servo and sensor control on small mobile platforms - Engineering ...

J. Blanch, S. Tosunoglu, ASME Southeastern Region XI Technical Journal, Volume 2, Number 1, April 2003; also presented atthe ASME Southeastern Region XI Technical Conference, Miami, Florida, April 4-5, 2003.SERVO AND SENSOR CONTROL ON SMALL MOBILE PLATFORMSJorge Blanch <strong>and</strong> Sabri TosunogluFlorida International UniversityDepartment of Mechanical Engineering10555 West Flagler StreetMiami, Florida 33174ABSTRACTSystem integration is an unavoidable <strong>and</strong>important part of a project. Considerable amounts oftime <strong>and</strong> resources are always devoted to make surethat all the components in a project work not onlyproperly, but also work together properly. This workdiscusses how different elements of a “desktop”robotic platform that was designed <strong>and</strong> constructed atFIU had to be <strong>control</strong>led to achieve an effective <strong>and</strong>mechanically stable platform. For this purpose, wereview the platform design, <strong>sensor</strong> utilization <strong>and</strong><strong>servo</strong> <strong>control</strong> developed for this project. We thendemonstrate that a proper <strong>servo</strong> <strong>and</strong> <strong>sensor</strong> <strong>control</strong>structure can indeed improve the platformperformance appreciably.INTRODUCTIONRobots relate to their environment via <strong>sensor</strong>s <strong>and</strong>actuators. It therefore follows that any short-comingof either <strong>sensor</strong>s or <strong>servo</strong>s will severely affect thecapabilities of a robot. Besides the almost inevitablenoise errors <strong>and</strong> other hitches inherent to electricalcircuits subject to dynamic loads, there are otherphysical limitations that affect both <strong>servo</strong>s <strong>and</strong>actuators. Knowing the exact position of a vehicle isa fundamental problem in mobile robotics. In searchfor a solution, researchers <strong>and</strong> engineers havedeveloped a variety of systems, <strong>sensor</strong>s, <strong>and</strong> techniquesfor mobile robot positioning; yet still there isno truly elegant solution for the problem. The manypartial solutions can be categorized into two groups:relative <strong>and</strong> absolute position measurements. Becauseof the lack of a single good method, two methods,one from each group, are usually combined toprovide reliable positioning [1]. Relative positionmeasurements (Odometry <strong>and</strong> Inertial Navigation)are derived from robot internal <strong>sensor</strong>s alone <strong>and</strong>have an uncertainty error associated to them;furthermore, this error propagates <strong>and</strong> becomes largerover time [2,3]. Absolute positioning methods can beused to reduce the error value so that a more accuraterobot position can be determined. Absolutepositioning methods include Magnetic Compasses,Active Beacons, Global Positioning Systems, L<strong>and</strong>markNavigation <strong>and</strong> Model Matching (or MapMatching) [1].Determining the odometry errors of a mobilerobot is very important (no use of inertial navigationin our platform), both in order to reduce them, <strong>and</strong> toknow the accuracy of the position estimated by deadreckoning. The odometry error contains both systematic<strong>and</strong> nonsystematic components. Systematicerrors are those inherent to the platform, they relateto the physical properties of the platform <strong>and</strong>, tosome extent, its relationship with the environment(for example different wheel diameter for each<strong>servo</strong>). Nonsystematic errors depend heavily on theenvironment <strong>and</strong> include unforeseen errors like wheelslippage. Because the platform being tested is forindoor use in a <strong>control</strong>led environment, nonsystematicerrors should be almost non-existent, sothey are assumed to be zero.In a configuration where there is no off-platformassistance (active beacons <strong>and</strong> positioning systemsare not available), the robot must solely rely on itsown <strong>sensor</strong>s to navigate in unknown terrains <strong>and</strong>, tothe extent possible, to compensate for odometryerrors. Although techniques like Map-making,L<strong>and</strong>mark Navigation <strong>and</strong> Map Matching