Quadcopter free essay sample

The Quad Copter presented in this project, is a type of quad rotor helicopter or quadrocopter that is lifted and propelled by four rotors. Early designs in the 1920s and 1930s suffered from poor performance and lack of stability due to limited controls and system integrations. Today with advanced electronics, accurate sensors and control system technology these limitations are becoming more a thing of the past, technology today has allowed these systems to grow more and more appealing due to increased stability and payload capacities. To overcome these obstacles, complex integration of various sensors would have to be incorporated to allow this configuration of flight to be successful, the quad copter. The overall goals of this project are the following: 1. Achieve Autonomous Take off and Landing. 2. Streamline Mechanical Construction/ Weight. 1 3. Attain a workable design that can be improved over time. The points presented above will be discussed thoroughly within this paper. 1. 2 History [1] The concept of a quad-rotor aircraft has existed since early in the 20th entury. Throughout the 20th century not many unique rotor-craft designs have been developed. The earliest workable designs for a quad-rotor were developed by George DeBothezat and Etienne Oemichen. The Oemichen‘s quad-rotor design is the earliest mention of a complete four-rotor hovering vehicle in past history. Oemichen‘s first design in 1920 failed in the initial attempt to become airborne, thereby requiring Oemichen to add additional lifting power and stability of a heliumfilled balloon. After a number of recalculations and redesigns, Oemichen was able to come up with a design that actually was capable of lift off and even established world helicopter flight records of the time, remaining airborne for up to 14 minutes at a time by 1923. Figure 1. 1 DeBothezats Quad-Rotor Design, 1922. The DeBothezat‘s design was created for a 1921 contract with the United States Air Corps as seen in Figure 1. 1. After working on his design for over 2 years, he was able to develop a fairly capable helicopter, which was able to take on a payload of up to 3 people in addition to the pilot. His design was deemed underpowered, unresponsive and susceptible to reliability issues. In 2 addition, instead of the calculated 100 meters cruising altitude, his craft was only capable of reaching a height of roughly 5meters. The early designs were propelled by additional rotors located somewhere on the rear or the front of the craft, perpendicular to the main rotors. Thus, they are not true quad-rotor designs. It was not until the mid-1950s that a true quad-rotor helicopter flew, which was designed by Marc Adam Kaplan. The prototype first flew in 1956, and did so with great success. The 2200 pounds craft was able to hover and maneuver using its two 90 horsepower motors, each capable of driving all four rotors in backup mode. Control in this case did not call for additional rotors on the sides of the craft, but was obtained by varying the thrust between rotors. This also was the first quad-rotor design that was able to fly successfully forward. Despite these early proofs-of-concepts, people saw little practical use for quad-rotors. They simply were not competitive with the performance specifications (speed, payload, range, etc. ) of more conventional aircrafts. No production contracts were awarded and interest in quad-rotors diminished. 3 1. 3 Prospective Applications [1] [6] Quad Copter designs are constantly progressing as the years go on. It wasnt too long ago that designs were limited and constrained, those days are history. The number of projects being undertaken regarding the topic has considerably increased, most of which are for commercial payload, human transport and military use. Currently Bell Helicopter Textron and Boeing Integrated Defense Systems are doing joint research and development of the Bell Boeing Quad Tilt Rotor, as depicted in Figure 1. 2. The initial design consists of four 50-foot rotors powered by V-22 engines. The main role of the Bell Boeing Quad Tilt Rotor will be that of a cargo helicopter with the ability to deliver pallets of supplies or also deploy paratroopers. The first wind tunnel tests were completed in 2006 and the first prototype is expected to be built in 2012,with great anticipation. Figure 1. 2 Bell Boeing Quad Tilt Rotor. 4 Chapter 2. Quad Copter Dynamics and Theory 2. 