertial sensor documentation, Web page of PATH, UC Berkeley, webed/sensor/papers.html. 19. Mostov, K.: Method for correction of systematic inertial sensor error, Web page of PATH, UC Berkeley, Mostov, K. S., Soloviev, A. A., and Koo, T.-K. J.: Accelerometer-based gyro-free multi-sensor generic inertial device for automotive applications, in: IEEE Intelligent Transportation System Conf., 1997, pp Scheding, S., Nebot, E. M., Stevens, M., Durrant-Whyte, H., Roberts, J., Corke, P., Cunningham, J., and Cook, B.: Experiments in autonomous underground guidance, in: Proc. of IEEE Internat. Conf. on Robotics and Automation, 1997, pp Technical Data, 68HC11F1, Motorola, Verplaetse, C.: Inertial proprioceptive devices: Self-motion sensing toys and tools, IBM System J. 35 (3 and 4) (1996).