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... - A lot of research has been done in this area. PID methods for stabilization and navigation [44, 5] are very simple and produce good results, however, more complicated technics such as backstepping =-=[24]-=-, sliding mode control [11, 43] and feedback linearization [42, 24] have been also researched. Adaptive control [21, 31, 39] that can accommodate to changes in the system, such as structural damage, i...

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...as system A) and the other is attached to the aircraft (system B). The orientation of system A relative to system B can be described by several methods including quaternion [26] and rotation matrixes =-=[30]-=-. In this work we chose to use rotation matrixes, as was done in [34]. 2.1. Orientation Representation Rotation matrixes. Let xab, yab, zab be the coordinates of the principal axes of B relative to A....

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...ASUREMENTS AND SENSORS 51 Figure 4.2: Thermopile based direct orientation measurement mechanism. The modified servo regulates the thermopiles orientation automatically. using a differential amplifier =-=[15]-=-. Since the only position where the thermopiles measurement difference is constant under any ground to sky temperature gradient is when the thermopiles are horizontal - that is both thermopiles measur...

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...e and produce good results, however, more complicated technics such as backstepping [24], sliding mode control [11, 43] and feedback linearization [42, 24] have been also researched. Adaptive control =-=[21, 31, 39]-=- that can accommodate to changes in the system, such as structural damage, is also being researched for quadrotor control, but to our knowledge with no publications at this time. In [7] S. Bouabdallah...

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...actual sensor board. In cases where only one dimensional rotation estimation is required, such as in the case of the segway robot [32], there are two common estimation methods used - Kalman filtering =-=[45, 23, 28]-=- and complementary filtering. A comparison between the two methods can be found in [16]. Regarding the three dimensional estimation problem, R. Mahony et al. have published several papers [34, 27, 35]...

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...e and produce good results, however, more complicated technics such as backstepping [24], sliding mode control [11, 43] and feedback linearization [42, 24] have been also researched. Adaptive control =-=[21, 31, 39]-=- that can accommodate to changes in the system, such as structural damage, is also being researched for quadrotor control, but to our knowledge with no publications at this time. In [7] S. Bouabdallah...

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...e and produce good results, however, more complicated technics such as backstepping [24], sliding mode control [11, 43] and feedback linearization [42, 24] have been also researched. Adaptive control =-=[21, 31, 39]-=- that can accommodate to changes in the system, such as structural damage, is also being researched for quadrotor control, but to our knowledge with no publications at this time. In [7] S. Bouabdallah...

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...ides in [36] a coupled estimation and control analysis using Lyapunov methods to prove stability. A work on trajectory generation and tracking for aggressive maneuvers was done by D. Mellinger et al. =-=[29]-=-, based on the two dimensional tracking algorithm presented in [14]. Another work on the subject of trajectory tracking was done by M. Hoffmann et al. in [17]. 1.2. Thesis Structure and Contribution T...

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...ntrol [21, 31, 39] that can accommodate to changes in the system, such as structural damage, is also being researched for quadrotor control, but to our knowledge with no publications at this time. In =-=[7]-=- S. Bouabdallah et al. provide a comparison between the use of backstepping and sliding mode controllers for full stabilization of both position and attitude of the quadrotor. In 1.2. THESIS STRUCTURE...

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...d in this problem because of the non linearity of the kinematic equation. The Extended Kalman Filter (EKF) [45], which is a near optimal filter adequate for use in non-linear systems, is used instead =-=[37]-=-. In this approach, the dynamic equation usually used in the prediction step is replaced with the kinematic equation which describes the relations between angular velocity and angular position, using ...

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...opter is its structural simplicity. Therefor, there is not a lot of work done on the structure itself. A very comprehensive work was done on the subjects of modelling and control by S. Bouabdallah in =-=[6]-=-. Most ”classical” quadrotors are composed of four parallel motors at the edges of a cross-like structure, as seen in fig. 3.1. However, some commercially available quadrotors, such as the Mikrokopter...

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...The overall transfer function of the Zero Order Hold and the system itself is given by multiplying 3.12 and 3.11. After some calculations (see 9.1) and using Laplace to Z transform conversion tables (=-=[10]-=- appendix 5), we 3.1. CLASSIC QUADROTOR 36 825.6 825.7 825.8 825.9 826 826.1 3.407 3.4075 3.408 3.4085 3.409 3.4095 3.41 3.4105 3.411 3.4115 x 105 Step Response Time (sec) Am pl itu de d_sys a_sys Fig...

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...[45, 23, 28] and complementary filtering. A comparison between the two methods can be found in [16]. Regarding the three dimensional estimation problem, R. Mahony et al. have published several papers =-=[34, 27, 35]-=- on the design of a complementary filter to combine angular velocity measurement, corrupted 1.1. LITERATURE REVIEW 15 by bias and noise with a direct attitude low frequency measurements, such as, but ...