1 Concepts of Quad Copter Flight [3] [4] [5] Copters are one of the most complex flying machines due to versatility and maneuverability to perform a number of tasks. Classical helicopters are usually equipped with a main rotor and a tail rotor. However the UAV (Unmanned Air Vehicle) presented in this paper is known as a quad copter. Quad rotors are symmetrical vehicles with four equally sized rotors at the end of four equal length rods. By making use of multiple rotors it allows for greater thrust and maneuverability. Each of the rotors on the quad-rotor helicopter produces both thrust and torque. Given that the front and rear motors both rotate counter-clockwise and the other two rotate clockwise , resulting in a net orque of zero due to the rotational axis. Lastly, the quad rotors symmetrical design allows for easier control of the overall stability of the aircraft. Figure 2. 1 Quad Copter Torque Pattern and Movement Generality. 5 The principle for maintaining an equal rate of change for the two opposing rotors is how the translation of the craft is determined, as shown in Figure 2. 1. Due to either a pitch or a roll, the lift force is displace d in the x and y axes, resulting in a horizontal force component that will direct the craft. The altitude of the quad-rotor is altered by changing the rate of all rotors by the same amount. The UAV representation is obtained by representing the quad copter as a solid body evolving in 3D to one force with three moments (Figure 2. 2). The general coordinates of this craft are: q=(x, y, z, , ) [2. 1] Where ( x, y, z) denotes the position of the center of the mass of the craft in relation to the frame base and ( , ) denotes the three angles yaw, pitch and roll (Euler angles) and represent the orientation of the copter. Figure 2. 2 Quad Copter General Inertial Frame Coordinates. 6 2. Dynamics of a Quad Rotor The kinematic relations relate the movements and rotations in the earth-fixed inertial reference to the body-fixed reference frame. The derivatives with respect to time of the angles ( , [ in which N( , ]T = N ( , , ) , ) can be expressed in the form: [2. 2] = [p q r]T are the angular velocities with respect to the body reference frame and , ) is the 33 matrix given by: N( , , )= [2. 3] This matrix depends only on ( , singularity hold. , ) and is invertible if the boundaries on ( , , ) for non Similarly, the derivative with respect to time of the position (x, y, z) is given by: [ ]T = V0 [2. ] where V0 = [u0 v0 w0]T is the absolute velocity of the quad rotor with respect to an earth-fixed inertial reference frame. Let V = [u v w]T be the absolute velocity of the quad rotor expressed in a body-fixed reference frame. V and V0 are related by: V0 = R( , , )V [2. 5] 7 where R( , R( , , )= , ) is the rotation matrix given by: [2. 6] After the rotation matrix has been applied, the translational equations of motion with respect to an inertial frame are given by: m( ) = m( )= ) [2. 7] m( ) = Following the Euler-Lagrange equations, the rotational dynamics include torques and Coriolis terms. The coriolis term, C( , ) , defines the gyroscopic effects on the system when the craft yaws. represents the vector of torques applied to the system. = ( C( , ) ( T ) [2. 8] + C( , ) = = J + C( , ) It follows that =[ , , ]T= [2. 9] Combined with [2. 7] the translational and rotational dynamics can be summarized as = = = [2. 10] 8 Where x and y are the coordinates in the horizontal plane, and z is the vertical position and are the yaw, pitch and roll angles respectively. 2. 3 Assumptions It is not possible to create a model that conforms to reality completely. Some assumptions need to be made, in this model the following is assumed: †¢ The quad rotor structure is rigid and its deformation characteristics will be disregarded. †¢ The quad rotor structure is symmetrical and material inconsistencies will be disregarded. †¢ The propellers are rigid and deflections will be ignored. †¢ The cross products of the inertia matrix can be neglected. †¢ The ground effect is neglected. 9 Chapter 3. Control Theory 3. 1 Closed-Loop Control Systems In closed-loop control systems the difference between the actual output and the desired output is fed back to the controller to meet desired system output. Often this difference, known as the error signal is amplified and fed into the controller. The general structure of a closed-loop feedback control system is seen in Figure 3. 1. A few examples of feedback control systems are elevators, thermostats, and cruise control in automobiles. Figure 3. 1 Typical Closed Loop Control. 10 3. 2 Classical Control using PID Method [2] [15] The PID (Proportional Integral Derivative) control is one of the earlier control methods implemented. Early on its execution was in pneumatic devices in the 1940s, followed by vacuum and solid state analog electronics, before arriving at today’s digital use of microprocessors. It offered a simple control structure that was understood by operators and was relatively easy to work with. The quad rotor will use a PID system, which will be tuned to determine the optimum response and settling time, illustrated in Figure 3. 