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An autonomous quad-rotor is an aerial helicopter with four horizontal rotors designed in a square configuration capable of locating lost victims, gathering military intelligence, and surveillance. This project deals with a rotary wing Unmanned Aerial Vehicle capable of Vertical Takeoff and Landing with hovering capability that is quad rotor. In Order to accomplish this, first a detailed analysis has been carried out. The in-depth model of Quad rotor is built in different parts. Main part of model is related to body dynamics of the vehicle. For this rigid body dynamics are modeled starting from basic laws of physics that is Newtonian laws to complex 6 DOF aircraft equations of motion. The other part of model comprises rotor thrust and drag models. An analysis of aircraft electronics has been carried out in order to correctly apply filtering on sensors. A physical model of quad rotor has been constructed in which weight, strength and balance were emphasized. Different experimental setups have been prepared for iterative testing of Quad rotor which give 3 and 5 degrees of freedom to the aircraft. After the construction of vehicle, the flight dynamic model has been rebuilt, in order to approximate the actual system. Multiple controllers have been designed and implemented to control attitude while inertial navigation sensors estimate the system states.
Potential Applications for an Innovative Base Design:
The goal of this project is to design and build a quad-rotor that is controlled completely autonomously. Programs have the craft turn on, lift off, hover, translate, and land, or any other combination of these tasks. More difficult tasks, such as a positioning or navigational system require additional components and more advanced programming, but are easily adapted to this project's quad-rotor. A practical use for the autonomous quad-rotor would be to explore rough terrain that cannot be easily accessed by a person. Photos and aerial videos could be acquired of volcanoes, glaciers or cavers that are susceptible to collapse and otherwise inaccessible. If there is a missing person on a mountain, heat sensors could be integrated onto the board to help find them. Any search and rescue mission that covers a large area, such as the open ocean, could use a large group of the craft communicating wirelessly with the rescue team to increase the chances of rescue considerably. Its capabilities in smaller areas with obstructions, such as indoors, are more limited, but with enough development and time it would be possible to redesign for specific environments. It is also possible to have multiple crafts linked together and controlled from a single computer. This makes it possible to use the same method of controlling for all the crafts from the computer. In fact, an entire heterogeneous system could be created, consisting of many quad-rotors all working in unison for a specific mission. In a military setting, the craft could be further optimized with more expensive materials and equipped with much more sophisticated sensors. This would allow missions requiring very precise maneuvers in tight settings, or long range missions employing many crafts at once to be performed easily and without risk to any troops.
Contribution of this Work:
This thesis focuses on design and control of unmanned, autonomous micro helicopters with application to a quadrotor helicopter. The contribution of this work lies in three fields.
â€¢ Dynamic modeling of quadrotors: the goal is to obtain a faithful mathematical representation of the mechanical system for system analysis and control design.
â€¢ System design and optimization: the objective is to maximize the operation time and minimize the weight of the helicopter.
â€¢ System control: the aim is to understand and then master the dynamics of quadrotors by applying the appropriate control techniques.
Unmanned aerial vehicles are those aircrafts which do not have any aircrew. There are two types of these vehicles first those which need a human operator controlling the vehicle from a ground station and others fly autonomously with a pre - programmed plan of flight using more complex automation systems. The difference between UAVs and missiles is that the UAVs are expendable or recoverable which can carry a payload (lethal or non-lethal) whereas the missiles are weapons themselves and cannot be reused although they come both in remotely guided and autonomous unmanned configurations.
1.2 Introduction of Helicopters:
Helicopters are better than fixed wing aircrafts for applications where turning in a congested area is required. Where the fixed wing aircraftwill take round flight to turn, rotorcrafts can turn on their axis without any forward motion. In a conventional helicopter there is main rotor that gives lift to the vehicle. The forward motion is achieved by changing the plane of rotor motion. This change in plane divides the lift vector into upward and forward/backward components which gives forward/backward motion to the aircraft. To counter the rotation of main rotor and to achieve yaw there is a tail rotor in vertical plane as shown in . The thrust of main rotor is increased by changing the pitch angle of the blades whereas the rotors run at a nominal rpm at which the engine has maximum efficiency.
1.3.1 Introduction of Quadrotor:
A quad rotor, also called a quad rotor helicopter or quad copter, is a multicopter that is lifted and propelled by four rotors. Quad rotors are classified as rotorcraft, as opposed to fixed-wing aircraft, because their lift is generated by a set of revolving narrow-chord airfoils. A quad rotor is a type of rotor-craft whose lift is generated by four rotors. All rotors lie in horizontal plane. Inquad rotor fixed pitch propellers are used and the thrust is varied by changing the rpms of individual motors. The motion in each of the three axes is accomplished by a perceptive control of motors rpm. In quad rotor the center of gravity of the system almost lies in the same plane as the 2 plane containing all the rotors. 
This differentiates the control of quadrotor from conventional helicopters and it's impossible to stabilize a quadrotor using human control and a sophisticated digital control system is required in order to stabilize and allow a balance flight. More recently quadrotor designs have become popular in unmanned aerial vehicle (UAV) research.
These vehicles use an electronic control system and electronic sensors to stabilize the aircraft. With their small size and agile maneuverability, these quadrotors can be flown indoors as well as outdoors.
There are several advantages to quadrocopters over comparably-scaled helicopters. First, quadrotors do not require mechanical linkages to vary the rotor blade pitch angle as they spin. This simplifies the design and maintenance of the vehicle.