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... the system is included in an Inertial Navigation System (INS). The estimation is not limited to being based on inertial sensors. The data required for estimation can be acquired using visual feedback=-=[22, 12, 4, 41]-=-. Control - A lot of research has been done in this area. PID methods for stabilization and navigation [44, 5] are very simple and produce good results, however, more complicated technics such as back...

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...actual sensor board. In cases where only one dimensional rotation estimation is required, such as in the case of the segway robot [32], there are two common estimation methods used - Kalman filtering =-=[45, 23, 28]-=- and complementary filtering. A comparison between the two methods can be found in [16]. Regarding the three dimensional estimation problem, R. Mahony et al. have published several papers [34, 27, 35]...

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...ov methods to prove stability. A work on trajectory generation and tracking for aggressive maneuvers was done by D. Mellinger et al. [29], based on the two dimensional tracking algorithm presented in =-=[14]-=-. Another work on the subject of trajectory tracking was done by M. Hoffmann et al. in [17]. 1.2. Thesis Structure and Contribution This thesis is composed of three main elements - structure and model...

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... the system is included in an Inertial Navigation System (INS). The estimation is not limited to being based on inertial sensors. The data required for estimation can be acquired using visual feedback=-=[22, 12, 4, 41]-=-. Control - A lot of research has been done in this area. PID methods for stabilization and navigation [44, 5] are very simple and produce good results, however, more complicated technics such as back...

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...al sensors. The data required for estimation can be acquired using visual feedback[22, 12, 4, 41]. Control - A lot of research has been done in this area. PID methods for stabilization and navigation =-=[44, 5]-=- are very simple and produce good results, however, more complicated technics such as backstepping [24], sliding mode control [11, 43] and feedback linearization [42, 24] have been also researched. Ad...

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...actual sensor board. In cases where only one dimensional rotation estimation is required, such as in the case of the segway robot [32], there are two common estimation methods used - Kalman filtering =-=[45, 23, 28]-=- and complementary filtering. A comparison between the two methods can be found in [16]. Regarding the three dimensional estimation problem, R. Mahony et al. have published several papers [34, 27, 35]...

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...as in the case of the segway robot [32], there are two common estimation methods used - Kalman filtering [45, 23, 28] and complementary filtering. A comparison between the two methods can be found in =-=[16]-=-. Regarding the three dimensional estimation problem, R. Mahony et al. have published several papers [34, 27, 35] on the design of a complementary filter to combine angular velocity measurement, corru...

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...en done in this area. PID methods for stabilization and navigation [44, 5] are very simple and produce good results, however, more complicated technics such as backstepping [24], sliding mode control =-=[11, 43]-=- and feedback linearization [42, 24] have been also researched. Adaptive control [21, 31, 39] that can accommodate to changes in the system, such as structural damage, is also being researched for qua...

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...irect orientation measurement taken from the accelerometers and magnetometers. It is worth noting that adding information from the dynamic model of the physical system can improve results, as seen in =-=[25]-=-. There, the dynamic model of the system is included in an Inertial Navigation System (INS). The estimation is not limited to being based on inertial sensors. The data required for estimation can be a...

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... the system is included in an Inertial Navigation System (INS). The estimation is not limited to being based on inertial sensors. The data required for estimation can be acquired using visual feedback=-=[22, 12, 4, 41]-=-. Control - A lot of research has been done in this area. PID methods for stabilization and navigation [44, 5] are very simple and produce good results, however, more complicated technics such as back...

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...’s quadrotor robots use BLDC (Brushless DC ) motors which are much more efficient, light and cheap. The disadvantage of this technology is the requirement of a complicated microcontroller based driver=-=[20]-=-. Attitude estimation - Attitude estimation is the heart of the system. During this research, we discovered that the flight characteristics are extremely sensitive to changes in the quality of attitud...

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...IS STRUCTURE AND CONTRIBUTION 16 another work [38] S. Bouabdallah et al. present a comparison between PID and LQ approaches. Some work on control using fuzzy logic approach was done by C. Coza et al. =-=[8]-=-. R. Mahony et al. provides in [36] a coupled estimation and control analysis using Lyapunov methods to prove stability. A work on trajectory generation and tracking for aggressive maneuvers was done ...

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...s a much better energy to weight ratio than the previously used nickel metal hydride batteries [33]. The electric motors have also improved significantly. A few years ago, brushed DC (Direct Current) =-=[19]-=- electric motors where used as on the ”Draganflyer V Ti RC Gyro Stabilized Electric Helicopter” [3], where today’s quadrotor robots use BLDC (Brushless DC ) motors which are much more efficient, light...

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... the system is included in an Inertial Navigation System (INS). The estimation is not limited to being based on inertial sensors. The data required for estimation can be acquired using visual feedback=-=[22, 12, 4, 41]-=-. Control - A lot of research has been done in this area. PID methods for stabilization and navigation [44, 5] are very simple and produce good results, however, more complicated technics such as back...

