臺灣博碩士論文加值系統

本論文主要是由多顆加速規量測空間中運動物體之角速度及線性加速度，此一做法統稱之為慣性量測單元。
傳統上慣性樑測單元由陀螺儀量測角加速度及加速規量測線性加速度，則在求得空間中物體位置及姿態時須經過兩次積分，此一作法會造成嚴重之誤差累積。於是20年前發展藉由加速規擺放位置不同求得角加速度，此種做法降低了慣性量測單元生產成本，但未能解決兩次積分造成的嚴重誤差。無論使用陀螺儀或是加速規得到角加速度，都是事先製作好再擺放至慣性量測單元上，這樣在擺放時會造成另外的誤差產生。
本論文的做法是利用微機電製程在同一平面上同時製作九顆加速規，不但降低成本也解決擺放時造成的誤差。並且，利用觀測器之觀念直接求得物體之角速度，在求得物體姿態上減低了一次積分的動作，對積分誤差之累積改善了不少。並在論文的最後並以實驗佐證此一構想是可行的。

IMU (Inertial Measurement Unit) is a sensor unit that can provide the position information (angular acceleration, angular velocity, linear acceleration and etc.) for an object in motion. Typical IMU uses three gyroscopes to sense the angular velocity and three linear accelerometers to sense the linear acceleration. The output from 3 gyroscopes undergoes integral operation to obtain 3 rotation angles; and the output from 3 linear accelerometers undergoes integration operation twice to obtain 3 coordinates for location. Another approach is named “Gyro-free IMU”, which only the linear accelerometers are utilized. The output of Gyro-free IMU consists of 3 angular accelerations and 3 linear accelerations, which need 2 consecutive integral operations to obtain rotation angles and 2 consecutive integral operations to obtain 3 location coordinates in space. The integral operation will result in the error accumulation and should be avoided or minimized, if possible.
Due to the convergence properties of Gyro-free IMU, the accelerometers utilized must be deployed in a 3D location manner. As a consequence, the accelerometers must be fabricated in prior to the IMU and then mounted on the various locations of IMU. This approach inevitably results in misalignment error for the placement of accelerometers.
In correspondence to the existing problems mentioned above, we proposed the brand new design “observer-base planar Gyro-Free IMU” to solve those problems.

摘要...................................................II
ABSTRACT..............................................III
ACKNOWLEDGENMENT........................................V
TABLE OF CONTENTS......................................VI
LIST OF TABLE..........................................IX
LIST OF FIGURES.........................................X
CHAPTER 1 INTRODUCTION..................................1
CHAPTER 2 THEORY AND ALGORITHM..........................5
2.1 Motion of Rigid Body in Space.......................5
2.2 Location of accelerometers and Dynamic system.......7
2.3 Kalman filter......................................13
2.3.1 The Extended Kalman Filter.......................13
State prediction.......................................15
Measurement prediction.................................15
Filter gain............................................16
Update.................................................16
2.3.2 The Iterated Extended Kalman Filter..............18
Overview of the Iteration Sequence.....................18
2.4 Orthogonal Transfer Matrix.........................19
2.5 Flow chart.........................................22
CHAPTER 3 SIMULATION AND PRELIMINARY TEST..............23
3.1 Test structure .....................................23
3.2 Generate Motion....................................24
3.3 One Axis Tested....................................25
3.4 Simulation and Resolution..........................27
Resolution.............................................31
CHAPTER 4 TEST OF THE IMU DESIGN.......................33
4.1 Experimental procedure.............................33
Basic procedure of experiment..........................34
Route of motion........................................36
Low-pass analog amplifier (single pole)................36
Butterworth filter .....................................37
4.2 Z-axis rotation with biaxial linear acceleration...38
4.3 Z-axis rotation with biaxial linear acceleration and non-zero initial condition.............................49
4.4 Y-axis rotation with biaxial linear acceleration...55
4.5 Discussion.........................................61
Linear vibrations of the optical table.................61
Rotational vibration of the optical table..............64
DC-drift or other noise................................65
CHAPTER 5 CONCLUSION AND FUTURE WORKS..................69
5.1 Conclusion.........................................69
5.2 Future works.......................................70
References.............................................71

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