Development of an optical landing aid system for light Unmanned Aerial Vehicles

Full text

(1)2008:192 CIV. MASTER'S THESIS. Development of an optical landing aid system for light Unmanned Aerial Vehicles. Per Berglund. Luleå University of Technology MSc Programmes in Engineering Space Engineering Department of Space Science, Kiruna. 2008:192 CIV - ISSN: 1402-1617 - ISRN: LTU-EX--08/192--SE.

(2) Development of an optical landing aid system for light Unmanned Aerial Vehicles Ref: Landing Aid System for UAV_20060623. Per Berglund Luleå University of Technology 2006-06-23. Master of Science Thesis conducted at Monash University, Clayton, Melbourne, Australia.

(3) ***This page is intentionally left blank***.

(4) Abstract Is it possible to build a small, cheap, easy implemented and reliable landing aid system for light UAVs? This question was raised by the UAV team at Monash University. The UAVs used by the team are based on remote controlled airplanes, reasonably small in dimensions and mass. The idea is to develop a system that will allow the planes to automatically guide themselves into a cargo net thereby eliminating the human factor in the landing sequence. The basic plan was to have a system that when switched on would turn the UAV into a “heat seeking” UAV locking on to a beacon placed behind the cargo net. The designed system is based on a 2.5KHz IR-beacon, a Hamamatsu S5991-01 2Doptical sensor and a 16F876 PIC that control two NES-537 servos. The optical sensor detects the light signal from the beacon. The output current from the sensor is transformed into four analogue voltage signals that are amplified in two steps, filtered and converted to digital signals that are interpreted by the processor that controls the servos accordingly. The goal for the final system is to detect a beacon from at least 200m away and using the servos to manoeuvre the rudders of the UAV to fly it towards the beacon. The main problems encountered during the development of the system were related to the signal processing segments. With the time constraint given the sensitivity requirement of this initial technology demonstrator was relaxed and the development of the signal processing segments was put to a hold in favour of the development of the other parts of the system. The result is a system that can detect a beacon and give an accurate response from 0.5m distance and manoeuvre the servos according to the movement of the beacon.. Per Berglund MSc. Student in Space Engineering Luleå University of Technology Berper-2@student.ltu.se. I.

(5) ***This page is intentionally left blank***. II.

(6) Sammanfattning UAV gruppen vid Monash Universitet i Melbourne, Australien ställde sig frågan om det skulle vara möjligt att bygga ett system som kunde få deras lätta UAVer att automatiskt landa på ett säkert och smidigt sätt? Systemet skulle vara relativt billigt och implementerbart i både gamla och nya UAVer. Dessutom skulle det gå att använda där utrymme är begräsat så som på båtar. Den här rapporten beskriver de första stegen tagna mot ett optiskt system för att leda UAVerna in i ett nät som fångar upp dem. Tiden allokerad för utvecklandet av teorin, designen och byggandet av systemet var 20 arbetsveckor. Systemet byggdes upp av en 2.5kHz IR-sändare, en Hamamatsu S5991-01 2D-Optisk sensor, en 16F876 PIC och två NES-537 servos. Systemet är tänkt att fungera enligt följande. IR-sändaren är placerad vid nätet och sensorn på UAVn. När UAVn detekterar sändaren väljer piloten att slå på det automatiska systemet och UAVn förvandlas till en målsökande robot som flyger rakt mot sändaren och nätet till dess att den fångas upp. Resultatet blev ett system som kan detektera och agera korrekt från 0.5m avstånd och manövrera servona i enlighet med förändringen i placering av sändaren i förhållande till sensorn. Målet var att ha ett system som kunde detektera sändaren från 200m avstånd. Största problemet i utvecklingen av systemet låg i signalbehandlingen. Stora förenklingar både i förstärknings- och filtreringssteget av systemet gjordes för att inom den givna tidsramen få fram ett system som kunde visa på att teorin bakom projektet fungerade. Återstående steg i utvecklingen är att förfina sändaren och signalbehandlingen i mottagarkretsen så att systemet får den önskade räckvidden samt att implementera servostyrningssystemet i UAVns styrsystem för att kontrollera dess roder.. Per Berglund Civilingenjörsstuderande, Rymdteknik Luleå Tekniska Universitet Berper-2@student.ltu.se. III.

(7) ***This page is intentionally left blank***. IV.

(8) Preface I would like to start by telling you what caught my eye with this project. I have working experience with search and rescue at sea and I couldn’t stop thinking about the potential a fleet of unmanned areal vehicles would have during a search and rescue mission. A UAV system with small planes covering a big area can search for people non-stop, when a distress light is detected the UAV simply transmits the coordinates for that position back to base. A rescue team can go directly to the site and more people can be picked up in shorter time in case of big disasters. It would be a system that could save a lot of lives. The possible future use of such system but that was what made me interested in building this Landing Aid system. On the draw board the system has a light beacon and an optical sensor in the UAV that will home in on the beacon. In my mind that beacon would in the future be mounted in with the visible light beacons on life vests used on airplanes and boats. The sensor on the UAV would not be used as a landing aid but as a search device pinpointing sites of the vests with the help of a GPS system in the UAV. The UAV team at Monash University wanted a simple system that could help them land their UAVs in various terrains. They had this idea with the beacon, the sensor and a cargo net to catch the UAV on for example a boat. This is the story of the challenges I met trying to build this system and what I learned along the way. I wish you a pleasant reading Per Berglund Noordwijk, The Netherlands, June 2006. V.

(9) ***This page is intentionally left blank***. VI.

(10) Table of Content Abstract ...................................................................................................................... I Sammanfattning ...................................................................................................... III Preface ...................................................................................................................... V Abbreviations............................................................................................................ 2 1. Introduction ....................................................................................................... 4 2. Task .................................................................................................................... 6 3. UAV Landing aid Systems ................................................................................ 8 3.1. RUAG Aerospace ......................................................................................... 8 3.2. University of Southern California .................................................................. 9 3.3. Advanced landing aid systems for UAVs.................................................... 10 4. Requirements .................................................................................................. 12 5. Design Justification ........................................................................................ 12 5.1. The Sensor................................................................................................. 12 5.1.1. Work specification suggestion ............................................................. 13 5.1.2. Alternative Solutions ........................................................................... 13 5.2. Operational Amplifier .................................................................................. 14 5.3. Analogue to Digital Converter .................................................................... 14 5.4. Processor ................................................................................................... 14 5.5. Beacon ....................................................................................................... 14 6. Technical Specification................................................................................... 16 6.1. Light Source ............................................................................................... 16 6.2. Optical Filter ............................................................................................... 16 6.3. Optical Sensor............................................................................................ 17 6.4. Signal processing ....................................................................................... 19 6.4.1. Signal Filter and Amplification ............................................................. 19 6.4.1.1. C.R. Filter ........................................................................................ 19 6.4.1.2. Amplification .................................................................................... 22 6.4.2. Peak Detector ..................................................................................... 23 6.5. A/D conversion and µ-controller ................................................................. 25 6.6. Servos ........................................................................................................ 26 6.7. Power Supply ............................................................................................. 27 6.8. Test Circuit ................................................................................................. 28 7. Results ............................................................................................................. 30 Light source ...................................................................................................... 30 7.1. Test Results ............................................................................................... 31 8. Future Development ........................................................................................ 34 9. Conclusion ....................................................................................................... 36 10. References ................................................................................................ 38 11. Appendices ............................................................................................... 40 11.1. Appendix 1 .............................................................................................. 40 11.1.1. Band Pass Filter .............................................................................. 40 11.1.1.1. High-pass section ........................................................................ 40 11.1.1.2. Low-pass section ......................................................................... 41 11.1.2. Component calculation .................................................................... 42 11.2. Appendix 2 .............................................................................................. 44 11.2.1. Code structure ................................................................................. 44 11.3. Appendix 3 .............................................................................................. 50 11.3.1. Theoretical signal amplification........................................................ 50. VII.

(11) ***This page is intentionally left blank***. 1.

(12) Abbreviations In order of appearance UAV – Unmanned Arial Vehicle IR – Infra Red GPS – Global Positioning System CCD – Charge Coupled Device PSD – Position Sensitive Device ADC / A/D – Analogue to Digital Converter 2-D – Two Dimensional. 2.


(14) 1. Introduction This paper considers the development and possibilities to use an optical system to autonomously lead a UAV to a safe landing even in hard to reach places. Many similar projects have been developed in the same area. Some use cameras on board the UAV and image processing to distinguish certain objects and ground patterns. The UAV use these as a map to guide its way to the landing sight. Others use lasers to track the UAV. Commands based on the data from the tracking are being radioed back to the UAV to land it safely. The same method is used in other systems but using comparison of GPS signals to determine the position of the UAV relative to the ground station instead of tracking it with a laser. The optical system developed in this thesis will need no commands to be sent to the UAV in order to guide it. No pre-programmed maps or even use of GPS signals. This makes the system very easy to set up and use anywhere by anybody and it could be used on any light UAV with just minor modifications.. 4.