2. The PID controller equation is a closed-loop feedback system which will output a control signal u and receive feedback from the sensors. The controller will calculate the difference between the desired position and current position, adjusting u accordingly. The equation for a PID controller is as follows: = + + [3. 1] e(t) = ed(t) ea(t) Where ed denotes the desired condition, ea the actual condition, and e(t) denotes the actual difference, error, the two at each individual time step. A PID controller has proportional, integral and derivative terms that can be represented in transfer function form as K(s) = Kp + + Kds [3. 2] Where Kp represents the proportional gain, Ki represents the integral gain, and Kd represents the derivative gain, respectively. By tuning these PID controller gains, the controller can provide control actions designed for specific process requirements. The integral term Ki is proportional to both, magnitude of the error and the duration of the error. It (when added to the proportional term) accelerates the movement of the process towards the set 11 point and often eliminates the remaining steady-state error that may occur with a proportional only controller. The rate of change of the process error is calculated by determining the differential slope of the error over time (i. e. , its first derivative with respect to time). This rate of change in the error is multiplied by the derivative gain Kd. Figure 3. 2 Typical PID Control Logic. Feed-forward control plus feedback control can considerably improve performance over a simple feedback control done whenever there is a major disturbance affecting the system. In idyllic situations, feed-forward control can entirely neutralize the effect of the measured disturbance. Feed-forward control is used along with feedback control as necessary to track set point changes and to curb unmeasured disturbances that are always present in any real process. For this project, feed-forward control accounts for the behavioral dynamics of the quad copter, such as its momentum and motor response time. The integral term determines the magnitude of the accumulated error by summing the instantaneous error over time. The integral control equation is: I= Ki [3. 3] Note that t is replaced with , which denotes the past time. 12 The derivative term accounts for the rate at which the error is varying. In addition, by decreasing the rate of change close to the set point reduces overshoot and increases settling time. D = Kd P = Kp e(t) [3. 4] [3. 5] 3. Control Tuning [16] For tuning of the PID controllers, several tuning algorithms have been developed, such as Ziegler-Nichols and Lambda tuning. The Zeigler-Nichols tuning method is a heuristic method of tuning a PID controller. It was developed by John G. Zeigler and Nathaniel B. Nichols. This tuning process is the response of a plant to unit-step input. If the response results in an S-shaped curve, both time constant and delay time are determined by a differential slope line at the inflection point of the curve. When iterative tuning is used, the following algorithm can be used to et the desired overall response: 1. Investigate the step response. 2. Add gain KP to reduce the rise time tr if necessary. 3. Add gain KD to improve the maximum overshoot Mp if necessary. 4. Add gain KI to eliminate steady state error ess if necessary. 5. Adjust gains till desired overall response is obtained. 13 The transfer function of this method equals: = [3. 6] The values of Kp, Ti, and Td are determined by the factors in Table 3. 1. This method demonstrates improvement in contrast to traditional manual tuning, but still is difficult to set exact values to critical gain. Table 3. Values Set by Zeigler-Nichol Tuning Method. Type of Controller P PI PID Kp T/L 0. 9 T/L 1. 2 T/L Ti ? L/0. 3 2L Td 0 0 0. 5 L 3. 31 Vertical Position Control When operating above the ground effect, the control output U1 is approximately proportional to the vertical acceleration in the body reference frame. To remain at constant height, a large value of U1 is required to counteract gravity, additionally a PID controller is added to stabilize the motion in the z direction (Figure 3. 3). The control law can be described by: r1 = U1 = zp (z zd) KZI ) [3. 7] Figure 3. 3 Vertical Position Controller [1]. 14 3. 2 Horizontal Position Control The horizontal position (x, y) of the quad rotor is controlled by adjusting the roll and pitch. The total thrust produces a lift acceleration approximately equal to the gravity (g) in a direction normal to the plane of the rotors (Figure 3. 