are allheavily software dependant <strong>and</strong> therefore not coveredin this article, they do require reliable <strong>sensor</strong> input.An extensive <strong>sensor</strong> package that can provide largeamounts of relevant information is always desirablebut often unavailable. When dealing with limited<strong>sensor</strong> inputs, smart utilization becomes paramount.Since an array of range <strong>sensor</strong>s was not available dueto budget constraints, <strong>sensor</strong>s were mounted on<strong>servo</strong>s so they could take readings in almost anydirection.Next, we will briefly review the platform that wasdeveloped for this project. Followed by a more

J. Blanch, S. Tosunoglu, ASME Southeastern Region XI Technical Journal, Volume 2, Number 1, April 2003; also presented atthe ASME Southeastern Region XI Technical Conference, Miami, Florida, April 4-5, 2003.detailed review of the main components such as the<strong>servo</strong>s <strong>and</strong> <strong>sensor</strong>s <strong>and</strong> how they are <strong>control</strong>led tomake this an effective <strong>and</strong> mechanically stableplatform. Finally, some conclusions will be drawn asto the quality <strong>and</strong> precision of a platform built withoff the shelf components meant for hobbyists.PLATFORMThe platform used in this case is HANCOR(H<strong>and</strong>held-Controlled Rover), a small rover createdat Florida International University to test the viabilityof using h<strong>and</strong>held devices as platform <strong>control</strong>lers.The platform is based on a Pontech SV203 <strong>servo</strong><strong>control</strong>ler board that uses Sharp GP2D120 infraredranger <strong>sensor</strong>s to detect obstacles <strong>and</strong> Futaba-type<strong>servo</strong>motors (<strong>servo</strong>s used in radio-<strong>control</strong>led modelairplanes, cars, etc.) to drive the wheels. An onboardPalm III h<strong>and</strong>held <strong>control</strong>s the platform [4,5,6].SERVOSSmall budget platforms like the HANCOR oftenreplace expensive <strong>servo</strong>s <strong>and</strong> position encoders withoff-the shelf radio <strong>control</strong>led <strong>servo</strong>motors. RC<strong>servo</strong>s are cheap, easy to <strong>control</strong>, come in a convenientform factor <strong>and</strong> are available in different sizes,speeds <strong>and</strong> power ratings. Servomotors are generallyemployed for position <strong>control</strong>; they use a potentiometeras feedback to determine their position. The<strong>servo</strong> compares its current position to an input PWMsignal, <strong>and</strong> then moves until its position matches theinput signal. The “width” of the signal pulse may lastanywhere from 0.6 milliseconds (minimum position),to 2.4 ms (maximum position). The Pulse is repeatedevery 14 to 20 milliseconds (figure 2) [9]. Regular<strong>servo</strong>motors are used for the positioning of the range<strong>sensor</strong>s, but <strong>control</strong>ling the driving <strong>servo</strong>s requiresome modifications.Figure 2. Futaba-type <strong>servo</strong> timing diagram.Figure 1. HANCOR platform (h<strong>and</strong>heldconnected but not mounted).The <strong>servo</strong> <strong>control</strong>ler board is based on aPIC16C73 microchip; it accepts serial data from ahost computer (replaced by the Palm III h<strong>and</strong>held inthis case) <strong>and</strong> outputs a PWM (Pulse WidthModulated) signal to <strong>control</strong> up to eight RC <strong>servo</strong>motors[10]. Two <strong>servo</strong>s, modified for continuousrotation, provide power for the driving wheels.Besides <strong>servo</strong>s, the board can <strong>control</strong> other digitaldevices that require an on/off signal to be activated.Up to 5 <strong>sensor</strong>s can be connected to the A/D inputheader, which reads analog voltages between 0 <strong>and</strong> 5Volts. The <strong>sensor</strong> package consists of two infraredrange <strong>sensor</strong>s <strong>and</strong> one digital compass. The digitalcompass has a resolution of +/- 22 o (it detects N, NE,E, SE, etc.), so it cannot be used as a reliable <strong>sensor</strong>input, but can later be used as aid during mapmatching [7]. The IR <strong>sensor</strong>s are mounted on twosmall <strong>servo</strong>s