(16) 2. Task To build a small, lightweight and easy to implement landing aid system for UAVs that will enable fully automatic landings and make a foundation for a system used to track other objects than just landing sites. A piloted guidance into the landing aid systems field of view is however allowed.. 6.


(18) 3. UAV Landing aid Systems There are several landing aid systems for UAVs on the market today and they all use a different approach to achieve the same goal, getting the UAV down safely. RUAG Aerospace has developed a system for landing Ultra light UAVs and so has people at the University of California. There are more sophisticated systems on the market as well but these are made for bigger and more advanced UAVs.. 3.1. RUAG Aerospace RUAG Aerospace has developed a system called OPATS [1] (Object Position And Tracing Sensor). OPATS, Figure 1, uses a ground-based laser to determine the position of the UAV during its descent. The only equipment that needs to be mounted on the UAV itself is an optical reflector somewhere on a leading edge on the UAV. This makes the system easy and cheap to use for several UAVs since one ground station can be used to guide all UAVs as long as they are fitted with the reflector. However the system can only guide one UAV at the time and the future extension of the system is limited to tracking and landing UAVs.. Figure 1: OPTAS landing aid system, curtsey RUAG Aerospace.. 8.

(19) 3.2. University of Southern California One approach is to use visual guidance to track the landing site. A system that does this was developed at the University of Southern California where the task was to land on a moving target with a UAV helicopter [2]. Assumptions were made that, the target shape is known and no distracting targets are present and that the target is allowed to move only in the x and y directions. It also has to be a high contrast between the target and the background in order to make the visual tracking system able to select the correct landing sight. This is a good approach if the vehicle can be navigated into the area from where it can locate the landing sight and then slowly take its time to land. But if the vehicle is not able to hover above the landing site it can be hard to make it locate the landing site from a longer distance. If the system is to operate in a rougher environment it can be hard for the visual detection system to select the landing site from other bright objects in the area.. 9.

(20) 3.3. Advanced landing aid systems for UAVs Sierra Nevada Corporation has a solution they have implemented in different landing aid systems for different areas of use but they are all using the same basic method. These systems are made for more sophisticated UAVs than the UAVs in question for this thesis. Table 1 shows three of the systems made by Sierra Nevada and how they basically work. It also shows one system from Roke Manor Research who has developed a system for the same application but with a different method.. Table 1: Systems by Sierra Nevada Corporation and Roke Manor Research. System Manufacturer UCARS, UAV Sierra Nevada Common Corporation Automatic Recovery System. Description Air based Transponder. Ground based tracking unit. Methode UAV sending out an identification and position signal that is received by the ground station. It compares the position to its own and guides the UAV during landing and takeoff.. UCARS-V2, UAV Sierra Nevada Common Corporation Automatic Recovery System – Version 2 For Shipboard Operations,. Designed for sustained operations in the shipboard environment. Has its own ship motion stabilization equipment and does not require GPS or position information from the ship.. Using the same method as UCARS.. TALS, Tactical Sierra Nevada Automatic Corporation Landing System. Roke Manor RAPiD, RealTime Attitude and Research Position Determination. UAV sending out an identification and position signal that is received by the ground station. It compares the position to its own and guides the UAV during landing and takeoff Low cost variant of Using the same the Common method as UCARS Automatic Recovery and UCARS-V2. System (UCARS). UAV sending out an Automatic recovery, identification and high mobility, two- position signal that is man transportability received by the and 15-minute set- ground station. It compares the position up time. to its own and guides the UAV during landing and takeoff. Air based visual UAV pre programmed detection system with landing sites and looking for obstacles in the area. predetermined The visual detection control points on system looks for the ground for pre-programmed sites and guides the UAV orientation and to the landing site. navigation.. 10.


(22) 4. Requirements 1. Make a small UAV fly automatically into a cargo net for recovery. 2. The UAV should be flown into the landing aid systems field of view by some other means, manually or by another automatic system. 3. The system should be usable in any type of open terrain.. 5. Design Justification To design a landing aid system for small UAVs that would be reliable, quick to develop and easy to implement on several UAVs a solution was to make a system that would turn the UAV into a sort of heat seeking missile when the system is turned on. The system will consist of a beacon, a sensor and a cargo net to catch the plane. This solution would fulfil all 3 requirements. See Figure 2. Figure 2: Landing aid system. The system is divided into two parts, the transmitter and the receiver. The main task in this project is to build the receiving end but a few words will be said about the transmitter as well. The receiving end needs to be able to pick out the wanted signal and that signal only so the UAV will not end up chasing the sun or any other strong light source. This can be done in several ways, for example by using optical shielding to block certain wavelengths and analogue electrical filters to block out unwanted frequencies. The wanted signal also has to be amplified before it is converted into a digital signal. The software in the on board computer will use the signals to determine the attitude changes it needs to do to keep the UAV on track. To speed up the process of the project to build the receiving end of the system a beacon is provided before hand and so are a couple of servos to simulate the control servos of a UAV.. 5.1. The Sensor. 12.

(23) A small study of different sensor types was made and here follows a discussion over the most interesting ones.. 5.1.1. Work specification suggestion Suggested in the work specification was the Hamamatsu S5991-01. A silicon PSD sensitive to IR-wavelengths built with pincushion technology. The measurements made near the sensor edges of a pincushion device are not linear and error will occur. Since the task of the sensor is to tell when it is pointing straight at a light source this however is not important in this application.. 5.1.2. Alternative Solutions •. One option is to use CCDs but it was soon found that they are unnecessary complicated for this application. At least at this first stage. If the system however is to be used to look for other things than a beacon it would be a better solution than a PSD and in that case the system can be altered to work with a CCD instead.. •. Other PSD constructions were looked into as well. A Tetralateral PSD could also be used with good enough accuracy for a cheaper price but since the Hamamatsu pincushion device was already in stock it was no need to go to this cheaper device for the first prototype of the system. If the system will be mass-produced and production costs are to be cut it would be more than enough to use the cheaper Tetralateral PSD type. The same argumentation leads to the conclusion that there is no use to have a more sensitive Dulateral type PSD that would increase the accuracy but also the costs.. •. Radio receiver. It would be possible to build the system around a radio transmitter/receiver system but that would lead to a problem in accuracy. In order to tell the UAV where the landing site is in relation to the plane a GPS unit on bord the UAV with an accuracy way higher than on commercial GPS units has to be used. This will increase the costs since GPS units with an higher accuracy of 15m is hard to come by and 15m is a way to large error if the UAV is to find its way into a net on a moving boat.. 13.

(24) 5.2. Operational Amplifier The choice of amplifiers will depend on the choice of optical sensor and recommended Op-Amps to use with the S5991-01 are LT1490 and the LT1490A. A similar device to these is the LM324N, an amplifier already available in stock at the department so out of convenience this is the devise that will be used in this application for both the filtering, amplifying and peak detection in the system.. 5.3. Analogue to Digital Converter The analogue signal has to be converted into a digital one before it can be processed. Since the S5991-01 has four outputs a four channel ADC is enough to do the job. The signal could be processed by an independent ADC before transmitted into the processor but in order to save money, space and weight a better solution is to have a processor on board with an internal ADC converter.. 5.4. Processor In order to minimize the amount of components used it was sensible to look at processors with internal A/D converters. Such a device is the 28-pin 16F876 PIC. It has four analogue input channels and the A/D conversion is implemented by software. It was available in stock at the department just as the Op-Amps were so there was no need to look further for another processor but any similar type would do. One more reason for choosing a PIC before any other processor was that people at the department were used to work with the PIC.. 5.5. Beacon Based on the choice of sensor the beacon will have a wavelength to mach the highest sensitivity of the sensor. Normally the S5991-01 is used with a laser. The laser is fixed and pointed to the sensor. In the scenario of using the light source as a beacon it might be hard to catch the laser in the sensors field of view if the beacon only sends out a small ray of light. Therefore the ray needs to be of a more conical type so the light source is visual from a wider range. Depending on the sensitivity of the sensor the light source must be chosen in a way that it is detectable from whatever range the user chooses. The S5991-01 is most sensitive to wavelengths around 960nm there are several lasers out on the market in this wavelength and any of them would do. Supplied at the start of the project was a small beacon circuit with a 940nm IR-diode with tuneable frequency to use instead of a laser. The S5991-01 is sensitive enough in this range as well so it is a perfect test beacon to start with. A 2.5kHz frequency was used in order to make sure the Op-amps in the signal-processing unit would keep up. However a more refined beacon would have to be built for a flying system to work.. 14.


(26) 6. Technical Specification The system will consist of seven blocks. See Figure 3. Figure 3: Block diagram.. 6.1. Light Source Throughout the project a supplied IR-beacon was used as light source with a wavelength of 940nm and a frequency of 2.5kHz.. 6.2. Optical Filter To shield out all unwanted signals the first step is to get rid of as much of the unwanted wavelengths as possible. This is done using an optical film that shields out visible light. The film is built into a small pinhole camera structure made out of 1mm cardboard and aluminium foil, Figure 4.. Figure 4: Pinhole camera with optical filter.. 16.