4). A small angle of roll acceleration ? g. results therefore in a lateral The commands in x and y direction are described by: Ux = Uy = P( d) KxI KyI ) ) [3. 8] yP (y yd) Corrected for the yaw angle they give the commands for the desired roll and pitch angle: d= d= Ux + Ux + Uy Uy [3. 9] Figure 3. 4 Horizontal Position Controller [1]. 3. 3 Roll and Pitch Position Control Because the quad rotors layout is symmetrical the roll and pitch control can be assumed independent for small attitude angles (Figure 3. 5). Relative to the yaw control a higher bandwidth is required, since the value has a direct relationship to the lateral acceleration in x and y direction. U2 = P( d) ) 15 U3 = P( d) ) [3. 10] Figure 3. 5 Roll Position Controller [1]. 3. 34 Yaw Position Control The yaw is the least critical of the controls since it has no direct effect on the quad rotors motion. It can be independently tested and tuned, while having manual control in the remaining channels (Figure 3. ). The PID control law for yaw is described by the following equation: U4 = P( d) I ) [3. 11] Figure 3. 6 Yaw Position Controller [1]. 3. 4 Rotor Theory Unlike other helicopters which require complex mechanical rotor mechanisms to control the pitch of the blades, a quad-rotor relies solely on differential torque and thrust, and thus uses fixed-pitch blades. One of the goals of the project is to increase total thrust; increasing thrust is accomplished by increasing the velocity of the air being moved by the rotor, or by increasing the amount of air being moved by the rotors. 3. 12] 16 Where T is the thrust, is the mass airflow, and u9 and u0 are the outgoing and incoming velocities, respectively. From a simple physics perspective, using the kinetic energy equation: [3. 13] Doubling the thrust by double m would lead to double the energy required. Doubling the thrust from doubling differential velocity would require four times the energy. The design of propellers is a complex subject, and as there were already dozens of readily available propellers on the market, it was both cost and time e ffective to select a commercial blade. The propellers are designed for radio control applications, and their airfoils are highly proprietary. The standard measure of propellers is diameter x pitch, where pitch refers to the angle of incidence at ? of the radius. Using this angle, the pitch is converted to inches by how far the propeller would move after one revolution if it were â€Å"screwed† into a solid substance. 17 Chapter 4. Electrical Control Systems 4. 1 The Microcontroller Arduino ATMega 2560 [8] The microcontroller we decided to utilize in our project was the Arduino Mega 2560, after careful review of several models. Considering that this single part is the heart of the project we selected with special care to characteristics like connectivity, available I/O and broad power integration. The microcontroller offered all the features we needed to develop the quad copter, with the characteristics we desired. It is based on Atmels ATMega 2560 microcontroller. The board comes with 54 digital input/output pins, 16 analog inputs, 4 UARTs (hardware serial ports), a 16 MHz crystal oscillator, a USB connector, and a power jack. The operating voltage of the microcontroller is 5V, with an input voltage of 7 to 12V. The ATMega 2560 has a flash memory of 256 KB, of which 8 KB are reserved for the boot loader. 8 KB of SRAM, 4 KB of EEPROM, and a clock speed of 16 MHz. The Arduino Mega 2560 can be powered through a USB connection or with an external power supply. Additionally, the Arduino platform was particularly attractive because of its open-source physical computing platform based on a simple i/o board and a development environment that implements the Processing/Wiring and language, seen below in Figure 4. 1. Figure 4. 1 Arduino Mega 2560 Microcontroller Board. 18 The ATMega 2560 comes with an Atmel AVR core which combines a wide instruction set with 32 general purpose working registers. All 32 registers are directly coupled to the ALU (Arithmetic Logic Unit), allowing two independent registers to be accessed in one single execution of the instruction per clock cycle. In order to maximize parallelism, the AVR uses a Harvard architecture – with separate memories and buses for program and data. Figure 4. 2 shows the block diagram of the AVR architecture. Figure 4. 2 Arduino Mega 2560 Microcontroller Block Diagram. 19 . 