so that they can pan to any direction in a135 o forward-looking field of viewFutaba-type Servomotors were not developed forcontinuous rotation. In order to utilize <strong>servo</strong>s insituations that require continuous rotation they haveto be modified. Servos were not designed forvelocity <strong>control</strong> either. The velocity of a <strong>servo</strong>depends on how far it is from the desired position.The <strong>servo</strong> will spin at top speed until it gets close tothe desired value, then it will quickly slow down toavoid over-shooting the target position. Usually,continuous rotation <strong>and</strong> velocity <strong>control</strong> go h<strong>and</strong> inh<strong>and</strong>. Servos that have been “hacked” for continuousrotation have the feedback potentiometer de-coupledfrom the output gear <strong>and</strong> set to a constant value (forexample 90 o ). The velocity is <strong>control</strong>led by givingthe <strong>servo</strong> a target position (0 to 180 o ), but since thefeedback has been fixed at 90 o , the <strong>servo</strong> will spinforever towards the target position. The further thetarget position from the fixed position (90 o ), thefaster the <strong>servo</strong> will spin.The Pontech SV203 <strong>control</strong>s its <strong>servo</strong>s via an 8-bit signal (PWM). An 8-bit signal can take 2 8 values(from 0 to 255). If we define the 0 signal as 0 o <strong>and</strong>

J. Blanch, S. Tosunoglu, ASME Southeastern Region XI Technical Journal, Volume 2, Number 1, April 2003; also presented atthe ASME Southeastern Region XI Technical Conference, Miami, Florida, April 4-5, 2003.the 255 signal as 180 o , then the 90 o signal will be128. As can be seen from the data in figure 3, the<strong>servo</strong> quickly reaches top speed, which leaves us witha relatively small range of useful bit values (roughlyfrom 90 to 170 in our case). Values outside thisrange will not result in a significant speed variation.revolutions per secondServo speedRange of interest10.80.60.40.20-0.2-0.4-0.6-0.8-10 100 200Bit valueleftrightFigure 3. Servo speed measurements.Servo speeds were measured (in revolutions persecond) at different bit signals <strong>and</strong> stored in Excel(figure 3). Data was then transferred to Matlab toperform some numerical analyses on it; the objectivebeing to find an equation that will return the bit valueneeded to achieve a desired rotational velocity.To effectively approximate the data, it first hat tobe transformed <strong>and</strong> formatted. Two processes wererequired. First, the order of the data pairs waschanged so that velocity would be our independentvariable (input) <strong>and</strong> the calculated bit our dependentvariable (output). Secondly, only values in the rangeof interest were used; this helped to generate atighter-fitting curve, since only relevant data wasbeing used (figure 4).The 3 rd degree polynomial approximation [13]that fit the data (from about –0.9 to 0.9) as given byMatlab was:Right bit(v) =31.224v 3 + 0.451v 2 + 15.72v + 128.948Left bit(v) = -33.272v 3 + 1.504v 2 -15.294v + 130.273The 3 rd degree approximation looked promisingbut when tested on the platform it did not perform aswell as expected; the platform could not describe astraight path. This approximation is not a methodthat is accurate enough to drive the platform.Bit ValueRPSFigure 4. Actual values <strong>and</strong> 3 rd degree polynomialapproximations.Another curve-fitting method that can betterapproximate the data is the use of splines [13].Splines are polynomial approximations that are usedto fit sub-regions of the data. Since the section of thecurve to be approximated is smaller, a much higherdegree of accuracy can be achieved.Data points were then chosen subjectively tobreak up the curves in sections that presented similarbehavior (curvature) (table 1). A simple linearapproximation from one point to the next (splines of1 st degree) provided a much better fit to the originaldata (figure 5) than the 3 rd degree polynomialscalculated previously. Of course, this came at thecost of having 9 linear equations for each 3 rd degreepolynomial.Bit ValueLeft <strong>and</strong> Right wheel velocitiesLeft <strong>and</strong> Right wheel velocitiesRPSFigure 5. Close-up of range of interest: Gathereddata with extracted points superimposed.