(27) 6.3. Optical Sensor The Hamamatsu S5991-01 is a 2-D optical position sensor with peak sensitivity at 960nm [4]. It has a four-channel current output. Each channel represents one of four directions from the centre of the sensor. See Figure 5.. Figure 5: Grid layout of the Hamamatsu S5991-01.. If the light source hits the origin the output on all four channels will be zero. The respective output current will increase linearly the further away in its direction from the origin the light hits. The Hamamatsu S5991-01 comes with a motherboard that provides the current to voltage conversion and the initial amplification of the raw signals from the sensor. See Figure 6. This board was used off the shelf but three changes were made to the components suggested.. 17.

(28) Figure 6: The Hamamatsu S5991-01 motherboard layout. Curtsey Circuit Cellar. The resistors R1, R2, R3 and R4 were changed from 2.4kΩ to 2.7kΩ and the LT1490 was replaced in favour for the LM324N. Both theses changes were based on what components were in stock at the department. For this application the C1, C2, C3 and C4 capacitors had no effect so they were left out from the board. The sensor is sensitive to light in the range from 320nm to 1100nm with a peak at 960nm. Tests were preformed on the board and it showed that the X and Y output signals from the motherboard did respond accordingly to light and gave out a voltage in the mV range.. 18.

(29) 6.4. Signal processing In the signal-processing block the signal will be amplified, filtered and peak detected.. 6.4.1. Signal Filter and Amplification In the final product a band pass filter has to be included. However since the final beacon frequency was never decided during the period this project was executed a band pass filter was never included in the test circuit. Tests were made on a series of different band pass filters for use in the final product and the one that gave the best result was a 6th order Butterworth band pass filter [5]. The development of the filter lead to too many problems so a decision was made to go on using just a simple C.R. high pass filter [6] for the test circuit and the indoor testing as it was sufficient enough. The theory on the band pass filter is included in Appendix 1 for future development.. 6.4.1.1.. C.R. Filter. This is the high pass filter that was used in the test circuit, Figure 7. It is not efficient enough to be used in a final product but it was enough for the indoor tests that were preformed to make sure the receiver circuit responded accordingly to a moving beacon. There was some trouble with the amplification of the signal so the filter was designed just to get rid of the DC and very low frequency noise and not to have any effect on the signal it self. See Table 2 and Figure 8.. Figure 7: C.R. Filter.. The cut off frequency of the filter corresponds to. f co =. 1 = 1,94 Hz 2πCR. (1). where C = 100nF and R = 820kΩ.. 19.

(30) Table 2: C.R. Filter characteristics. C = 100nF R = 820kohm fco = 1.94Hz f (Hz). Vo/Vi Re 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 1000 2000 3000 4000. |Vo/Vi| Im 0.21 0.52 0.71 0.81 0.87 0.91 0.93 0.94 0.96 0.96 0.99 1 1 1 1 1 1 1 1 1 1 1 1. 0.41 0.5 0.46 0.4 0.34 0.29 0.26 0.23 0.21 0.19 0.1 0.06 0.05 0.04 0.03 0.03 0.02 0.02 0.02 0 0 0 0. 0.460651712 0.721387552 0.845990544 0.903382532 0.934077085 0.955091619 0.965660396 0.967729301 0.982700361 0.978621479 0.995037688 1.001798383 1.00124922 1.00079968 1.000449899 1.000449899 1.00019998 1.00019998 1.00019998 1 1 1 1. Phase shift 1.097440285 0.765792833 0.574888601 0.458697154 0.372554258 0.308506296 0.27260982 0.239966174 0.2153577 0.195391555 0.100668652 0.059928155 0.049958396 0.039978687 0.029991005 0.029991005 0.019997334 0.019997334 0.019997334 0 0 0 0. DB -6,732546204 -2.836627121 -1.452689828 -0.882566221 -0.592345644 -0.399099321 -0.303511595 -0.284922183 -0.151577686 -0.187705126 -0.043209395 0.015606526 0.010843813 0.006943159 0.003906892 0.003906892 0.001736831 0.001736831 0.001736831 0 0 0 0. 20.

(31) In Table 2 the Vo = Vi. Vo ratio is calculated as Vi. 1. (2). = Re+ j Im f co 1− j f and the absolute value and phase shift as. Vo Im   = Re 2 + Im 2 ; Phase arctan . Vi Re  . (3). Finally the gain is given by. dB = 20 log. Vo . Vi. (4). 10 00 30 00. 90. 70. 50. 30. 10. 8. 6. 4. 2. 1 0 -1. 1,2. -2 -3 -4 -5 -6. 0,8. -7 -8. 1. dB. 0,6. Phase shift. 0,4. Phase shift. dB. f. Frequency. 0,2 0. Figure 8: C.R. Filter characteristics.. 21.

(32) 6.4.1.2.. Amplification. The signal from the sensor motherboard has to be further amplified. In the test circuit the amplification is made in two steps. The first amplification step in the test circuit is shown in Figure 9, which includes a high pass filter to cut off the low frequencies introduced by the DC signal generator simulating the incoming signal during the stand alone tests of the amplifier. In the final test circuit all filtration needed is provided by the C.R filter described in the previous section, therefore the 0.47uF capacitor in front of the amplification stage is omitted in the final design as shown in Figure 13.. Figure 9:Signal amplifying circuit.. The gain is regulated with a potentiometer depending on the distance between the beacon and the sensor according to. Rf Vo =− . Vi Ri. (5). Too high gain when the beacon is close will saturate the amplifier and too low gain when the beacon is far away will give no signal out at all. With Rf set to max the gain is 50 and that made it possible to detect the incoming signal at Vo with the beacon at 0.7m distance from the receiver. This makes it clear that a much more sufficient amplification is needed for a final working system since the signal has to be detectable from at least 200m away. But this amplification at least made it possible to show that the theory behind the system works. The second amplification step will be explained in the Test Circuit section.. 22.

(33) 6.4.2. Peak Detector The signals peak value is the only thing relevant at this stage of testing so an ordinary peak detector with a pull down resistor, see Figure 10, is used to prepare the four signals for the A/D conversion.. Figure 10: Peak Detector.. The Peak detector work in such a way that the capacitor charges via the diode to the peak value of Vi. The feedback removes the volt drop across the diode and the use of an input buffer also prevents the source of Vi from being loaded when the capacitor charges. The pull down resistor helps to pull the output down when the signal goes down. That will lead to some ripple on the signal. The ripple is calculated as follows. Vc I = s C. (6). where. Vc = Vi → Vmax = 5V , which gives I max =. Vmax Ω. (7). and at. Ω = 100k → I max = 50µA . Putting these values in (6) gives the equilibrium rate. I 50 µ = = 25V / s . 2µ C. (8). At. 23.

(34) f = 2,5kHz → s =. 1 = 0,0004s 2,5k. (9). the max ripple becomes VMaxRipple = 25 ×. 0,0004 = 5mV . 2. (10). The equilibrium rate of 25V/s means that it will take the Peak detector 500ms to equilibrate from 5V down to 0V when the signal disappears. That rate is quick enough and the ripple of 5mV on a 5V signal is acceptable for this application.. 24.

(35) 6.5. A/D conversion and µ-controller The PIC 16F876 is a 28-pin device that features both sufficient analogue input channels and digital output channels for the application, see Figure 11. It was programmed using the WIZ C environment available at the department. For detailed information see data sheet on the 16F876.. Figure 11: PIC 16F876.. The software for this first stage test circuit was designed to do the following.. • • • •. Read in the four analogue signals from the signal processing stage. Convert the analogue signals to digital signals. Translate the digital signals into pulse widths for the servos. Put out two Pulse width modulated signals one for each servo.. The software was also prepared for a future development of the circuit but more will be said about that in the future development section. See Appendix 2 for the code.. 25.

(36) 6.6. Servos Two NES-537 servos were used to test the system, one to control the X signals and one to control the Y signals. These servos will at a later stage in the development of this system be used to control the UAV rudders.. Data on NES-537: Power Supply: 5V, 900mA Pulse width modulated: frequency 20ms, pulse width 1.0ms to 2,0ms. Since the servos require such a high current they need a separate 5V power line from the power supply unit. A pulse of 1.0ms will result in full left turn and 2,0ms result in full right turn. A 1.5ms pulse centres the servo.. 26.

(37) 6.7. Power Supply No final power supply was designed since the system never left the test board. During the tests the power supply was a 12V line from a power cube regulated down to a ±5V for the sensor motherboard by the use of LM7805 and LM7905, One ±8V using LM7810 and LM7910 for the signal-processing block and a single +5V to supply the servos using a LM78S05. See Figure 12.. Figure 12:Power Regulators.. 27.