Second, the use of four rotors allows each individual rotor to have a smaller diameter than the equivalent helicopter rotor, allowing them to possess less kinetic energy during flight. This reduces the damage caused should the rotors hit anything. For small-scale UAVs, this makes the vehicles safer for close interaction. Some small-scale quadrotors have frames that enclose the rotors, permitting flights through more challenging environments, with lower risk of damaging the vehicle or its surroundings.
Due to their ease of both construction and control, quadrotor aircraft are frequently used as amateur model aircraft projects.
Figure1.2 3D Model of Quadrotor
1.3.2 Quadrotor Physics:
A quad-rotor is an aerial vehicle with four rotors arranged in a symmetric, square configuration around a central hub, which houses the battery and processing components. While flying, the quad-rotor is positioned with a propeller in front and back. Moving counter-clockwise from the front propeller, Let Fi be the force of each rotor i for i = 1; 2; 3; 4 such that F1 and F3 rotate counter-clockwise and F2 and F4 rotate clockwise. To perform a stationary hover, all four rotors rotate at the same rate and the total thrust of the craft is equal to its mass, m. Since both pairs of rotors spin in opposite directions, the net torque on the craft due to drag from the propellers is zero.
To create yaw movement in a counter-clockwise direction, F1 and F3 are sped up inversely proportional to F2 and F4. As a result, the net torque on the craft is negative via the right hand rule and it will yaw while remaining at the same altitude. If F1 and F3 do not increase proportionally to F2 and F4 decreasing, the craft will move in the z-direction because the net thrust will no longer equal zero. To yaw clockwise F2 and F4 must increase proportionally to F1 and F3's decrease.
A roll to the left is accomplished by decreasing the speed of F2 while increasing F4. Again, F2 must decrease at the same rate that F4 increases to maintain zero net torque. Increasing F2 and decreasing F4 results in rolling to the right. Pitching forward and back is done in the same fashion as rolling, but with F1 and F3. The principle for maintaining an equal rate of change for the two opposing rotors is how the translation of the craft is determined.
Due to either a pitch or a roll, the lift force is displaced in the x and y planes by angles and respectively, resulting in a horizontal force component that will translate the craft. The altitude of the quad-rotor is altered by changing the rate of all rotors collectively by the same amount. The thrust from each rotor exists only in the z-direction with respect to the body frame.
The total thrust can be represented by u = F1 + F2 + F3 + F4 and Fi is the force of rotor i.
Figure 1.3 Quad rotor Physics
1.3.3 Major Advantages of the Quadrotor Concept:
These advantages, compared to the other configurations, are the following:
(a). Higher payload capacity.
(b). Simplicity of the control system.
(c). Improved stability.
1.3.4Higher Payload Capacity:
The more obvious advantage is the first one. The thrust developed by a rotor increases with its diameter. Thus, by increasing the diameter it is possible to increase the thrust and therefore the payload which can be lifted. However, there is a limit as to how much the diameter can be increased, which is imposed by the compressibility effects that occur at the tip of the blade when it is moving so fast that it approaches the transonic region. Even then, it is possible to augment the thrust by adding more blades to the rotor, but this also has a limit, imposed both by the increasing mechanical complexity and by the interaction between the wakes of the blades. So if the thrust has to be raised even more, it is necessary to add more rotors. And there is no special reason why the number of rotors should be limited to two. However, as the number of rotors increases the empty weight of the helicopter rises too, and so the ratio payload/weight is reduced. It would be possible to reach a point in which no payload can be carried because all the thrust is used to lift the empty vehicle. It should be noted that the configurations with an odd number of rotors are unadvisable, because it is not possible to arrange them in pairs, with one rotating in the opposite direction of the other. Since it is not possible to arrange them in pairs, it is more complicated to balance all the reaction torques.
1...3.5Simplicity of the Control System:
It is possible to control the attitude of the quadrotor just by adjusting separately the rpm of each rotor. There are also other control methods which do not consist in varying the rpm. But what it is said here applies only to the first method. In all the other mentioned configurations (single rotor, tandem, side by side, coaxial) the attitude control is achieved by varying the pitch angle of the blade, while the rotational speed of the rotors remains constant. In order to vary the pitch angle complex mechanical systems are required. These systems are prone to failure, increase the weight and need frequent maintenance. But if the attitude control can be achieved just by modifying the rpm of the rotors, then there is no need for those systems, saving costs, weight and volume. In particular, the reduction in weight and volume can be very interesting for some applications, such as small UAVs. On the other hand, the conceptual simplicity of this control system makes it easy to automate, which is another reason why the quadrotor configuration is so attractive for UAV's.
1.3.6Improved Stability and Controllability:
For the same mass, a quadrotor has larger moments of inertia around its three axes, compared to a single rotor helicopter. On the other hand, it can be demonstrated that the time constant associated to the motion around each of those axes is proportional to the square root of the corresponding moment of inertia. Hence, the quadrotor will have larger time constants than the single rotor helicopter, at least in theory. Larger time constants mean that the pilot has more time to react to divergent modes and to make the necessary corrections or, in other words, that the controllability is better. Full scale helicopters are easier to pilot that their reduced scale counterparts because the moments of inertia of the former are much larger.
1.3.7Major Drawbacks of the Quadrotor Concept:
These drawbacks, compared to the other configurations, could be summarized as:
(a). High weight, lower payload/weight ratio
(b). Bigger power consumption
(c). Coupling between controllability and motor dynamics
(d). Nascent Technology
184.108.40.206Higher Weight, Lower Payload/Weight Ratio:
As for the higher takeoff weight, it is an obvious conclusion of the fact that, instead of one or two main rotors, there are four. Regarding the low payload/takeoff weight ratio, it is not so obvious. On the one hand, the takeoff weight is larger, as it has been explained. But on the other hand, the payload is also larger, because the thrust available is bigger. In the end it is more an empirical evidence than a conclusion of theoretical studies.