J. Blanch, S. Tosunoglu, ASME Southeastern Region XI Technical Journal, Volume 2, Number 1, April 2003; also presented atthe ASME Southeastern Region XI Technical Conference, Miami, Florida, April 4-5, 2003.Table 1. Data extracted from range of interest.Left Rightbit rps rps90 0.880282 -0.8787394 0.857633 -0.85106104 0.802568 -0.78125112 0.673401 -0.64516120 0.423729 -0.36058140 -0.4 0.454545146 -0.59032 0.648508152 -0.72464 0.761035164 -0.82781 0.859107168 -0.8489 0.874126Two observations that persuade against searchingfor more accurate approximations are: 1, theexperimental measurements are subject to error;depending on the accuracy of the reading or even onthe battery charge, values will vary slightly from onerun to the next. And 2, bit comm<strong>and</strong>s are integers;therefore there will be gaps in the velocity curves forvalues that could never be reached because theycorrespond to a bit value between two integers. Onthe other h<strong>and</strong>, the closeness of the splineapproximation to the actual data showed thatselecting a few finite points can offer sufficient<strong>control</strong> over the velocity. Not using an equation (orseveral) to find the bit value corresponding to adesired velocity, results in a crude <strong>control</strong> over speedvalues; but, by finding the bit values that correspondto specific velocities (0.8, 0.6, 0.4, 0.2, 0.0, -0.2, -0.4,-0.6 <strong>and</strong> –0.8 rps, per se), the velocity of the platformcan be properly <strong>control</strong>led for its full range of values.Figure 6. Distance <strong>and</strong> angle calculation.SENSORSThe main <strong>sensor</strong> used by the HANCOR is theSharp GP2D12 analog infrared ranger [10]. Sharp IRrangers use triangulation <strong>and</strong> a small linear CCDarray to compute the distance or presence of objectsin the field of view (Figure 6), which results ingreater reliability <strong>and</strong> accuracy than many IR <strong>sensor</strong>sthat use time-of-flight techniques. Also, these newrangers offer much better immunity to ambientlighting conditions <strong>and</strong> to the color of the reflectedsurface than other IR <strong>sensor</strong>s [11]. These <strong>sensor</strong>shave a minimum range of 10 cm (~ 4in) <strong>and</strong> amaximum range of 80 cm. The beam is very tight,just about 3 cm wide <strong>and</strong> less than 3 cm in height at40 cm. Such characteristics make the <strong>sensor</strong>s quitesuitable for unidirectional measurements, but not sogreat for general obstacle detection. Someadvantages over ultrasound ranger <strong>sensor</strong>s,traditionally used for obstacle detection, are: IR<strong>sensor</strong>s do not suffer from ghost images; furthermore,the angle at which they face an obstacle can be ashigh as 60 o without affecting distance reading [11].IR <strong>sensor</strong>s also have much lower power requirementcompared to the battery-hungry ultrasound <strong>sensor</strong>s.Finally, price becomes an issue when ultrasound<strong>sensor</strong>s are over five times more expensive than IR<strong>sensor</strong>s. Of course, sornars will always be greatdetection <strong>sensor</strong>s thanks to their range (2 to 120 cm)<strong>and</strong> their wider detection area.Table 2: IR range values for given distancesDistance (cm)10Sensor1239Sensor223512 210 20414 185 17716 169 16118 152 1412022139129132120242612011311310528 108 9930 101 9132349587877836 81 7938 79 7140 74 6742 69 6344 65 5946 61 5548 57 5250 54 48525450484341The analog output of the infrared does not changelinearly with the distance being measured; table 2shows the readings taken from the <strong>servo</strong>s from 10 to