(38) 6.8. Test Circuit Whilst putting all the stages together minor modifications had to be made. A second amplification step was put into the Peak Detecting stage. Here, also like in the first amplification stage, in the form of a feed back potentiometer so the gain could be altered as the distance between beacon and sensor was changed. The final test circuit can be seen in Figure 13. It is capable of detecting the beacon from a distance of 0.7m and it accurately manoeuvres the servos when the beacon is at 0.5m distance or closer.. Figure 13: Test Circuit lay out. 28.


(40) 7. Results A fully working system to implement in UAVs was not achieved; therefore none of the three requirements were met at the end of the scheduled project timeline. However the experiences from this project and the results obtained can help in the future development of the system. Light source The supplied 940nm IR-diode light source worked well. At the beginning the beacon was set to a frequency of 5kHz but the operational amplifiers could not keep up so the frequency was changed to 2.5kHz. Lens optical filtering A lens was never implemented instead a pinhole camera was used, a solution that proved to work well throughout the project. For the final product a lens should be considered with features suited for the application. Signal processing The signal-processing unit was redesigned several times. At the end major cut backs were made due to time limitations leaving it with only the most essential bits to be able to continue the work. It ended up having one amplifying stage, a high pass filter and a peak detector with a built in amplification, a system that made it possible to detect a signal from 0.7m away and send it on to the A/D conversion. This amplification however is not enough for a final product. So like with the filtering the amplification has to be modified and strengthened to get a properly working system in the end. A/D and PIC The programming of the 16F876 with its internal A/D converter proved successful. Some of the code written regarding the amplifying stage was neglected in the final executive programme but it is easily implemented again if the work on an amplification stage with digital potentiometers continues. The executive programme used read in the values on the analogue inputs, converted the signals to digital values and transformed those values to pulses for the control of the servos. Servos Both NES-537:s were used off the shelf with no modification made to them and they worked fine. Power The 78XX and 79XX series was well suited to supply the power needed by the circuits. The use of the NES-537 servos did however introduce a small problem in the power supply circuit since they drew 900mA each but with an extra 78S05 that problem was solved and the servos got their own power line.. 30.

(41) 7.1. Test Results Table 3 shows the circuit response during final test of the full circuit. Unfortunately data that would have been useful for final evaluation was never collected, data such as measured photo current, signal levels after first and second amplification stage and exact gain levels of the two amplification stages. With the aid of the summary of the calculated values in Table 4 it is possible to extract a conclusion based on theoretical behaviour verses visually observed test results that the circuit do respond as predicted on incoming light from the selected source. To obtain a response from the required 200m distance the amplification must be much higher, the filtering more precise and the light better focused. The full list of calculated values is given in Appendix 3, Table 5. Table 3: Measured Data of the test circuit’s behaviour Distance from Result Comments sensor to beacon (cm) 100 No reaction from the servos The beacon is too far from the sensor to provide the required minimum photo current needed for the system to amplify it to a 05v range. 70 Servos show reactions but do The beacon is in the range where not rotate to their full extent. it gives an input photocurrent that can almost be amplified to supply the full 0-5V signal to the processor. 60 Same as at 70 cm. The beacon is in the range where it gives an input photocurrent that can almost be amplified to supply the full 0-5V signal to the processor. 50 Servos react quick and precise The peak detector is on the boarder of saturating when set at full gain. 40 Servos react quick and precise Peak Detector gain tuned down to avoid saturation 30 Servos react quick and precise Peak Detector gain set to -1 for this and coming measurements 20 Servos react quick and precise Amplifier gain gradually turned down as the distance decreases from 30 to 10 cm. 15 Servos react quick and precise 10 Servos react quick and precise 5 System Saturates System saturates even when no gain is applied in the circuit, an indication that the PSD is saturated. 1 System Saturates. 31.

(42) Table 4: Summary of theoretical circuit behaviour Input to Peak Peak MAX Photo signal Amplifier Detector detector (V) Gain current (A) X,Y (V) Gain. Peak Input to A/D converter (V) Comments The A/D converter needs an input of 0-5V for the servos to give an accurate response.. 3.3333E-06 3.7037E-06 7.40741E-06 3.7037E-05 4.62963E-05 6.14815E-05 9.25926E-05 0.000185185 0.00037037. 0.00050037. 0.009 0.01 0.02 0.1 0.125 0.166 0.25 0.5 1. 1.351. -50 -50 -50 -50 -40 -30.1205 -20 -10 -5. -3.70096. -0.45 -0.5 -1 -5 -5 -5 -5 -5 -5. -5. -11 -10 -5 -1 -1 -1 -1 -1 -1. -1. 4.95 5 5 5 5 5 5 5 5. 5. The PSD saturates at 500uA. In Table 4 the values for peak input to the A/D converter are and the photocurrent are derived from the different gain options and the inverse of the current to voltage conversion made on the Hamamatsu S5991-01 mother board based on the assumption that the max signal X,Y ranges from 0.001V to 1.357V.. 32.


(44) 8. Future Development • •. Find a way to amplify the signal in a way so that the beacon can be detected from longer distances. Filter the signal in such a way that it can be used even if there are disturbing signals in the area where the system is used.. Future development already taken into account is the use of digital potentiometers on the amplifying stage. Crude tests were made on such devices and the software is prepared for them. The system would have a differential gain on the amplification of the signal depending on the distance between the UAV and the beacon. The system would strive after always having as high input signal to the processor A/D stage as possible but not to high. When no signal is detected the gain would be at a maximum and as soon as a signal is detected the gain would tune in to suit the signal strength. This system would make it possible to also determine the distance to the UAV from the landing site as well as increase the distance from where the UAV is detectable. One future feature could be to alter the system so that information can be carried on the beacon signal as well. Each UAV could be programmed only to lock on to the beacon when the signal has a certain modulation. This way many circling UAVs could land on the same beacon on for example a boat without risking two planes coming in for landing at the same time. One other safety feature with this system would be to have a hold flight plan programmed into the UAV in case it would lose visual contact with the bacon. Something that could happen if the terrain is rough and the plane detects the beacon from a high altitude but when it gets closer to the ground looses the signal behind a tree, a house or any other obstacle. It would then return to a pre set path and try again. When the system is fully developed it could be used for more than just landing aid. Different sensors could be placed on the UAV each looking in its own direction for its own thing. Like for a search and rescue mission. Each UAV would have one sensor for landing and one looking straight down for life vests equipped with beacons that the UAV would detect, register and send back the position of. The landing sensor would be placed in the nose end of the UAV for detecting the base ship and land on it when it is time for refuelling.. 34.


(46) 9. Conclusion At hand is a system that can detect a beacon and aim towards it as it changes position. This circuit proves that a system like this can be built using relatively inexpensive components and with some future tuning of the system it could be usable as a landing aid for small UAVs. This project has also shown that it takes long time to develop a fully working system. The biggest lesson learnt was that projects like this need to have clear guidelines and requirements from the start. In the absence of guidelines the timeline was laid out to optimistically. Hence at the end of the project the conclusion is that there were many things that could have been made in a more sufficient way from the start. Smaller goals should have been put up along the way with clear requirements. Work hours should have been allocated in order to reach each goal. Such a set up would have made it possible to reach further in the time given by evaluating each goal reached and changing the main goal of the project according to these evaluations. The lack of such a set up lead to that several cut backs were made just to get a system that would work in some way at the end. The way it has been done now means that even though the system built shows that this type of optical guidance is possible, all parts in the system needs more work to turn it into the final product. All this makes it harder for someone else to pick up the work and continue the construction of the system compared to if sub system requirements had been put up and met during this first phase of designing the landing aid system.. 36.


(48) 10.. References. [1] RUAG Aerospace, “OPATS – The Automatic Landing System for UAVs”. [2] Srikanth Saripalli and Gaurav S. Sukhatme, “Landing on a Moving Target using an Autonomous Helicopter”, Robotic Embedded Systems Laboratory Center for Robotics and Embedded Systems University of Southern California Los Angeles, California, USA. [3] Circuit Cellar, Issue 152 March 2003. 2-D Optical Position Sensor by Roger Johnson & Chris Lentz. [4] Hamamatsu s5990-01 data sheet. http://sales.hamamatsu.com/assets/pdf/parts_S/S5990-01_S5991-01.pdf [5] Analogue Electronics, Version 4.0 October 2000. By D. M. Weighton. [6] Basic Electric Circuitry, Version 2.0 March 97. By D. M. Weighton.. 38.


(50) 11.. Appendices. 11.1. Appendix 1 11.1.1.. Band Pass Filter. Butterworth band pass filters is a widely used filter type. A Butterworth Band-pass filter can be built in different orders. The higher the order of the filter, the more precise it is, i.e. the higher order, the steeper the slopes around the two cut-off frequencies are. See Figure 14. However, high order filters have a high sensibility when it comes to external distortion. Weighing these pros and cons against each other will determine the order of the filter.. Figure 14: As an example. The amplitude response of each stage, creating a 6th order Butterworth Band-pass filter.. 11.1.1.1.. High-pass section. Figure 15: Circuit diagram of one High-pass section of a Butterworth Band-pass filter.. To calculate the components and the gain, K, in the high pass circuit it is convenient to select values of the resistors, R1 and R2, and of the capacitors, C1 and C2 in Figure 15. The response can be written as. Vo s 2C 2 R 2 K = . Vi 1 + sCR[3 − K ] + s 2 C 2 R 2. (11). Let R = R1 = R2 =1Ω. 40.