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... - The state vector of a quadrotor robot is composed of attitude, position and both angular and linear velocities. In older flying machines, which required attitude estimation, a mechanical gyroscope =-=[40]-=- was used. Mechanical gyroscopes are very accurate and provide a direct measurement of attitude, but they are also heavy and expensive. They cannot be used in MAV’s due to their size and weight. MEMS ...

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...commercially available quadrotors the power source used is a lithium-ion polymer battery pack [9] that has a much better energy to weight ratio than the previously used nickel metal hydride batteries =-=[33]-=-. The electric motors have also improved significantly. A few years ago, brushed DC (Direct Current) [19] electric motors where used as on the ”Draganflyer V Ti RC Gyro Stabilized Electric Helicopter”...

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...system will be referred to as system A) and the other is attached to the aircraft (system B). The orientation of system A relative to system B can be described by several methods including quaternion =-=[26]-=- and rotation matrixes [30]. In this work we chose to use rotation matrixes, as was done in [34]. 2.1. Orientation Representation Rotation matrixes. Let xab, yab, zab be the coordinates of the princip...

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...nother work [38] S. Bouabdallah et al. present a comparison between PID and LQ approaches. Some work on control using fuzzy logic approach was done by C. Coza et al. [8]. R. Mahony et al. provides in =-=[36]-=- a coupled estimation and control analysis using Lyapunov methods to prove stability. A work on trajectory generation and tracking for aggressive maneuvers was done by D. Mellinger et al. [29], based ...

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...r stabilization and navigation [44, 5] are very simple and produce good results, however, more complicated technics such as backstepping [24], sliding mode control [11, 43] and feedback linearization =-=[42, 24]-=- have been also researched. Adaptive control [21, 31, 39] that can accommodate to changes in the system, such as structural damage, is also being researched for quadrotor control, but to our knowledge...

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...esult of the advances which took place in the electrical power systems that can be used in MAV’s. In most commercially available quadrotors the power source used is a lithium-ion polymer battery pack =-=[9]-=- that has a much better energy to weight ratio than the previously used nickel metal hydride batteries [33]. The electric motors have also improved significantly. A few years ago, brushed DC (Direct C...

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...he estimation unreliable. However, the high frequencies of this estimation method stays sufficiently reliable. Infrared thermopiles - An infrared thermopile is a sensor that can measure thermal energy=-=[18]-=-. Since the earth is warm (approx. 14◦C) and the sky is cold (approx. −40◦C), they can be used to measure orientation by measuring the various temperatures in different directions. For example, if one...

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...al sensors. The data required for estimation can be acquired using visual feedback[22, 12, 4, 41]. Control - A lot of research has been done in this area. PID methods for stabilization and navigation =-=[44, 5]-=- are very simple and produce good results, however, more complicated technics such as backstepping [24], sliding mode control [11, 43] and feedback linearization [42, 24] have been also researched. Ad...

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...quality of attitude estimation, much more than they are to control gains. A very comprehensive work was done on the subject of Inertial Measurement Unit (IMU) for attitude estimation by Samuel Fux in =-=[13]-=-. This work deals with the algorithms, sensors and implementation of the actual sensor board. In cases where only one dimensional rotation estimation is required, such as in the case of the segway rob...

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...[45, 23, 28] and complementary filtering. A comparison between the two methods can be found in [16]. Regarding the three dimensional estimation problem, R. Mahony et al. have published several papers =-=[34, 27, 35]-=- on the design of a complementary filter to combine angular velocity measurement, corrupted 1.1. LITERATURE REVIEW 15 by bias and noise with a direct attitude low frequency measurements, such as, but ...

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...his work deals with the algorithms, sensors and implementation of the actual sensor board. In cases where only one dimensional rotation estimation is required, such as in the case of the segway robot =-=[32]-=-, there are two common estimation methods used - Kalman filtering [45, 23, 28] and complementary filtering. A comparison between the two methods can be found in [16]. Regarding the three dimensional e...

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...[45, 23, 28] and complementary filtering. A comparison between the two methods can be found in [16]. Regarding the three dimensional estimation problem, R. Mahony et al. have published several papers =-=[34, 27, 35]-=- on the design of a complementary filter to combine angular velocity measurement, corrupted 1.1. LITERATURE REVIEW 15 by bias and noise with a direct attitude low frequency measurements, such as, but ...

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...omparison between the use of backstepping and sliding mode controllers for full stabilization of both position and attitude of the quadrotor. In 1.2. THESIS STRUCTURE AND CONTRIBUTION 16 another work =-=[38]-=- S. Bouabdallah et al. present a comparison between PID and LQ approaches. Some work on control using fuzzy logic approach was done by C. Coza et al. [8]. R. Mahony et al. provides in [36] a coupled e...

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...en done in this area. PID methods for stabilization and navigation [44, 5] are very simple and produce good results, however, more complicated technics such as backstepping [24], sliding mode control =-=[11, 43]-=- and feedback linearization [42, 24] have been also researched. Adaptive control [21, 31, 39] that can accommodate to changes in the system, such as structural damage, is also being researched for qua...