J. Blanch, S. Tosunoglu, ASME Southeastern Region XI Technical Journal, Volume 2, Number 1, April 2003; also presented atthe ASME Southeastern Region XI Technical Conference, Miami, Florida, April 4-5, 2003.50 cm. To find a numerical approximation that canyield a governing equation, the average of <strong>sensor</strong> 1<strong>and</strong> <strong>sensor</strong> 2 was found <strong>and</strong> then analyzed.value (bit)250200150100500IR readingsHoerl Pow Avg10 18 26 34 42 50 58Distance (cm)Figure 7. IR distance approximations.The average values can be approximated by thefollowing power equation:V(d) = 1917.709*d^(-0.8941)which is very similar to that of [11]V(d) = 2141.72055*d^(-1.078867)A better approximation can be found using aHoerl Model, which is a modified power equation:V(d) = 997.82*0.985^d*d^(-0.563), but it is notreally necessary to perform the extra power functionfor a marginal increase in accuracy.To turn IR range <strong>sensor</strong>s into effective obstacledetectors, the <strong>servo</strong>s must reposition the <strong>sensor</strong>s toget several readings of the terrain ahead of the robot.If the <strong>sensor</strong>s have to be reoriented, timing becomesan issue. Several factors have to be taken intoaccount to determine the frequency at which readingscan be taken. First of all, the refresh rate of the IR<strong>sensor</strong>s determines the maximum frequency at whichreadings can be taken. The velocity of the <strong>servo</strong>sdictate how long it will take to reach the desiredorientation. The response of the <strong>control</strong>ler boardindicates how long it takes for the board to poll theAD header for a new reading <strong>and</strong> return it to theh<strong>and</strong>held. The h<strong>and</strong>held connects to the <strong>control</strong>lerboard at a certain speed. Finally, the Palm has toperform many computations, <strong>and</strong> can only read fromthe serial port every so often.The IR <strong>sensor</strong>s continuously takes distancereadings every 38 ms, for a total of about 25 readingsevery second (25Hz)[10]. The Hitec ht-85 <strong>servo</strong>shave a nominal operating speed of 0.11sec/60° at4.8V. Even though the speed of the <strong>servo</strong> isproportional to the displacement covered, thenominal speed can be used to approximate the time ittakes the <strong>servo</strong> to move a certain arc. At 9600 baud,which is the st<strong>and</strong>ard connection speed for the<strong>control</strong>ler board, it takes 4ms to transmit a simpleoutput comm<strong>and</strong> of 4 bytes. For more complexcomm<strong>and</strong>s it takes the Palm 25ms to transmit thecomm<strong>and</strong> <strong>and</strong> receive the result as ASCII data. Afterthe data is received, it must then be converted to aninteger for it to be useful. In practice, is rare to get<strong>sensor</strong> readings faster than 50ms. It is possible toconnect the <strong>control</strong>ler board to transmit at up to38400 baud, which should reduce considerably thecommunication delays, but since the <strong>servo</strong> responseis the main cause for delays in the architecture, it isnot necessary.-30 o-8 o 8 o 30 oFigure 8. Obstacle detection.The GP2D12 takes continuous readings, but thePalm takes discrete readings individually. In order toeffectively cover the front area of the rover, each<strong>sensor</strong> takes three readings as seen in figure 8. Giventhe Hitec’s nominal velocity, the different times ittakes a <strong>servo</strong> to go from one position to the next are:Position 1 to Position 2: 46 o ~ 0.084sec; Position 2 toPosition 3: 24 o ~ 0.044sec; Position 3 to Position 1:22 o ~ 0.04sec. Since the IR ranger takes 38ms torefresh, the robot should wait that much longer beforereading from the <strong>sensor</strong>. Therefore, the time delaybefore a reliable reading can be taken is at least:To position 1: 0.040 + 0.038 = 0.079secTo position 2: 0.084 + 0.038 = 0.122secTo position 3: 0.044 + 0.038 = 0.082secPosition 1Position 30 o 0 o-54 o 54 o24 o 22 oPosition 246 oUnfortunatelly, PalmOS does not have a wait( )or delay( ) function, to wait long enough beforetaking the reading. Fortunately, Palm does have a