(51) C = C1a = C2a = 1F Then. Vo s2K = Vi 1 + s1 *1[3 − K ] + s 2 1 *1. ⇒. Vo s2K = . Vi 1 + s[3 − K ] + s 2. (12). Again lets use a 6th order filter as an example. Then the Normalised Butterworth Filter Polynomial of order 6 is as given in equation ( s 2 + 0,518s + 1 )( s 2 + 1,414s + 1 )( s 2 + 1,932s + 1 ),. (13). where the bottom line of equation (12) answers to each parentheses in equation (13), like follows: 1st stage. 2. nd. stage. 3ed stage. K=. s 2 + 0,518s + 1 s 2 + [3 − K ]s + 1. } 3-K = 0.518 } 3-K = 1.414. (15). } 3-K = 1.932. (16). s 2 + 1,414s + 1 s 2 + [3 − K ]s + 1 s 2 + 1,932 s + 1 s 2 + [3 − K ]s + 1. (14). R3 + R4 ⇒ R4. (17). R3 = (K − 1)R4. 11.1.1.2.. Low-pass section. Figure 16: Circuit diagram of one Low-pass section of a Butterworth Band-pass filter.. To calculate the components and the gain, K, in the low pass circuit it is also here, like for the High-pass, convenient to select values of the resistors, R1 and R2, and of the capacitors, C1b and C2b in Figure 16. 41.

(52) The response can be written as. Vo K = Vi 1 + s[C 2 R1 + C 2 R2 + (1 − K )C1 R1 ] + s 2. (18). Let R = R1 = R2 =1Ω C = C1b = C2b = 1F Then. Vo V K K = ⇒ o = 2 Vi 1 + s[1 + 1 + 1 − K ] + s Vi 1 + s[3 − K ] + s 2. (19). where the bottom line of equation (19) answers to each parentheses in equation (13). This gives the same equations as for the High-pass section: st. 1 stage. 2nd stage. 3. ed. stage. K=. s 2 + 0,518s + 1 s 2 + [3 − K ]s + 1. } 3-K = 0.518 } 3-K = 1.414. (15). } 3-K = 1.932. (16). s 2 + 1,414s + 1 s 2 + [3 − K ]s + 1 s 2 + 1,932 s + 1 s 2 + [3 − K ]s + 1. (14). R3 + R4 ⇒ R4. (17). R3 = (K − 1)R4. 11.1.2.. Component calculation. One way to calculate the components in a Band-pass filter is to backtrack from two given cut-off frequencies. When a final beacon frequency is determined this method can be used to select the values of the components in the circuit. Low frequency cut-off: fcoL High frequency cut-off: fcoH Calculating the two cut-off angular frequencies.. ωcoL= 2πf. ⇒ ωcoL rad/sec. ωcoH= 2πf. ⇒ ωcoH rad/sec. 42.

(53) Calculating the values of R1, R2, R3, R4 and C1a, C2a, C1b, C2b in the circuit: C is impedance and frequency responding: Xc =. 1 ω *C. ⇒C=. 1 ω * Xc. (20). R is impedance responding but not frequency responding ⇒ R1 = Z Then the K values for each stage are taken from formula (14), (15) and (16). Then let R1 = R2= R4 = Z By using formula (13) the value of the resistors R3 is calculated. Let CcoL= C1a= C2a and CcoH = C1b= C2b For higher order Butterworth filters the R3:s are calculated for each stage until all component values are known. After choosing practical component values based on the calculated once, the theoretical cut off frequencies for the Band-pass filter is f =. 1 2πRC. (21). (R = R1= R2 = R4 = Z, C = C1a= C2a) => fcoL (R = R1= R2 = R4 = Z, C = C1b= C2b) => fcoH. 43.

(54) 11.2. Appendix 2 11.2.1.. Code structure. #include "C:\\Documents and Settings\\Per\\Mina dokument\\Examensarbete\\Wizc\\Program\\F rsta f rs ket\\Servostyrare_Auto.h" #include <delays.h> #define #define #define #define #define #define #define #define. HIGH 1013 LOW 102 HOLD 0 UP 1 DOWN 2 PotMax 0xFF PotMin 0x00 PotStep 0x01. BYTE Val_servo = 1; unsigned char PulseX; unsigned char PulseY; unsigned char Gain; unsigned char PotRev; long x1, x2, y1, y2; //long test1, test2; long x, y; int res, i; // // This file includes all user definable routines. It may be changed at will as // it will not be regenerated once the application has been generated for the // first time. // //******************************************************************************* // // Insert your interrupt handling code if required here. // Note quick interrupts are used so code must be simple // See the manual for details of quick interrupts. // void UserInterrupt() { TMR1H = 0; TMR1L = 0; // Clear Timer 1 INTCON = 0; // Disable GIE interupt and PEIE interrupt, set INTCON reg =00000000 PIE1 = 0; // Disable CCP1IE interrupt, set PIE1reg = 00000000 if (Val_servo == 1) { ServoX=1; TMR0=0; do{ LED = !LED; }while(TMR0 < int(PulseX)); ServoX=0; Val_servo = 0; }. //Delay, 1ms = 39; 2ms = 78. 44.

(55) else if (Val_servo == 0) { ServoY=1; TMR0=0; do{}while(TMR0 < PulseY); ServoY=0; Val_servo = 1; }. //Delay, 1ms = 39; 2ms = 78. PIR1 = 0; //Clear all interrupt flags, set PIR1 reg = 00000000 PIE1 = 4; // Enable CCP1IE interrupt, set PIE1reg = 00000100 INTCON = 192; // Enable GIE interupt and PEIE interrupt, set INTCON reg =11000000. #asmline SETPCLATH UserIntReturn,-1 #asmline goto UserIntReturn. ; SETPCLATH for interrupt routine ; Assembler - go back to interrupt routine. } //******************************************************************************* // // Insert your initialisation code if required here. // Note that when this routine is called Interrupts will not be enabled - the // Application Designer will enable them before the main loop // void UserInitialise() { PIR1 = 0; //Clear all interrupt flags, set PIR1 reg = 00000000 TMR1H = 0; TMR1L = 0; // Clear Timer1 PIE1 = 4; // Enable CCP1IE interrupt, set PIE1reg = 00000100 INTCON = 192; // Enable GIE interupt and PEIE interrupt, set INTCON reg =11000000 CCP1CON = 10; // Compare mode, generate software interrupt on match T1CON = 48; // Prescaler 1:8, osc disabled, [ignore], internal clock, TMR1 off CCPR1H = 24; CCPR1L = 105; // CCPR1 = 12500, i.e. period is 10ms - 12498 T1CON = 49; // Prescaler 1:8, osc disabled, [ignore], internal clock, TMR1 on OPTION_REG=4+2; // TMR0 counts rising edge, prescaler 1:128 TRISA=TRISA | (2+4+8+32); //Seting AN1, AN2, AN3, AN4 as input LED = 1; PulseX = 39; //Tidsvariabel motsvarande 1.5ms PulseY = 39; //Tidsvariabel motsvarande 1.5ms // // }. PotRev=0xFF Set_Pot(PotRev);. //******************************************************************************* // // PaInsert your main loop code if required here. This routine will be called // as part of the main loop code // //void Blink() //{ // LED=0; // TMR0=0;. 45.

(56) // // // // // // // //}. do{}while(TMR0 < 200); //Delay, 1ms = 39; 2ms = 78 LED=1; TMR0=0; do{}while(TMR0 < 39); //Delay, 1ms = 39; 2ms = 78 LED=0; TMR0=0; Wait(200);. int Read_Channel(BYTE ch) { ADCON1=128;. //Right Justified. 6 most significant bits of ADRESH //are read as ‘0’. ADCON0=128+(ch<<3)+1; //bit 7-6: ADCS1:ADCS0: A/D Conversion Clock //Select bits 10 = FOSC/32 =>20Mhz clock 1,6us, //bit 5-3: CHS2:CHS0: Analog Channel Select bits //shift AN channel, bit 0: ADON: A/D On bit 1 = A/D //converter module is operating. for(i=40; i>0; i--) { }. //Wait for the settings to set. ADCON0=ADCON0 | 4; do{}while ((ADCON0 & 4) == 4);. // bit 2 set 1 AD conv. starts //Converts as long as bit 2 is set 1. res=ADRESH; res=(res<<8)+ADRESL; return res;. //reads the two MSB //Reads the last 8 of the 10 bit value //Return the result. } //void Set_Pot(unsigned char Pot_Value); //{ // unsigned int OutData, i; // unsigned char StackSelect=0; // //. Pot_CLK=0; wait(1);. // // // //. Pot_RST=1; //Enable transmission Pot_DQ=StackSelect; Pot_CLK=1; wait(1);. //. OutData=Pot_Value|(Pot_Value<<8); //16bits-Pot_Value 2 times. // // // //. For(i=0;i<17;i++) { Pot_CLK=0; wait(1);. // // //. Pot_DQ=1 & OutData; //Mask out all but bit 0 and output on Pot_DQ Pot_CLK=1; wait(1);. //. OutData = OutData >> 1;. 46.