220.127.116.11Bigger Power Consumption:
This is another consequence of having more rotors. Bigger power consumption implies bigger power plants and bigger energy reserves (either batteries or fuel tanks), and this in turn implies higher takeoff weight, which was already high because of the increased number of rotors. In small, unmanned quadrotors powered by electric motors this issue can be very important. The power consumption is indeed very large and this reduces significantly their flight endurance.
18.104.22.168Coupling between controllability and motor dynamics:
The attitude of the quadrotor can be controlled just by independently modifying the speeds of each rotor. This is a great advantage, because it renders unnecessary all the complex mechanical systems needed to change the blade pitch angle. However, the speed of the rotors depends strongly on the dynamics of the motors driving them. Any motor or engine, no matter of what type (electric, internal combustion, gas turbine, steam powered) has a certain inertia to changes in its regime (i.e., speed). The larger the inertia, the larger the time lag. Depending on the type of motor/engine and its size, the time lag may differ in several orders of magnitude, but it will never be zero (no engine has an instantaneous response). Because of this, whenever a change in the speed of the rotor (motor) is demanded, there will be a time lag until this change is fully implemented, its length being of the same order of magnitude as the time constant of the motor. The flight dynamics of the quadrotor are characterized by several time constants, as it was first said when referring to its stability. If the value of the time lag of the motor gets close to one of these, then the control of the quadrotor will become very difficult, or even impossible. Usually this is not a problem with electrical motors, because their time lag is very small, but it could be with internal combustion engines, which have a larger inertia. This is the reason why all the quadrotors powered by internal combustion engines are controlled by other methods rather than rpm control, or by a combination of those methods with rpm control.
This problem has also been commented on before. Unlike the rest of the disadvantages, this will disappear as soon as many quadrotors are designed and operated. Until then it remains a primary concern, especially for manned vehicles, where reliability is essential.
1.3.8 Comparison of Brushed and Brushless:
DC Motors Brushless DC (BLDC) motors offer several advantages over brushed DC motors. Brushless motors have higher efficiency and reliability, reduced noise, elimination of ionizing sparks from the commutator, overall reduction of electromagnetic interference (EMI) and no brush erosion which creates a longer lifetime. The maximum power that can be applied to a BLDC motor is exceptionally high, limited almost exclusively by heat, which can damage the magnets. To reduce excessive heating, the servos and their controllers are strategically positioned in the down-wash of the propeller blades which offer a cooling effect. Brushless DC motors 'primary disadvantage is their high cost compared to brushed DC motors, which is due to two issues. First, the BLDC motors require complex ESCs to run. Brushed DC motors are regulated by a variable resistor and potentiometer or rheostat, which is inefficient but satisfactory and cost effective. Second, few practical uses have been developed for commercial purposes. For example, RC hobby helicopters 'commercial brushless motors are often hand-wound, whereas brushed motors use armature coils, which are inexpensively machine-wound. Brushless DC motors are more efficient than brushed DC motors. The absence of friction in the brushes of a Brushless DC motor will convert more electrical energy into mechanical power than a brushed motor. Brushless DC motors are designed to operate over a broad range of speeds and have the advantage of reduced maintenance since there are no brushes or commutators. In conclusion, DC brushless motors offer increased speed and superior performance with higher torque-to-inertia ratio.
Figure 1.4Comparison of Brushed and Brushless motors
In the development of rotary wing aircraft the concept of quadrotor was started as early as 1907. The first flight of manned helicopter with four rotors as shown in Figure 3 took place on 24th August, 1907 when Breguet - Richet Gyroplane No. 1 lifted from ground in France. The flight was brief and the plane took off only two feet. Due to lack of
stability and control the gyroplane was leashed on four sides to limit the motion.
Figure 1.5Hiller Aviation Museum
Dr. George-Bothezat started another quadrotor in 1921 which is depicted in Figure 4. This quadrotor had four main propellers plus two propellers for directional control and two propellers to provide cooling and extra lift which were placed above the engine . For testing the stability, asymmetric weight distribution was provided by hanging three men underneath three out of four engines.
Figure1.6De Bothezat'squadrotor flying at McCook Field (1922)
3. With the passage of time stability of quadrotor continued to increase. Later in 1956, D. H. Kaplan controlled the aircraft attitude. The PA-4 Sea Bat was built as the first quadrotor UAV. In 1958, during testing, it maintained its level flight. 
Figure 1.7 Hiller Aviation Museum
1.5 Recent Developments:
Radio-controlled models of quadrotor UAVs increased its research in the area of flight control. Quadrotors are getting smaller in size and lighter in weight now-a-days. Different optical sensor mounted on the quadrotors has made their place. 
"Sensor is a device that receives and responds to a stimulus or signal. Sensors measure real-world conditions, such as heat or light, and then convert this condition into analog or digital representation". 
"MEMS stand for micro-electro-mechanical systems. They are tiny mechanical devices that are built onto semi-conductor chips and are measured in micrometers. They are used to make pressure, temperature, chemical and vibration sensors, light reflectors and switches as well as accelerometers for airbags, vehicle control, pacemakers and games".