2 Electronic Speed Controllers An electronic speed control or ESC is a circuit with the purpose to control an electric motors speed, its direction and possibly also to act as a dynamic brake in some cases. ESCs are often used on electrically powered brushless motors essentially providing an electronically-generated three phase electric power, with a low voltage source. An ESC interprets control information in a way that var ies the switching rate of a network of field effect transistors (FETs), not as mechanical motion as would be the case of a servo. The quick switching of the transistors is what causes the motor itself to emanate its characteristic highpitched whine, which is especially noticeable at lower speeds. It also allows much smoother and more precise variation of motor speeds in a far more efficient manner than the mechanical type with a resistive coil and moving arm once in common use. The ESC generally accepts a nominal 50 Hz Pulse Width Modulation (PWM) servo input signal whose pulse width varies from 1ms to 2ms. When supplied with a 1ms width pulse at 50 Hz, the ESC responds by turning off the DC motor attached to its output. A 1. 5ms pulse-width input signal results in a 50% duty cycle output signal that drives the motor at approximately 50% speed. When presented with 2. 0ms input signal, the motor runs at full speed due to the 100% duty cycle (on constantly) output. The correct phase varies with the motor rotation, controlled and monitored by the ESC. The orientation of the motor is determined by the back EMF (Electromotive Force). The back EMF is the voltage induced in a motor wire by the magnet spinning past its internal coils. Finally, a PID algorithm in the controller adjusts the PWM to maintain a constant RPM. Reversing the motors direction may also be accomplished by switching any two of the three leads from the ESC to the motor. 20 4. 21 Turnigy Plush 18A ESC Modules [13] [14] The ESC controller chosen for this project was the Turnigy Plush 18A series, shown in Figure 4. 3. Many considerations had to be made in making the appropriate selection. Ideally the ESC controller should be paired to the motor and rotor craft with the following considerations. 1. Temperature and thermal characteristics. 2. Max Current output and Impendence. 3. Needs to be Equipped with a BEC (Battery Eliminator Circuit) to eliminate the need of a second battery. 4. Size and Weight properties. 5. Magnet Rating. The Plush series Turnigy ESCs offered several outstanding performance features that fulfilled our needs, fast sync timing, a generous current rating and a small size to weight footprint (Table 4. 1). Specifications as follows: Table 4. 1 Turnigy Plush18A Specifications. Continuous Current Rating Burst Current Rating BEC Mode BEC LiPo Cells Weight Size 18 Amp 22 Amp Linear 5V/ 2 Amp 2-4 Cells 19 grams 24x45x11mm Additionally, the speed controller has fixed throttle settings so that the stop and full throttle points of all the various modes which can be cut through cleanly. The controller produces audible beeps to assist in navigating through the program modes and troubleshooting logs. 21 Figure 4. 3 Turnigy Plush18A ESC Packs. 4. 3 The Battery Pack Selecting the proper battery for our rotor copter was a challenging task. Nickel Cadmium (NiCd), Nickel Metal Hydride (NiMH), and Lithium Polymer (LiPo) were common choices with the advantages and disadvantages of each battery pack. NiCd batteries are reasonably inexpensive, but they have a number of negatives. NiCd batteries need to be fully discharged after each use. If they aren’t, they will not discharge to their full potential (capacity) on following discharge cycles, causing the cell to develop what’s commonly referred to as a memory. Additionally, the capacity per weight (energy density) of NiCd cells is commonly less than NiMH or LiPo cell types as well. Finally, the Cadmium that is used in the cell is quite destructive to the environment, making disposal of NiCd cells an issue. NiMH cells have many advantages over their NiCd counterparts. NiMH cell manufacturers are able to offer significantly higher capacities in cells approximately the same size and weight of equivalent NiCd cells. NiMH cells have an advantage when it comes to cell memory as well, as they do not develop the same issues as a result of inappropriate discharge care. Lithium Polymer (LiPo) cells are one of the newest and most revolutionary battery cells available. LiPo cells maintain a more consistent voltage over the discharge curve when compared to NiCd or NiMH cells. The higher nominal voltage of a single LiPo cell (3. 7V vs 1. 