(57) // // //}. } Pot_RST = 0;. //void Trimpot(unsigned char ch); //{ // // // // //. if(ch == UP) { Set_Pot(PotMax); PotRev=PotMax; }. // // // // //. else if ((ch == LOW) & (PotRev > PotMin)) { Set_Pot(PotRev-PotStep); PotRev=PotRev-Potstep; } //else ;. //}. //void ServoX1(x); //{ //unsigned int i; // //. For(i=x;i>0;i++) {. //. }. //}. //void ServoX2() //{ // ServoX=0; // Wait(18); // ServoX=1; // Wait(2); //} //void ServoY1(); //{ //} //void ServoY2(); //{ //}. 47.

(58) void UserLoop() { // LED = !LED; x1=Read_Channel(1); x2=Read_Channel(2); y1=Read_Channel(3); y2=Read_Channel(4); //Test för att styra servon med en potensiometer //test1=((62*x1)/900)+19; //Scale AD convertion value 0-1023 to timer delay value 19-90 //test2=((62*x2)/900)+19; //by transfoming ((71/1023)*AD)+19, which is not int, // to ((((71*900)/1023)*AD)/900)+19 = ((62*AD)/900)+19. //PulseX = test1; //Delay, 0.592ms = 19; 1.484ms = 55; 2.400ms = 90 //PulseY = test2; //Delay, 0.592ms = 19; 1.484ms = 55; 2.400ms = 90 //Så långt fungerar allt. // //. if((x1 | x2 | y1 | y2) > HIGH) Trimpot(DOWN); else if ((x1 & x2 & y1 & y2) < LOW) Trimpot(UP); //else Trimpot(HOLD); if ((x1+x2+y1+y2)==0) { x = 0; y = 0; } else { INTCON = 0; x=(((x2+y1)*1000-(x1+y2)*1000)/(x1+x2+y1+y2))*(5); y=(((x2+y2)*1000-(x1+y1)*1000)/(x1+x2+y1+y2))*(5); INTCON = 192; } //test1 = ((x+5000)/303); //test2 = ((y+5000)/303); INTCON = 0; PulseX=((7*x)/1000)+54); PulseY=((7*y)/1000)+54);. INTCON = 192; // // // //. if(x>0) if(x<0) if(y>0) if(y<0). //Scale x and y value -5000-+5000 to timer delay value 19-90 //by transfoming ((71/10000)*(x+5000))+19, //which is not int, to ((((71*900)/10000)*(x+5000))/900)+19 //= ((6*(x+5000))/900)+19. //Delay, 0.592ms = 19; 1.484ms = 55; 2.400ms = 90 //Delay, 0.592ms = 19; 1.484ms = 55; 2.400ms = 90. ServoX1(x); ServoX2(x); ServoY1(y); ServoY2(y);. } // // User occurrence code //. 48.


(60) 11.3. Appendix 3 11.3.1.. Theoretical signal amplification. Table 5 display the full list of the theoretical signal amplification. Table 5 Calculated signal amplification Italic indicates span where the system does not respond properly, Italic + bold indicates the reason Beacon's Photo MAX Amplifier Input to Peak detector Peak Input Commernts distance current (A) signal Gain Peak Gain to A/D from X,Y (V) Detector converter sensor (V) (V) Far. 3.7037E-07 7.4074E-07 1.1111E-06 1.4815E-06 1.8519E-06 2.2222E-06 2.5926E-06 2.963E-06 3.3333E-06 3.7037E-06 4.07407E-06 4.44444E-06 4.81481E-06 5.18519E-06 5.55556E-06 5.92593E-06 6.2963E-06 6.66667E-06 7.03704E-06 7.40741E-06 7.77778E-06 8.14815E-06 8.51852E-06 8.88889E-06 9.25926E-06 9.62963E-06 0.00001 1.03704E-05 1.07407E-05 1.11111E-05 1.14815E-05 1.18519E-05 1.22222E-05 1.25926E-05 1.2963E-05 1.33333E-05 1.37037E-05 1.40741E-05. 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015 0.016 0.017 0.018 0.019 0.02 0.021 0.022 0.023 0.024 0.025 0.026 0.027 0.028 0.029 0.03 0.031 0.032 0.033 0.034 0.035 0.036 0.037 0.038. -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50. -0.05 -0.1 -0.15 -0.2 -0.25 -0.3 -0.35 -0.4 -0.45 -0.5 -0.55 -0.6 -0.65 -0.7 -0.75 -0.8 -0.85 -0.9 -0.95 -1 -1.05 -1.1 -1.15 -1.2 -1.25 -1.3 -1.35 -1.4 -1.45 -1.5 -1.55 -1.6 -1.65 -1.7 -1.75 -1.8 -1.85 -1.9. -11 -11 -11 -11 -11 -11 -11 -11 -11 -10 -9.090909091 -8.333333333 -7.692307692 -7.142857143 -6.666666667 -6.25 -5.882352941 -5.555555556 -5.263157895 -5 -4.761904762 -4.545454545 -4.347826087 -4.166666667 -4 -3.846153846 -3.703703704 -3.571428571 -3.448275862 -3.333333333 -3.225806452 -3.125 -3.03030303 -2.941176471 -2.857142857 -2.777777778 -2.702702703 -2.631578947. 0.55 The A/D 1.1 converter need an 1.65 input of 0-5V 2.2 for the 2.75 servos to 3.3 give an 3.85 accurate 4.4 response. 4.95 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 50.

(61) 1.44444E-05 1.48148E-05 1.51852E-05 1.55556E-05 1.59259E-05 1.62963E-05 1.66667E-05 1.7037E-05 1.74074E-05 1.77778E-05 1.81481E-05 1.85185E-05 1.88889E-05 1.92593E-05 1.96296E-05 0.00002 2.03704E-05 2.07407E-05 2.11111E-05 2.14815E-05 2.18519E-05 2.22222E-05 2.25926E-05 2.2963E-05 2.33333E-05 2.37037E-05 2.40741E-05 2.44444E-05 2.48148E-05 2.51852E-05 2.55556E-05 2.59259E-05 2.62963E-05 2.66667E-05 2.7037E-05 2.74074E-05 2.77778E-05 2.81481E-05 2.85185E-05 2.88889E-05 2.92593E-05 2.96296E-05 0.00003 3.03704E-05 3.07407E-05 3.11111E-05 3.14815E-05 3.18519E-05 3.22222E-05 3.25926E-05 3.2963E-05 3.33333E-05 3.37037E-05. 0.039 0.04 0.041 0.042 0.043 0.044 0.045 0.046 0.047 0.048 0.049 0.05 0.051 0.052 0.053 0.054 0.055 0.056 0.057 0.058 0.059 0.06 0.061 0.062 0.063 0.064 0.065 0.066 0.067 0.068 0.069 0.07 0.071 0.072 0.073 0.074 0.075 0.076 0.077 0.078 0.079 0.08 0.081 0.082 0.083 0.084 0.085 0.086 0.087 0.088 0.089 0.09 0.091. -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50. -1.95 -2 -2.05 -2.1 -2.15 -2.2 -2.25 -2.3 -2.35 -2.4 -2.45 -2.5 -2.55 -2.6 -2.65 -2.7 -2.75 -2.8 -2.85 -2.9 -2.95 -3 -3.05 -3.1 -3.15 -3.2 -3.25 -3.3 -3.35 -3.4 -3.45 -3.5 -3.55 -3.6 -3.65 -3.7 -3.75 -3.8 -3.85 -3.9 -3.95 -4 -4.05 -4.1 -4.15 -4.2 -4.25 -4.3 -4.35 -4.4 -4.45 -4.5 -4.55. -2.564102564 -2.5 -2.43902439 -2.380952381 -2.325581395 -2.272727273 -2.222222222 -2.173913043 -2.127659574 -2.083333333 -2.040816327 -2 -1.960784314 -1.923076923 -1.886792453 -1.851851852 -1.818181818 -1.785714286 -1.754385965 -1.724137931 -1.694915254 -1.666666667 -1.639344262 -1.612903226 -1.587301587 -1.5625 -1.538461538 -1.515151515 -1.492537313 -1.470588235 -1.449275362 -1.428571429 -1.408450704 -1.388888889 -1.369863014 -1.351351351 -1.333333333 -1.315789474 -1.298701299 -1.282051282 -1.265822785 -1.25 -1.234567901 -1.219512195 -1.204819277 -1.19047619 -1.176470588 -1.162790698 -1.149425287 -1.136363636 -1.123595506 -1.111111111 -1.098901099. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 51.