For control of a very sophisticated flying object like quadrotors where weight and volume are big constraints heavy gimbaled sensors cannot be used. And hence MEMS sensors are used which do not give the systems states as accurate but are tiny and best suited for the purpose.
A gyroscope is a device that measures the angular orientation of itself in body axis. Generally the gyroscopes measure rate of change of angle about its own axis. Such gyros giving the rate information are known as rate gyros.
During the 1960s typical gimbaled systems weighed around 50 to 75 lb. (without cables) and consumed approximately 200 w of power. Until 1996 the weight had dropped down to 20 to 30 lb. and power consumed was 30w.Gyroscopes are extremely important devices having wide range of usage from simple computer pointing devices to space shuttle navigation systems. It is calculated in three dimensions Rolling, Pitching and Yawing.
The MEMS gyroscopes are beneficial for the applications where weight is a big constraint. Such gyros have a tradeoff on the sensitivity and cross axis effect. The following Figure 6 shows conventional terminologies for Euler angles and their relation to any general aircraft rotation.
Figure 2.1 Roll, pitch and yaw angles for general aircraft rotation
An accelerometer is device which measures the acceleration in body axis. Acceleration is basically the change in pressure experienced by the body initially at rest. This change in pressure causes the center bar move towards one side depending on the acceleration as shown in Figure 7. The change in position varies the capacitance and hence the acceleration is measured. 
Figure 2.2 MEMS accelerometer
2.4.1Angles Extraction Using Accelerometers:
Accelerometers are devices that measure acceleration of a body on which it is mounted. If an accelerometer is mounted on a vehicle which moves with an acceleration "a" and the body is moving in Newtonian Gravitational field "G". Then the force acting on the body can be written as:
There are different types of accelerometers used in aircraft's inertial navigation system. The one we are using is "Micro-machined accelerometer with electrostatic nulling". Fig 10 shows the basic structure of a micro-machined accelerometer. Single-crystal Silicon forms the frame, hinges and the proof mass motion and for rebalancing. This electrostatic centering of the proof-mass makes the use of heavy magnetic coils and other materials unnecessary.
Accelerometer testing is an important phase to determine the quality of the accelerometer. Accelerometers are statistically tested and calibrated in earth's gravity field. The dividing head causes the input axis to rotate in a vertical plane, around a horizontal axis, thus measuring a component of gravity that varied from 0 to Â±1 g. As a convention any accelerometer used in aircraft should be capable of handling acceleration conditions greater or at least equal to 12 g (for military aircrafts). Accelerometers with wide bandwidth are preferred as they are the inputs to strapped down navigation systems or Flight control Systems (FCS). 
Figure 2.3 G-cell of a micro machined Silicon accelerometer
Pitch and Roll angles can be calculated using the accelerometer readings only. Yaw angle cannot be measured using this technique because the yaw movement is parallel to the surface of ground and the gravity vector which acts as a reference for accelerometers doesn't change . Calculation of pitch is done by resolve the triangle using trigonometric ratios as shown figure below.
Figure 2.5 pitch angle calculation
2.5 DC motor limitations:
Limitations of brushed DC motors include need of servicing due to mechanical-wear of commutation-assembly. Brushed DC are also susceptible to electrical noise as electric sparks are produced when connections at brushes are commutated, these sparks are one of the cause of lower efficiency. Main disadvantage of brushed DC motor in quadrotor application is that it has increased weight due to carbon brushes and less efficiency which reduces its thrust generation capability less than its weight. 
Disadvantages of brushed DC motor discussed above have been handled by using BLDC motor, which overcome these problems by having permanent magnet rotor and electromagnetic stator energized directly by batteries through ESC. This brushless configuration frees DC motor from carbon brushes thus, eliminating weight, inefficiency and noise caused by these brushes. Trade off involved here is that to rotate BLDC motor, its poles need to be energized sequentially. This requires a complex controller and rotor position sensor. Hall Effect sensors are used for this propose as shown in Figure 2.6. 
Figure 2.6 Hall Effect sensors
BLDC motor is a type of synchronous motor in which stationary coils are clustered together into phases and a permanent magnet is connected to the shaft. The coils are energized by a separate electronic circuit in a sequence, which causes the magnet to rotate. In this type of motor the speed of motor and speed of magnetic field rotation by the stator are same. Contrary to induction motors and these motors don't experience â€žslipâ€Ÿ. The stator has three windings conforming to the three phase configurations of motor. 
2.5.2 Speed control of BLDC motor:
The ESC is connected to the microcontroller by three wires. Two of these are for providing power to the microcontroller of ESC while one gives the reference signal. This is called BEC or battery eliminator circuit which removes the need of a separate 5V battery for the microcontroller. To control the motor a signal is required with a pulse width varying from 1ms to 2ms. At 1ms speed controller will be initialized and will give beeps. At 2ms the motor, will rotate at maximum rpm. By varying the pulse width from 1ms to 2ms speed of the motor can be varied and controlled and this signal was generated from the microcontroller using PWM pins.
Figure 2.7BLDC Controller
2.6 ESC Firmware Upgrade:
One of the lessons we learned from Project Wyvern was that the Brushless Motor Controllers (ESCs) weren't able to update the motors at a fast enough rate to ensure proper flight stability. We used ESCs that accepted PWM at 50 Hz, and this was adequate for taking off, hovering, and landing, any gust of wind or even AC breeze would send the unit unstable. Ideally, I2C ESCs should be used that can accept PWM commands in the kHz range. We have chosen to follow the lead of the Aero Quad team (www.aeroquad.com) and reflash ESCs from Hobby King (HK SS 18-20 Amp) using assembly code made available by Bernhard Konze (Quax). This will allow us to control the ESCs with PWM signals from our Flight Control Unit at frequencies up to ~450Hz.