2V for a typically NiCd or NiMH cell), making it possible to have an equivalent or even higher total 22 nominal voltage in a much smaller package. LiPo cells typically offer very high capacity for their weight, delivering upwards of twice the capacity for ? the weight of comparable NiMH cells. Lastly, a LiPo cell battery needs to be carefully monitored during charging since overcharging and the charging of a physically damaged or discharged cell can be a potential fire hazard and possibly even fatal. LiPo Pros: ? ? Highest power/weight ratio. Very low self-discharge. Less affected by low temperatures than some. LiPo Cons: ? ? ? Intolerant of over-charging. Intolerant of over-discharging. Battery. Significant fire risk. Figure 4. 4 Zippy 4000 mAh 4. 31 Zippy 4000mAh Battery Pack Module [17] Considering our copters weight, current load and predicted discharge rates, the Zippy 4000mAh battery pack seemed to fit the bill (Figu re 4. 4). The Zippy 4000mAh battery pack offered the following characteristics seen in Table 4. 2: Table 4. 2 Zippy 4000 mAh Battery Specifications Table. Capacity Voltage Discharge Weight Dimensions Balance Plug Discharge Plug Max Charge Rate 4000 mAh 3 Cell 11. 1 V 20C Constant 30C Burst 306 grams 146x51x22mm JST-XH Bullet Connector 2C 23 To approximately calculate the run time, the following equation was used: Run Time (Mins) = Battery mAh Rating [4. 1] Considering the average hovering current consumed by the motors is 12Amps per motor. We were able to calculate a min run time of 5 minutes and a max run time of 10 minutes, which was sufficient in our case, since we would be running at reduced speeds for testing with spare batteries. . 4 The Gyroscope Transducer A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. A MEMS gyroscope takes the idea of the Foucault pendulum and uses a vibrating element, known as a MEMS (Micro Electro-Mechanical System). These typically are packaged similarly to other integrated circuits and provide either analog or digital outputs. In addition, they are inexpensive and have become widely available today. They provide accurate 3 axis positioning of a craft and are highly reliable over the years with no internal moving parts. 4. 1 ITG3200 Gyro Module [11] The Gyro Sensor chosen for this project was the ITG 3200 by Invensense (Figure 4. 5). The ITG3200 featured a three 16-bit analog-to-digital converters (ADCs) for digitizing the gyro outputs, a user-selectable internal low-pass filter bandwidth, and a Fast-Mode I2C (400kHz) interface as shown in the block diagram below (Figure 4. 6). In addition it included a embedded temperature se nsor and a 2% accurate internal oscillator. 24 The ITG-3200 had a wide power supply range of anywhere between 2. 1 and 3. 6V with a low operating current of 6. 5mA. The sensor also featured a interrupt output, and an optional clock input. Figure 4. 5 ITG 3200 Gyro Board. Figure 4. 6 ITG 3200 Gyro Functional Block Diagram. The ITG-3200 detects the rotational rate of the x, y, and z axes for roll, pitch, and yaw respectively. This is achieved through its three independent vibratory MEMS gyroscopes. When 25 the gyros are rotated about any of the sense axes, it causes a deflection that is detected by a capacitive pickoff. 4. 5 The Accelerometer Sensor An accelerometer is a device that measures proper acceleration by measuring weight per unit of mass, a quantity of force, or g-force (although it is not a force). Consequently, by measuring weight, an accelerometer measures the acceleration of the free-fall reference frame (inertial reference frame) relative to itself (the accelerometer). Single- and multi-axis models of accelerometers are available to detect magnitude and direction of the proper acceleration (or g-force), as a vector quantity, and can be used to sense orientation, coordinate acceleration (so long as it produces g-force or a change in g-force), vibration, shock, and falling (a case where the proper acceleration changes, since it tends toward zero). Micro machined accelerometers are increasingly present in modern electronic devices, to detect the position of the device or provide for the game system input. Pairs of accelerometers extended over a region of space can be used to detect differences in the proper accelerations of frames of references associated with those points. 4. 51 BMA180 Accelerometer Module [12] The Accelerometer Sensor chosen for this project was the BMA180 by Bosch (Figure 4. 8). The Bosch BMA180 three-axis, high performance digital accelerometer was chosen because of its superior variable characteristics. The BMA180 provides a digital 14-bit output signal via a 4-wire SPI or I2C interface. The full-scale measurement range can be set to A ±1g, 1. 5g, 2g, 3g, 4g, 8g or 16g. 26 The sensor also has two operating modes consisting of low-noise and low-power. The input power supply voltage should be between 1. 62 and 3. 6V for VDD and 1. 2 to 3. 