J. Blanch, S. Tosunoglu, ASME Southeastern Region XI Technical Journal, Volume 2, Number 1, April 2003; also presented atthe ASME Southeastern Region XI Technical Conference, Miami, Florida, April 4-5, 2003.getTicks( ) <strong>and</strong> TicksInASecond( ) functions. Withthese two an approximate waiting function can bewritten:void WaitMS (int milisecs){UInt32 zero, ticks, time;zero = TimGetTicks( );ticks = zero +1;//convert time from ms to tickstime = (milisecs / 1000.0) *SysTicksPerSecond( );while(ticks - zero read IRs⇒ move to Position 2⇒ waitMS(130) => read IRs⇒ move to Position 3⇒ waitMS(90) => read IRs]⇒ collision avoidance [⇒ change motion (if necessary)]⇒ increment counter.This means that the HANDCOR needs at least0.015 + 0.079 + 0.122 + 0.082 = 298ms to gather thereadings for the obstacle avoidance subroutine.Because there are two forward looking <strong>sensor</strong>s <strong>and</strong>each has three positions, if an object appearsimmediately after a reading is taken, it will take onefull cycle before that object is detected. A full cycleis 298 ms plus the time it takes the palm to run anyinternal functions (this varies, but is generally lessthan 50 ms). Each sweep pattern covers just over 45degrees, <strong>and</strong> they complement each other to providereasonable detection of obstacles ahead of the robot.When the obstacles are closer, the overlapping fieldsprovide even better detection. Given that theeffective range of the <strong>sensor</strong> is just over 40 cm(reliability starts failing after about 50 cm), the <strong>sensor</strong>refresh rate limits the forward speed of the robot to40 cm in 300 ms, or it would be possible to hit anobject before seeing it. The driving <strong>servo</strong>s’maximum speed is under 0.89 revolutions persecond; with a wheel diameter of 7.6cm (3in), themaximum velocity the robot can achieve is under 24cm in 1 second, which is well within safe range.And advantage to having both <strong>sensor</strong>s mounted on<strong>servo</strong>s is that they can be directed, <strong>and</strong> they can becombined for greater accuracy. By usingtrigonometry [12], two readings can be taken fromthe same obstacle <strong>and</strong> then compared to determine itsdistance with greater accuracy. If a <strong>sensor</strong> detects anobstacle at a distance d R when its orientation is θ R (figure 9) it is very simple to convert it tocoordinates relative to the robot < 2 >, <strong>and</strong> then tocoordinates relative to the other <strong>sensor</strong> < 3 >.⎡dRX ⎤ ⎡d⋅cos(θR)⎤dR= ⎢ ⎥ = ⎢ ⎥⎣dRY⎦ ⎣d⋅sin(θR)⎦< 1 >⎡DX⎤ ⎡URX ⎤ ⎡dRX⎤D = ⎢ ⎥ = ⎢ ⎥ + ⎢ ⎥⎣DY⎦ ⎣URY ⎦ ⎣dRY⎦< 2 >⎡dLX⎤ ⎡DX⎤ ⎡ULX ⎤dL= ⎢ ⎥ = ⎢ ⎥ − ⎢ ⎥⎣dLY⎦ ⎣DY⎦ ⎣ULY ⎦< 3 >Finally, θ L is⎛ d ⎞LYθL= arctan⎜⎟< 4 >⎝ dLY⎠From the platform, U R = U L = 4 cm <strong>and</strong> the anglesφ R = 35 o φ L = -35 o . Back substituting into < 4 >⎡d⎢⎣dLXLY⎤ ⎡U⎥ = ⎢⎦ ⎣URXRY+ d+ dRXRY−U−ULXLY⎛ 4 ⋅ sin(35) + d ⋅ sin( θ⎞R)− 4 ⋅ sin( −35)θL= arctan⎜⎟⎝ 4 ⋅ cos(35) + d ⋅ cos( θR)− 4 ⋅ cos( −35)⎠Assuming that there is no other obstacle betweenthe second <strong>sensor</strong> <strong>and</strong> the original obstacle, θ L can beused to get a second reading, d L from the obstacle,which can then be transformed to a second distancereading D. The redundant distance readings shouldresult in a more accurate reading when compilingmaps.⎤⎥⎦