Steps taken to flash Hobby King ESCs with new firmware:
Install AVRStudio (easiest to use and allows you to make future edits to the firmware if needed).
Download Quax firmware: www.aeroquad.com
Solder wire connections to the ESC SPI breakout pads. The pads (with the motor leads at the top) are aligned as follows: RESET, VCC, GND, SCLK, MISO, and MOSI.
Connected the programmer to the computer with the USB cable (and made sure that the computer had the correct drivers for it).
Connected the programmer to the breakout cables.
In AVRstudio, click "Tools" and then "Program AVR"
In the "Main" tab, change the device to "Atmega8â€³ and the programming mode to "ISP".
In ISP settings, we used 125 kHz since the board has a 8MHz clock (ISP requires something under 1/4 the system clock for any board running below 12 MHz. 8/4 -> anything under 2MHz). We chose this just to stay on the safe side.
Click "Read Signature". If you see a hex string, this means that the programmer is correctly connected and is able to read data from the microcontroller on the ESC.
In the "Program" tab under "Flash", find the firmware update (this is the hex file from the Quax firmware download).
Click "Program". The programmer will write the firmware to the ESC microcontroller, and let you know if there are any errors. To double check that the firmware was successfully updated, click "Verify."
Lastly, the fuses need to be set. Click the "Fuses" tab and set the fuses as follows:
Figure 2.9ATmega88 firmware updater
Connect the ESC to a power source/battery. If you hear three beeps, then the ESC firmware was successfully updated to accept faster PWM frequencies.
3.1 Torques model:
To calculate torque generated in body we need to first calculate the individual torques contribution from each rotor in all three axis. The torque generated at any point is cross multiplication / vector product of force applied and moment arm. Whereas force generated by any individual rotor is modeled as and moment arm is distance between point of application force that is center of motor/rotor and point of application of torque.
The direction of torque is measured by Right Hand Rule (RHR) by which when thumb points is direction of axis, curl of fingers show positive torque. As number of rotors/forces are four and overall torque is the sum of all the individual torques.
As all of the rotors are perpendicular to moment arm so torque equation simplifies to
Figure 3.1 3D Torque Model
First, torque about x-axis is modeled as Tx i.e. rolling moment. Now r (moment arm) is distance of individual forces form x-axis.
As the rotors 1 and 3 are placed along with body x-axis so their moment arm is zero and they do not contribute in rolling moment as shown in Figure
The moment arm for rotor 2 is positive as it will create positive moment (counter-clockwise), while for that of rotor 4 is negative because it will tend to rotate the system in clockwise fashion and as a convention clockwise torque is taken as negative.
When rotor 4 applies force it tends to rotate the system about x-axis opposite to curl of fingers so using RHR its torque contribution in x-axis is negative. Similarly the rotor 2 produces positive torque about x-axis according to RHR.
Now, torque about y-axis is modeled as Ty i.e. pitching moment. Now r (moment arm) is distance of individual forces form y-axis. Using:
Where r is distance of individual force form y-axis.
Finally the yawing moment is modeled as Tz and is the torque about z-axis. As the motors rotate the rotors encounter a reactive torque due to air drag on rotor blade, this reactive torque is modeled as Q. The yaw is accomplished by rotor rpm imbalance between clockwise and counter-clockwise rotating propellers. The reactive torque as a convention is taken positive for counter clockwise rotating motors/rotors and negative for clockwise rotating ones. All the four rotors contribute in yawing moment.
An overall torque matrix can be defined as:
Whereas torques Tx,Ty and Tz have been calculated in equations 3, 4 and 5 representing torques about x-axis, y-axis and z-axis respectively.
3.4Rotor thrust model:
To correctly model the system thrust it requires to first model the motor then the gear box is modeled if used, then the propellar model is built and then the over model is combined to give a final model of rotor which relates the thrust with the duty cycle.
This techniques doubt-lessly correctly models all of the individual components, but it has been seen in the literature that in quadrotors all over the world, the model does not approximates the actual system which results into the response of the system which is not there in simulations. So to approximate the model to the actual system a technique has been employed named as thrust bed. In this technique a setup has been prepared similar to the shown in Figure
Figure 3.2 Rotor thrust model
3.4.1STRUCTUTRE AND TESTBED:
This discusses the hardware used in this project for the development of Quadrotor and an experimental setup. The physical integration of system involves multiple steps which have been discussed.
After frame concept selection the Quadrotor frame has been modeled in Solid Edge.
Figure 3.3 Frame Modeling Diagram
3.5.1 Symmetry and balance:
Symmetry of structure was one of the main considerations, because if the platform is not balanced there would be many undesired forces and moments. Frame is supposed to be rigid while keeping the weight to a minimum . So the center of gravity of Quadrotor was verified at each step as shown in the above Figure the frame is balanced. Structural design of quadrotor UAV demands a simple but very precise geometry, for this a graph paper was used and all the measurements were cross checked on graph paper.
3.5.2 Components integration:
For safe connections and placement of components perspex sheet has been used. Placement of Li-Po battery exactly in center was required, because of balance in the structure and there was a requirement of IMU to be mounted correctly aligned with the body axis . So a dual story component compartment has been prepared.