6V for VDDIO. The sensor will typically only consume 650uA in standard mode. Figure 4. 7 BMA180 Accelerometer Block Diagram. As seen in Figure 4. 7 the BMA180 diagram shows: 1. The micromechanical g-sensors elements which measure acceleration in the x,y and z directions. . The front end circuit including pre amplifiers and multipelxers. 3. The 14 bit Analog to digital controller. 4. The Interrupt generator and output interface. Figure 4. 8 BMA180 Accelerometer Board. 27 4. 6 The Barometer Transducer Bosch BMP085 [9] A barometer is a scientific instrument used to measure atmospheric pressure (Figure 4. 9). We chose Bosch’s BMP085 Digital Bar ometric Pressure sensor for this project. The ultra-low power and low voltage electronics of the BMP085 are ideal for navigation devices. With a low altitude noise of merely 0. 5m at fast conversion time, the BMP085 offers superior performance for an application such as ours. It comes equipped with I2C capabilities for easy system integration with microcontrollers and offers a measuring range of 300 to 1100 hPa with an absolute accuracy of down to 0. 03 hPa. This sensor supports a voltage supply between 1. 8 and 3. 6VDC. Figure 4. 9 BMP085 Barometer Board. 4. 61 Barometric Pressure in Altimetry Barometric pressure has a measurable relationship with altitude, meaning you can use the BMP085 to deduce how high the quad copter has climbed. At sea level the air pressure is on average 1013hPa. The measuring limits of the BMP085 should allow us to measure pressure at elevations anywhere between -1640 to about 29,000 ft above sea level. 28 Figure 4. 10 BMP085 Barometer and Altitude Relationship. With the measured pressure p and the pressure at sea level p0, the altitude in meters can be calculated with the international barometric formula. p0 is the average pressure at sea level (1013hPa), and p is the pressure that we measured. This relationship is observed in Figure 4. 10. Note that this equation gives you altitude in units of meters. Altitude (meters) = 44330 [4. 2] 4. 7 The Brushless Motors Each of the four rotors comprises of a Brushless DC Motor attached to a propeller. The Brushless motor differs from the conventional Brushed DC Motors in their concept essentially in that the commutation of the input voltage applied to the armatures circuit is done electronically, whereas in the latter, by a mechanical brush. As any rotating mechanical device, it suffers wear during operation, and as a consequence it has a shorter nominal life time than the newer Brushless motors. In spite of the extra complexity in its electronic switching circuit, the brushless design offers several advantages over its counterpart, to name a few: higher torque/weight ratio, less operational noise, longer lifetime, less generation of electromagnetic interference and much more 29 power per volume. Virtually limited only by its inherent heat generation, whose transfer to the outer environment usually occurs by conduction. 4. 71 KDA20-22L Brushless Motors [10] The KDA Brushless motors were chosen for our copter because of their superior specifications (Table 4. ), weight, power output and availability (Figure 4. 11) . Additionally, this motor offered a wide variety of securing provisions which was extra helpful in its mounting and use. Table 4. 3 KDA 20-22L Brushless Motor Specifications. Kv (rpm/v) Weight Max Current Max Voltage Motor Length Motor Diameter Total Length 924 56 grams 17 Amps 11V 32mm 28mm 46mm Figure 4. 11 KDA 20-22L Brushless Motor. 30 Figure 4. 12 Quad Copter H ardware Block Diagram. Figure 4. 13 Quad Copter As Constructed. 31 4. Software Development General Concepts All of the electrical hardware components previously mentioned provide the necessary ground work for the software subsystems to allow the copter to function as desired, as depicted in block diagram Figure 4. 12. The software plays one of the most important roles controlling and facilitating the features of the device discussed in this paper. All of the inputs from the various sensors gyroscope, accelerometer and barometric sensor are to be taken and evaluated by the microcontroller to facilitate flight (Figure 4. 13). The goal of this project is to successfully achieve unmanned flight by simply hovering and landing. The quad copter must be able to take off from a stationary position to a hovering state and then land once again using the following organization illustrated in Figure 4. 14. Figure 4. 14 Software Architecture Organization. 4. 81 Operating Modes of Flight The quad copter has three main operating states known as, take off, hover and land. These states together form what is known as VTOL (Vertical Takeoff Landing) with characteristics shown in Figure 4. 