(62) 3.40741E-05 3.44444E-05 3.48148E-05 3.51852E-05 3.55556E-05 3.59259E-05 3.62963E-05 3.66667E-05 3.7037E-05 3.74074E-05 3.77778E-05 3.81481E-05 3.85185E-05 3.88889E-05 3.92593E-05 3.96296E-05 0.00004 4.03704E-05 4.07407E-05 4.11111E-05 4.14815E-05 4.18519E-05 4.22222E-05 4.25926E-05 4.2963E-05 4.33333E-05 4.37037E-05 4.40741E-05 4.44444E-05 4.48148E-05 4.51852E-05 4.55556E-05 4.59259E-05 4.62963E-05 4.66667E-05 4.7037E-05 4.74074E-05 4.77778E-05 4.81481E-05 4.85185E-05 4.88889E-05 4.92593E-05 4.96296E-05 0.00005 5.03704E-05 5.07407E-05 5.11111E-05 5.14815E-05 5.18519E-05 5.22222E-05 5.25926E-05 5.2963E-05 5.33333E-05. 0.092 0.093 0.094 0.095 0.096 0.097 0.098 0.099 0.1 0.101 0.102 0.103 0.104 0.105 0.106 0.107 0.108 0.109 0.11 0.111 0.112 0.113 0.114 0.115 0.116 0.117 0.118 0.119 0.12 0.121 0.122 0.123 0.124 0.125 0.126 0.127 0.128 0.129 0.13 0.131 0.132 0.133 0.134 0.135 0.136 0.137 0.138 0.139 0.14 0.141 0.142 0.143 0.144. -50 -50 -50 -50 -50 -50 -50 -50 -50 -49.505 -49.0196 -48.5437 -48.0769 -47.619 -47.1698 -46.729 -46.2963 -45.8716 -45.4545 -45.045 -44.6429 -44.2478 -43.8596 -43.4783 -43.1034 -42.735 -42.3729 -42.0168 -41.6667 -41.3223 -40.9836 -40.6504 -40.3226 -40 -39.6825 -39.3701 -39.0625 -38.7597 -38.4615 -38.1679 -37.8788 -37.594 -37.3134 -37.037 -36.7647 -36.4964 -36.2319 -35.9712 -35.7143 -35.461 -35.2113 -34.965 -34.7222. -4.6 -4.65 -4.7 -4.75 -4.8 -4.85 -4.9 -4.95 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5. -1.086956522 -1.075268817 -1.063829787 -1.052631579 -1.041666667 -1.030927835 -1.020408163 -1.01010101 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 52.

(63) 5.37037E-05 5.40741E-05 5.44444E-05 5.48148E-05 5.51852E-05 5.55556E-05 5.59259E-05 5.62963E-05 5.66667E-05 5.7037E-05 5.74074E-05 5.77778E-05 5.81481E-05 5.85185E-05 5.88889E-05 5.92593E-05 5.96296E-05 6E-05 6.03704E-05 6.07407E-05 6.11111E-05 6.14815E-05 6.18519E-05 6.22222E-05 6.25926E-05 6.2963E-05 6.33333E-05 6.37037E-05 6.40741E-05 6.44444E-05 6.48148E-05 6.51852E-05 6.55556E-05 6.59259E-05 6.62963E-05 6.66667E-05 6.7037E-05 6.74074E-05 6.77778E-05 6.81481E-05 6.85185E-05 6.88889E-05 6.92593E-05 6.96296E-05 7E-05 7.03704E-05 7.07407E-05 7.11111E-05 7.14815E-05 7.18519E-05 7.22222E-05 7.25926E-05 7.2963E-05. 0.145 0.146 0.147 0.148 0.149 0.15 0.151 0.152 0.153 0.154 0.155 0.156 0.157 0.158 0.159 0.16 0.161 0.162 0.163 0.164 0.165 0.166 0.167 0.168 0.169 0.17 0.171 0.172 0.173 0.174 0.175 0.176 0.177 0.178 0.179 0.18 0.181 0.182 0.183 0.184 0.185 0.186 0.187 0.188 0.189 0.19 0.191 0.192 0.193 0.194 0.195 0.196 0.197. -34.4828 -34.2466 -34.0136 -33.7838 -33.557 -33.3333 -33.1126 -32.8947 -32.6797 -32.4675 -32.2581 -32.0513 -31.8471 -31.6456 -31.4465 -31.25 -31.0559 -30.8642 -30.6748 -30.4878 -30.303 -30.1205 -29.9401 -29.7619 -29.5858 -29.4118 -29.2398 -29.0698 -28.9017 -28.7356 -28.5714 -28.4091 -28.2486 -28.0899 -27.933 -27.7778 -27.6243 -27.4725 -27.3224 -27.1739 -27.027 -26.8817 -26.738 -26.5957 -26.455 -26.3158 -26.178 -26.0417 -25.9067 -25.7732 -25.641 -25.5102 -25.3807. -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5. -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 53.

(64) 7.33333E-05 7.37037E-05 7.40741E-05 7.44444E-05 7.48148E-05 7.51852E-05 7.55556E-05 7.59259E-05 7.62963E-05 7.66667E-05 7.7037E-05 7.74074E-05 7.77778E-05 7.81481E-05 7.85185E-05 7.88889E-05 7.92593E-05 7.96296E-05 8E-05 8.03704E-05 8.07407E-05 8.11111E-05 8.14815E-05 8.18519E-05 8.22222E-05 8.25926E-05 8.2963E-05 8.33333E-05 8.37037E-05 8.40741E-05 8.44444E-05 8.48148E-05 8.51852E-05 8.55556E-05 8.59259E-05 8.62963E-05 8.66667E-05 8.7037E-05 8.74074E-05 8.77778E-05 8.81481E-05 8.85185E-05 8.88889E-05 8.92593E-05 8.96296E-05 9E-05 9.03704E-05 9.07407E-05 9.11111E-05 9.14815E-05 9.18519E-05 9.22222E-05 9.25926E-05. 0.198 0.199 0.2 0.201 0.202 0.203 0.204 0.205 0.206 0.207 0.208 0.209 0.21 0.211 0.212 0.213 0.214 0.215 0.216 0.217 0.218 0.219 0.22 0.221 0.222 0.223 0.224 0.225 0.226 0.227 0.228 0.229 0.23 0.231 0.232 0.233 0.234 0.235 0.236 0.237 0.238 0.239 0.24 0.241 0.242 0.243 0.244 0.245 0.246 0.247 0.248 0.249 0.25. -25.2525 -25.1256 -25 -24.8756 -24.7525 -24.6305 -24.5098 -24.3902 -24.2718 -24.1546 -24.0385 -23.9234 -23.8095 -23.6967 -23.5849 -23.4742 -23.3645 -23.2558 -23.1481 -23.0415 -22.9358 -22.8311 -22.7273 -22.6244 -22.5225 -22.4215 -22.3214 -22.2222 -22.1239 -22.0264 -21.9298 -21.8341 -21.7391 -21.645 -21.5517 -21.4592 -21.3675 -21.2766 -21.1864 -21.097 -21.0084 -20.9205 -20.8333 -20.7469 -20.6612 -20.5761 -20.4918 -20.4082 -20.3252 -20.2429 -20.1613 -20.0803 -20. -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5. -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 54.

(65) Close. 9.2963E-05 9.33333E-05 9.37037E-05 9.40741E-05 9.44444E-05 9.48148E-05 9.51852E-05 9.55556E-05 9.59259E-05 9.62963E-05 9.66667E-05 9.7037E-05 9.74074E-05 9.77778E-05 9.81481E-05 9.85185E-05 9.88889E-05 9.92593E-05 9.96296E-05 1E-04 0.00010037 0.000100741 0.000101111 0.000101481 0.000101852 0.000102222 0.000102593 0.000102963 0.000103333 0.000103704 0.000104074 0.000104444 0.000104815 0.000105185 0.000105556 0.000105926 0.000106296 0.000106667 0.000107037 0.000107407 0.000107778 0.000108148 0.000108519 0.000108889 0.000109259 0.00010963 0.00011 0.00011037 0.000110741 0.000111111 0.000111481 0.000111852 0.000112222. 0.251 0.252 0.253 0.254 0.255 0.256 0.257 0.258 0.259 0.26 0.261 0.262 0.263 0.264 0.265 0.266 0.267 0.268 0.269 0.27 0.271 0.272 0.273 0.274 0.275 0.276 0.277 0.278 0.279 0.28 0.281 0.282 0.283 0.284 0.285 0.286 0.287 0.288 0.289 0.29 0.291 0.292 0.293 0.294 0.295 0.296 0.297 0.298 0.299 0.3 0.301 0.302 0.303. -19.9203 -19.8413 -19.7628 -19.685 -19.6078 -19.5313 -19.4553 -19.3798 -19.305 -19.2308 -19.1571 -19.084 -19.0114 -18.9394 -18.8679 -18.797 -18.7266 -18.6567 -18.5874 -18.5185 -18.4502 -18.3824 -18.315 -18.2482 -18.1818 -18.1159 -18.0505 -17.9856 -17.9211 -17.8571 -17.7936 -17.7305 -17.6678 -17.6056 -17.5439 -17.4825 -17.4216 -17.3611 -17.301 -17.2414 -17.1821 -17.1233 -17.0648 -17.0068 -16.9492 -16.8919 -16.835 -16.7785 -16.7224 -16.6667 -16.6113 -16.5563 -16.5017. -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5. -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 55.