3.6 Increasing the Battery's Life:
There are several options to increase flight time are available. The one option is called Zapping. Several highly charged capacitors are discharged in parallel through the cells in the battery pack. If the current is high enough, the connections on the batteries will spot-weld themselves to their connectors, lowering the battery's overall internal resistance. In previous studies this process increases battery performance by as much as ten percent. Another way is to create a larger battery pack, placing several additional batteries in parallel. For instance, create three 'hubs,' made of three battery cells placed in series, then connecting the hubs in parallel. There are other configurations that are useful for increased battery life. This process is not useful for nickel batteries because they self-discharge when connected in parallel. In contrast, when two Li-poly (lithium ion polymer) packs are connected two in parallel, they double their capacitance, while delivering half of the current draw through each cell. One workable pack configuration has three cells wired in series with two of these three cell configurations wired in parallel, which is known as 3s 2p packs.
3.6.1 Lithium Polymer Batteries versus Nickel Batteries:
The development of Lithium ion polymer packs is an improvement in battery technology, slowly rendering its cheaper counterpart, nickel, obsolete. The Li-poly packs test very consistently, with random drops in voltage a thing of the past. Li-poly batteries are also three times more energy dense than nickel batteries; consequently, they have a lower weight, which increases flight time drastically. A Li-poly battery solves the majority of the issues with nickel batteries, although it introduces some new ones. The lithium batteries are very expensive. A model with 11.1 volts and 6,000 mAh costs about $210. Even with educational discounts the cheapest battery found was about $185. To avoid high costs, modification of a cheaper pack can be explored. The Li-poly batteries are so energy dense there is a possibility they will catch fire because they operate very hot, which will ruin the battery. Running a high current through such an energy dense battery can be very dangerous. Another option is to connect several smaller batteries in a configuration like the one described above in the 3s 2p packs. The issue with that configuration is the batteries need to be discharged at the exact same rates. If one cell performs slightly better than the others and drains slower, the cell becomes unbalanced, accumulating charge with each charge and discharge. This can result in the pack actually catching fire in addition to lowering performance on the unbalanced cells, however with a computing system the battery's charge can be controlled.
Nickel batteries need to be completely discharged often to retain their charging capacity because they develop memory or voltage depression characteristics. An easy way to assure the battery is fully discharged is to allow the RC vehicle to continue running after the battery's power has been depleted past flight capability. Contradictorily, Li-poly packs cannot be discharged too much. There is a cutoff point where the battery should not be used anymore even though there is still a little energy left. To avoid the cells being discharged too much, they are equipped with a device that cuts off all current from the cell once it has reached its minimum charge. Due to these new complications an already made, standard, Li-poly battery is worth the added cost and the best selection for the project.
Table 3.2 Batteries prices, ratings
A Comparison of lithium polymer batteries with voltage of 11.1 volts. Many of the cheaper batteries have been discontinued.
3.7 Propeller Balancing:
The quad-rotors propellers are designed to rotate as fast as 6,000 times per minute, making balance a crucial factor. The blades of the propeller may vary in weight due to imperfections and therefore, at certain revolutions per minute (RPMs), the propeller will vibrate uncontrollably. Balancing the propeller insures it will rotate without causing undue vibrations to the airframe and the electrical components. If left unchecked the vibrations may become destructive to the quad-rotor loosening its bolts and eventually damaging components to the point of failure. First, the propellers and servos must be mounted symmetrically. Next, ensure both blades of the propeller are balanced over their span. There are more complicated balancing issues, with respect to the hub, however they apply to much larger propellers than those used on a miniature quad-rotor. The propellers focused on here are 9 in length and have 6 pitch angles, (9X6) propellers. A specially designed propeller balance measurement device is used to balance the propeller. There are many types of model propeller balancers. Master Airscrew developed a propeller balancing device that suspends the propeller in a magnetic field with very low friction. Top Flites Power Point Precision Balancer seen in Figure works in a similar manner. Great Planes Fingertip Propeller Balancer offers a propeller balancer for less than $5.00. All of these model propeller balancers are suitable for the (9X6) propellers used on the quad-rotor. To operate the balancer position the propeller on the spindle as above, and place the spindle on the balancer allowing only one side to contact the magnet. Rotate the propeller to a horizontal orientation and release the blade. If the propeller balances horizontally, rotate it 180 circ and check it again. If one blade is heavier than the other the propeller will rotate until the heavy blade is pointing down as in Figure
Figure 3.5 Top Flits Power Point Precision Balancer
Figure 3.6An unbalanced propeller
An unbalanced propeller is corrected by removing material from the trailing edge of the blade near the tip as. Be careful to preserve the airfoil shape while removing material conservatively. Very little material should be removed between each balancing test as shown in Figure
Figure 3.7Balancing the propeller
3.8 Vibration Reduction:
One of the major issues that come to light when the Quad-rotor is running off the computer is the amount of vibrations that occur. The servos themselves are quite powerful, and with the larger propellers and high RPMs, the motors themselves create a lot of vibrations. To reduce the vibrations several connection areas between components need to be fastened using different techniques. The areas that require improvement are the propellers, gearbox mounts and the circuit board holders. First, the propellers' for the vertical bars are too big and create a loose connection between the gear boxes and the propellers. Fastening bolts and thin tape are added to the gearbox bar to reduce the wiggle in the propeller. Next, the gearbox bracket has a short vertical post that slides into the gearbox. A pin is then slid through the gearbox, into a hole drilled in the vertical post and then fastened with a nut on the other side. The problem is the gearbox does not fit snug enough on the post. Masking tape is wrapped around the posts to try to tighten the connection, but it is too thick and does not stick to the aluminum. The posts have to be sanded down. After that each face has to be rubbed with the sticky side of a scrap piece of tape to remove any dust. Now the gearbox is able to fit over the tape and the tape didn't pull off. This small improvement makes a huge difference, decreasing the amount of vibrations drastically. Another method is to elastic bands connecting the spars together. The pull on the spars from the elastic bands helps to reduce any vibration. Finally, a lot of noise in the circuit board makes the sensors unreliable; therefore it is necessary to add padding between the aluminum frame and the circuit board. The padding drastically reduces the vibration experienced by the circuit board. All of these methods reduce the vibrations of the quad-rotor and reduce the noise experienced in the circuit board, which makes all the sensors more accurate. 