5. 32 The Take Off stage involves several procedures, which include motor/ESC initializations, data acquisition of the attached sensors and any human input. If after evaluating this data the quad copter senses that it has not met the necessary criteria it will slowly ramp up the necessary motor thrust until it reaches the desired set point while the microcontroller is verifying the sensor data. When the actual altitude equals the desired position, the quad copter can now go to hovering mode. Hovering is the most challenging component of flying any copter. While in the hovering stage, the copter must take into account many factors that assist the craft in steady flight. Among the most common causes for a quad copter to not perform sufficiently is drifting in the horizontal plane. Movements in all four directions such as forward, back, right, and left, are consequences of drifting, accumulation of small errors in various values leading to uncontrollable oscillations which have to be accounted for. Landing is the final stage of flight, the landing process is the opposite of the take off phase. The system checks for x and y levels; if they are leveled, the altitude is checked. At this point, the acquired value is checked with the ground level. If the acquired values are not at ground level, thrust from all motors are decreased and decelerated until the ground level is reached, only then will the system halt activity. 33 Figure 4. 15 Quad Copter Operating Modes Of Flight. 4. 2 Position Flight Control Position control is currently implemented using a PID controller design which actuates the vehicle’s roll and pitch as control inputs. Tilting the vehicle in any direction causes a component of the thrust vector to point in that direction, so commanding pitch and roll is directly analogous to commanding accelerations in the X-Y plane. However, the current control implementation has little ability to reject 34 disturbances from wind and translational velocity effects. For this scale aircraft, even mild winds can cause large disturbances. A key weakness of this and similar position controllers used is the assumption that the velocity of the free stream and attitude control are decoupled. This is in fact only true for very small velocities. 4. 83 Kalman Filter Design[7] A Kalman filter is used to reduce the error in tracking. The Kalman filter operates by predicting the next value from the current value and the previous value. This is then corrected once the next measurement is taken to be between the measurement and the predicted value. This reduces the influence of noise on the measurement of the position. Over time errors in measurements tend to accumulate causing the sensors inefficiencies for long term measurements and thus they tend to drift. The ideal solution to the problem described above would be combining both, gyroscope and accelerometer data values resulting in the offset of the deficiencies of each with the strengths provided by the two sensors. Kalman filtering is an iterative approach that requires two varying input values. At every iteration, the Kalman filter will change the variables in the linear model, so the output of the model will be closer to the second input (Figure 4. 16). For the project, two inputs will consist of the gyroscope and accelerometer data, the model using the gyroscope data looks like: ) [4. 3] Since individual applications are favored and computed, equations for the filter in one dimension are required. Equations [4. 3] are reduced for the latter two dimensions. Where, K is the Kalman gain, P 35 s the estimation error covariance, measurement. is the filtered value, S is the sensor noise, and z is the The process noise p is reduced gradually, when tuning the filter for optimal performance. Concurrently, sensor noise S is increased until a satisfactory speed/noise level is achieved. Figure 4. 16 Kalman Filter Recursive Algorithm. 36 Chapter 5. Structural and Mechanical Approaches 5. 1 The Frame of the Quad Copter Typical quad-rotors utilize a four-spar method, with each spar anch ored to the central hub like the spokes on a wheel. The frame of the quad copter is composed of a combination of materials chosen for their strength, weight and flexibility. When designing an autonomous quad-rotor, there are several material options which must be considered. When designing a machine capable of flight, weight must be greatly well thought-out. The materials considered for our project aluminum, plastic, and carbon fiber. Historically, aluminum historically, has been the material of choice for RC helicopters. Aluminum is light and strong, dissipates heat well, and is relatively inexpensive compared to the other