J. Blanch, S. Tosunoglu, ASME Southeastern Region XI Technical Journal, Volume 2, Number 1, April 2003; also presented atthe ASME Southeastern Region XI Technical Conference, Miami, Florida, April 4-5, 2003.YU Lφ Ly Lφ Ry RU Rθ Lφx Lθ Rx RFigure 9. Obstacle detection.CONCLUSIONSSystem integration is indeed a difficult <strong>and</strong> timeconsuming task, especially when components haveloose tolerances that can only be overcome bycombining hardware <strong>and</strong> software modifications.Radio-<strong>control</strong>led Servos are a low cost alternativeto steppers <strong>and</strong> <strong>servo</strong>s, but they do not allow for fine<strong>control</strong> of position or motion <strong>and</strong> therefore should notbe used in places where precision is critical. RC.<strong>servo</strong>s worked great to orient the <strong>sensor</strong>s, albeit notvery quick for autonomous running, they made itvery simple to face the <strong>sensor</strong>s in any desireddirection, on the other h<strong>and</strong>. using RC <strong>servo</strong>s to drivethe rover, resulted in a difficult to <strong>control</strong> platformInfrared rangers worked consistently <strong>and</strong> coulddeliver data extremely fast, but they had to be timedso that the <strong>servo</strong> would reach the desired positionbefore readings were taken.One source of errors that could not be overcomewas the electrical noise. This noise was caused bythe dynamic electric loads generated by the <strong>servo</strong>s,<strong>and</strong> inability of the platform to filter them out. Itshould also be noted that during testing, the time ittook for the WaitMS( ) function to end varied widely(this is not a reliably consistant delay method).Xd LDd Rtransactions on robotics <strong>and</strong> automation, vol. 18,no. 3, June 2002.[3] Kelly A., “General solution for linearizedsystematic error propagation in vehicleodometry,” in Proc. Int. Conf. Intelligent Robot<strong>and</strong> Systems (IROS01), Maui, HI, Oct. 29–Nov.3 2001, pp. 1938–1945.[4] Blanch J., <strong>and</strong> Tosunoglu S., “H<strong>and</strong>-HeldComputers as Mobile Platform Controllers,”Florida Conference on Recent Advances inRobotics, Florida State University, Tallahassee,Florida, May 10-11, 2001.[5] Blanch J., <strong>and</strong> Tosunoglu S., “Enhanced SmallMobile Platforms Controlled by H<strong>and</strong>-HeldComputers,” IASTED International Conferenceon Robotics <strong>and</strong> Application (RA 2001), Tampa,Florida, November 19-22, 2001.[6] Blanch J., <strong>and</strong> Tosunoglu S., “Control of MobilePlatforms via H<strong>and</strong>-Held PDA’s,” the 15thFlorida Conference on Recent Advances inRobotics, Florida International University,Miami, Florida, May 23-24, 2002.[7] Varveropoulos V., “Robot Localization <strong>and</strong> MapConstruction Using Sonar Data.” The RossumProject, available at http://rossum.sourceforge.net/ accessed on December 2002.[8] “Futaba Servo Motors,” accessed fromwww.futaba-rc.com/<strong>servo</strong>s/futm0029.html,accessed on October 2002.[9] Pontech SV203 Servo motor <strong>control</strong>ler boarduser manual. Available online at www.pontech.com. Accessed on December 2002.[10] “Acroname Articles Demystifying the Sharp IRRangers,” accessed from www.acroname.com/robotics/info/articles/sharp/sharp.html. Accessedon October 2002.[11] Technical info for the PPRK http://www-2.cs.cmu.edu/~pprk/ Accessed on January 2003.[12] Leon, S. J. “Linear Algebra with Applications.”Upper Saddle River, New Jersey. Prentice Hall,Inc. 1998.[13] Gerald C. F., <strong>and</strong> Wheatley P. P., “AppliedNumerical Analysis.” Reading, Massachusetts.Addison Wesley Longman, Inc. 1999.REFERENCES[1] Borenstein J. <strong>and</strong> Feng L., “Measurement <strong>and</strong>correction of systematic odometry errors inmobile robots,” IEEE Trans. Robot. Automat.,vol. 12, pp. 869–880, Dec. 1996.[2] Martinelli A., “The Odometry Error of a MobileRobot With a Synchronous Drive System” IEEE