LiPo Battery- ZIPPY Flightmax 3000mAh 3S1P 20C:
The Li-Po battery used has an overall cell capacity of 3000mAh and maximum allowable current is 20Amp. Further specifications and analysis is given in Specs below.
Voltage: 3S1P / 3 Cell / 11.1v
Discharge: 20C Constant / 30C Burst
Weight: 239g (including wire, plug & shrink wrap)
Balance Plug: JST-XH
Discharge Plug: XT60
Figure 4.1 LiPo Battery- ZIPPY Flightmax 3000mAh 3S1P 20C
4.1.2 Electronic Speed Controller:
22.214.171.124Brushless motor speed controller 60 Amps:
Turnigy ESC has been used which allows maximum current of 18 Amp. Normally the RC brushless ESCs give refresh rate of 50Hz. whereas this BESC output to the motor at an updated refresh rate of 400Hz.
Constant current 60A Max 80A <10s
Size : 65 x 39 x 13mm
Weight : 61g
High Voltage Li-Poly 2-7 cells, Ni-MH 6-20 cells
Low resistant 0.0014 ohms
BEC : OPTO
Auto shut down when lose signal
Slow down at 3.0V per cell Lipo, Cut-off at 2.9V per cell Lipo 0.8V Nimh
User programming options
Brake Setting 4 options
Direction and Cutoff Type
Timing Mode Setting: 1° /7° /15°/30°
PWM Setting: 8K/16K
Figure 4.2 Brushless motor speed controller 60 Amps
4.1.3 Brushless Motor:
CF2822 1200KV Brushless Outrunner Motor
Figure 4.3 Brushless Outrunner Motor
Dimension 28.2mm x 31.2mm (bottom to shaft end)
Shaft size 3mm
Max Current (Full Loaded) 12A (10s)
Voltage 6-12V lipo battery (2-3 cells)
Internal resistance 150 Ohms
KV (RPM) 1220kv
Propellor APC 7x4 to APC 9x4.5
These are great little motors - click here Emax CF2822 Test Data for independent test results against other motors in its class and prop recommendations.
Figure 4.4 Propellers
RC Parts & Accs = Propellers
Model Number = RM237
Prop static rpm = 7166 rpm.
Static pitch speed = 51 Km/h.
Prop static tip speed = 0.28 MACH.
High quality and light weight.
10 * 4.5" propeller.
With 2 sets of hubs for motor shaft of 3, 3.2, 4, 5, 6, 6.35 and 7.95mm.
Length: 10" (25.4cm)
Slope: 4.5" (11.43cm)
Single propeller weight: 7g
Package size: 28 * 7 * 1cm
Package weight: 27g
4.1.5 Propeller Adapter:
Prop adapters fit standard size propellers onto a motor shaft.Easy to use - adapter's split end goes onto a prop shaft and compresses as the nut is tightened in front of the propeller at the opposite end.
Figure 4.5 Propeller Adapter
Propeller Adapter (Colet Type) 3MM
Motor Shaft: 3mm
Prop Shaft: 6mm
Prop Shaft length: 24mm
Weight: 13.2 grams
The high-performance, low-power Atmel 8-bit AVR RISC-based microcontroller combines 8KB ISP flash memory, 1KB SRAM, 512B EEPROM, an 8-channel/10-bit A/D converter (TQFP and QFN/MLF), and debug WIRE for on-chip debugging. The device supports a throughput of 20 MIPS at 20MHz and operates between 2.7-5.5 volts.By executing powerful instructions in a single clock cycle, the device achieves throughputs approaching 1 MIPS per MHz, balancing power consumption and processing speed.
Fig 4.5 At mega 88
Wii Motion Plus - 3 DOF IMU
Figure 4.5 Sensor
Wii Motion Plus is a MEMS gyroscope accessory for the Wii controller that is easy to obtain and repurpose as a 3 DOF IMU. WMP details can be found on Wiimote/Extension Controllers - Wikipedia web page link. In addition to the OEM version there are many clones and some even using better parts then the original. Wii mote extensions use I2C bus to communicate which makes them easy to interface to the MCUs.
ECO6 50W 5A Balancer/Charger w/ accessories:
Figure 4.10 ECO6 50W 5A Balancer/Charger w/ accessories
Delta-peak sensitivity (NiMH/NiCd)
Individual cell balancing
Li-ion, LiPo and LiFe capable
Ni-Cd and NiMH capable
Large range of charge currents
Store function, allows safe storage current
Time limit function
Input voltage monitoring. (Protects car batteries at the field)
Data storage (Store up to 5 packs in memory)
Battery break in and cycling.
Input Voltage: 11~18v
Circuit power: Max Charge: 50W / Max Discharge: 5W
Charge Current Range: .1~5.0A
Ni-MH/NiCd cells: 1~15
Li-ion/Poly cells: 1~6
Pb battery voltage: 2~20v
Note: Power supply not included.