(66) 0.000112593 0.000112963 0.000113333 0.000113704 0.000114074 0.000114444 0.000114815 0.000115185 0.000115556 0.000115926 0.000116296 0.000116667 0.000117037 0.000117407 0.000117778 0.000118148 0.000118519 0.000118889 0.000119259 0.00011963 0.00012 0.00012037 0.000120741 0.000121111 0.000121481 0.000121852 0.000122222 0.000122593 0.000122963 0.000123333 0.000123704 0.000124074 0.000124444 0.000124815 0.000125185 0.000125556 0.000125926 0.000126296 0.000126667 0.000127037 0.000127407 0.000127778 0.000128148 0.000128519 0.000128889 0.000129259 0.00012963 0.00013 0.00013037 0.000130741 0.000131111 0.000131481 0.000131852. 0.304 0.305 0.306 0.307 0.308 0.309 0.31 0.311 0.312 0.313 0.314 0.315 0.316 0.317 0.318 0.319 0.32 0.321 0.322 0.323 0.324 0.325 0.326 0.327 0.328 0.329 0.33 0.331 0.332 0.333 0.334 0.335 0.336 0.337 0.338 0.339 0.34 0.341 0.342 0.343 0.344 0.345 0.346 0.347 0.348 0.349 0.35 0.351 0.352 0.353 0.354 0.355 0.356. -16.4474 -16.3934 -16.3399 -16.2866 -16.2338 -16.1812 -16.129 -16.0772 -16.0256 -15.9744 -15.9236 -15.873 -15.8228 -15.7729 -15.7233 -15.674 -15.625 -15.5763 -15.528 -15.4799 -15.4321 -15.3846 -15.3374 -15.2905 -15.2439 -15.1976 -15.1515 -15.1057 -15.0602 -15.015 -14.9701 -14.9254 -14.881 -14.8368 -14.7929 -14.7493 -14.7059 -14.6628 -14.6199 -14.5773 -14.5349 -14.4928 -14.4509 -14.4092 -14.3678 -14.3266 -14.2857 -14.245 -14.2045 -14.1643 -14.1243 -14.0845 -14.0449. -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5. -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 56.

(67) 0.000132222 0.000132593 0.000132963 0.000133333 0.000133704 0.000134074 0.000134444 0.000134815 0.000135185 0.000135556 0.000135926 0.000136296 0.000136667 0.000137037 0.000137407 0.000137778 0.000138148 0.000138519 0.000138889 0.000139259 0.00013963 0.00014 0.00014037 0.000140741 0.000141111 0.000141481 0.000141852 0.000142222 0.000142593 0.000142963 0.000143333 0.000143704 0.000144074 0.000144444 0.000144815 0.000145185 0.000145556 0.000145926 0.000146296 0.000146667 0.000147037 0.000147407 0.000147778 0.000148148 0.000148519 0.000148889 0.000149259 0.00014963 0.00015 0.00015037 0.000150741 0.000151111 0.000151481. 0.357 0.358 0.359 0.36 0.361 0.362 0.363 0.364 0.365 0.366 0.367 0.368 0.369 0.37 0.371 0.372 0.373 0.374 0.375 0.376 0.377 0.378 0.379 0.38 0.381 0.382 0.383 0.384 0.385 0.386 0.387 0.388 0.389 0.39 0.391 0.392 0.393 0.394 0.395 0.396 0.397 0.398 0.399 0.4 0.401 0.402 0.403 0.404 0.405 0.406 0.407 0.408 0.409. -14.0056 -13.9665 -13.9276 -13.8889 -13.8504 -13.8122 -13.7741 -13.7363 -13.6986 -13.6612 -13.624 -13.587 -13.5501 -13.5135 -13.4771 -13.4409 -13.4048 -13.369 -13.3333 -13.2979 -13.2626 -13.2275 -13.1926 -13.1579 -13.1234 -13.089 -13.0548 -13.0208 -12.987 -12.9534 -12.9199 -12.8866 -12.8535 -12.8205 -12.7877 -12.7551 -12.7226 -12.6904 -12.6582 -12.6263 -12.5945 -12.5628 -12.5313 -12.5 -12.4688 -12.4378 -12.4069 -12.3762 -12.3457 -12.3153 -12.285 -12.2549 -12.2249. -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5. -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 57.

(68) 0.000151852 0.000152222 0.000152593 0.000152963 0.000153333 0.000153704 0.000154074 0.000154444 0.000154815 0.000155185 0.000155556 0.000155926 0.000156296 0.000156667 0.000157037 0.000157407 0.000157778 0.000158148 0.000158519 0.000158889 0.000159259 0.00015963 0.00016 0.00016037 0.000160741 0.000161111 0.000161481 0.000161852 0.000162222 0.000162593 0.000162963 0.000163333 0.000163704 0.000164074 0.000164444 0.000164815 0.000165185 0.000165556 0.000165926 0.000166296 0.000166667 0.000167037 0.000167407 0.000167778 0.000168148 0.000168519 0.000168889 0.000169259 0.00016963 0.00017 0.00017037 0.000170741 0.000171111. 0.41 0.411 0.412 0.413 0.414 0.415 0.416 0.417 0.418 0.419 0.42 0.421 0.422 0.423 0.424 0.425 0.426 0.427 0.428 0.429 0.43 0.431 0.432 0.433 0.434 0.435 0.436 0.437 0.438 0.439 0.44 0.441 0.442 0.443 0.444 0.445 0.446 0.447 0.448 0.449 0.45 0.451 0.452 0.453 0.454 0.455 0.456 0.457 0.458 0.459 0.46 0.461 0.462. -12.1951 -12.1655 -12.1359 -12.1065 -12.0773 -12.0482 -12.0192 -11.9904 -11.9617 -11.9332 -11.9048 -11.8765 -11.8483 -11.8203 -11.7925 -11.7647 -11.7371 -11.7096 -11.6822 -11.655 -11.6279 -11.6009 -11.5741 -11.5473 -11.5207 -11.4943 -11.4679 -11.4416 -11.4155 -11.3895 -11.3636 -11.3379 -11.3122 -11.2867 -11.2613 -11.236 -11.2108 -11.1857 -11.1607 -11.1359 -11.1111 -11.0865 -11.0619 -11.0375 -11.0132 -10.989 -10.9649 -10.9409 -10.917 -10.8932 -10.8696 -10.846 -10.8225. -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5. -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 58.

(69) 0.000171481 0.000171852 0.000172222 0.000172593 0.000172963 0.000173333 0.000173704 0.000174074 0.000174444 0.000174815 0.000175185 0.000175556 0.000175926 0.000176296 0.000176667 0.000177037 0.000177407 0.000177778 0.000178148 0.000178519 0.000178889 0.000179259 0.00017963 0.00018 0.00018037 0.000180741 0.000181111 0.000181481 0.000181852 0.000182222 0.000182593 0.000182963 0.000183333 0.000183704 0.000184074 0.000184444 0.000184815 0.000185185 0.000185556 0.000185926 0.000186296 0.000186667 0.000187037 0.000187407 0.000187778 0.000188148 0.000188519 0.000188889 0.000189259 0.00018963 0.00019 0.00019037 0.000190741. 0.463 0.464 0.465 0.466 0.467 0.468 0.469 0.47 0.471 0.472 0.473 0.474 0.475 0.476 0.477 0.478 0.479 0.48 0.481 0.482 0.483 0.484 0.485 0.486 0.487 0.488 0.489 0.49 0.491 0.492 0.493 0.494 0.495 0.496 0.497 0.498 0.499 0.5 0.501 0.502 0.503 0.504 0.505 0.506 0.507 0.508 0.509 0.51 0.511 0.512 0.513 0.514 0.515. -10.7991 -10.7759 -10.7527 -10.7296 -10.7066 -10.6838 -10.661 -10.6383 -10.6157 -10.5932 -10.5708 -10.5485 -10.5263 -10.5042 -10.4822 -10.4603 -10.4384 -10.4167 -10.395 -10.3734 -10.352 -10.3306 -10.3093 -10.2881 -10.2669 -10.2459 -10.2249 -10.2041 -10.1833 -10.1626 -10.142 -10.1215 -10.101 -10.0806 -10.0604 -10.0402 -10.02 -10 -9.98004 -9.96016 -9.94036 -9.92063 -9.90099 -9.88142 -9.86193 -9.84252 -9.82318 -9.80392 -9.78474 -9.76563 -9.74659 -9.72763 -9.70874. -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5. -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5. 59.

No results found