4.1.11 Transmitter And Reciver:
Hobby King 2.4Ghz 6Ch Tx & Rx V2 (Mode 2):
Figure 4.11 Hobby King 2.4Ghz 6Ch Tx & Rx V2 (Mode 2)
HobbyKing 2.4Ghz 6Ch Tx & Rx V2:
Hobbykings T6A 2.4ghz system is an entry level transmitter offering the reliability of 2.4Ghz signal technology and a receiver with 6 channels. This transmitter requires a PC to modify any of the channel variables including mixing and servo reversing.
4.1.12 .1 Key Features;
6-channel 2.4GHz transmitter with servo reversing.
Easy to use control for basic models.
Includes 6-channel receiver
Trainer system option.
This system must be programmed via PC cable for servo reversing and adjustments.
4.1.12 .2 Working:
This information has been gleaned from the discussion section. Thought it might make it
easier on the rest of you sweating over how to do this.
Connections: negative is at bottom of receiver case (away from label).
Connect bind plug to battery port.
Connect battery to any other channel and red light starts flashing.
Power up transmitter while holding down bind button at back of transmitter case
until red light on receiver stops flashing and glows continuously.
Release bind button on transmitter.
Remove bind plug from receiver.
Power down receiver.
Power down transmitter.
4.2 Controller modes:
The controller has been designed for three different configurations which are named as the acrobatic mode, the stable mode and the heading hold mode. These modes are explained as follows:
4.2.1 Acrobatic mode:
In this mode the controller has been implemented on the rate of rotation of system in all three axes that are roll, pitch and yaw. The transmitter commands in these three axis is depicted as the desired rates of rotation for Quadrotor. The sensor values from gyroscopes, after filtering, give the current rates of rotation and the controller implemented corrects the system rates of rotation as per the command of pilot through transmitter. As there is no controller applied on Euler angles of quadrotor, the transmitter commands are required to stabilize the quadrotor. Hence this mode can be categorized as semi-autonomous mode.
Figure 4.12 Controller modes block Diagram
During flight the Quadrotor can be switched from any other mode to acrobatic mode by switching the transmitterâ€Ÿs gear channel to off position.
4.2.2Pros and cons:
This mode enhances the maneuverability of Quadrotor. Errors due to vibrations in the accelerometer are neglected as the accelerometer inputs are not required for this mode. The complimentary filter errors are abandoned and the integration error in gyroscopes is abandoned as the angles are not required for this mode. But this mode requires the concentration of human control as the transmitter is used to stabilize the system in inertial frame of reference for this system.
In this mode the fast and accurate angular rates are received from gyroscopes. A moving average based low pass filter has been applied to remove jitter in the sensor data.
In this mode the controller has been implemented on the Euler angles of the system as well as the rates of rotation. First the accelerometer is used as gravity sensor6 to measure the Euler angles. Then the integration of gyroscopes data give other set of Euler angles. After applying the designed complimentary filter the correct Euler angles are estimated that give the current state of the system.
In this mode the commands from transmitter in roll, pitch and yaw axis is interpreted as the desired Euler angles. One set of controllers keeps on correcting the error in Euler angles of the system whereas other set of controllers corrects the error in rates of rotation.
After successful completion of experimentation of Quadrotor, there are some recommendations in terms of approach and sensors improvement.
In next phase of Quadrotor the magnetometer can be added to correctly estimate the yaw angle, because current method of taking yaw angle from gyroscopes has demanded efficient filtering and the ultimate correct yaw angle can be taken if a MEMS magnetometer or a compass is used.
Controller can be applied on altitude of the vehicle for this ultrasound sensor can be used. Ultrasound range sensor can be used to estimate the low altitude. Attitude hold can be added as autonomous control. Quadrotor can be able to takeoff autonomously without human control. The transmitter throttle stick can be used to increase or decrease the altitude and the on-board controller will estimate the throttle as per the altitude command and ultrasonic sensor data.
For high altitude estimation and control MEMS based barometric pressure sensor can be used.
On-board battery voltage and current indicator can be used. The controller can be able to autonomously land the vehicle when the battery goes down the critical level.
CMOS based camera can be added. The camera can be rotatable and the motion can be controlled by additional servos. For that a servo driver IC8 can be used.
The frame of Quadrotor can be improved. For that carbon fiber rods can be manufactured. That will give the vehicle strength and will reduce the overall weight, enhancing efficiency.
State-of-the-art 66 channel GPS can be used to correctly estimate the position of Histaal-I. A set of controller will also be applied on position in inertial axis. This will enhance the hovering of vehicle.
5.2 Sensor selection:
A detailed analysis for the components has been carried out. In analysis the focus remained with the sensor that gives the measurement which is suitable for the purpose. The update rate of the sensors and sensitivity remained concentrated while a lot of already built quadrotors around the globe along with open source quadrotors have been consulted and a set of sensors have been selected.
In the recent past Quadrotors have created high interest in control community due to their complex dynamics and obvious advantages over conventional aerial vehicles.This category of vehicles promises large number of applications like area navigation, reconnaissance/surveillance, precision agriculture, and geological surveys etc. While modeling the system, various external disturbances e.g. wind effect, initial attitude offset etc. have been incorporated. After successful controller designing, the actual quadrotor system has been built. All the non-linarites in the system have been indicated.
COMPREHENSIVE PARTS LIST
Pusher Propeller 10x6
Tractor Propeller 10x6
Wii motion sensor
Project Completion Chart: