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Jan 01, 2016
Odometry Error Detection & Correction
- Sudhan Kanitkar
Papers & DocumentsWhere am I ? Sensors & Methods for Mobile Robot Positioning Ch.5J. Borenstein, H.R.Everett, L.Feng.Measurement and Correction of Systematic Odometry Errors In Mobile RobotsJ. Borenstein, L. Feng.
What is Odometry ?Fundamental idea is incremental motion information over time.Based on assumption that wheel revolutions can be translated into linear displacement relative to the floor.This however also leads to accumulation of errors.It provides good short term accuracy, inexpensive, allows high sampling rates
Significance & UsesFused with position measurements to provide better position estimationIncreased accuracy can result in lesser absolute position updatesIn some cases when no external references are available odometry is the only navigation information available.Many mapping and landmark matching algorithms assume that the robot can maintain its position well enough to allow it to look for landmarks in a limited region.
Errors in OdometrySystematicUnequal wheel diametersActual diameter different from nominal diameterActual wheelbase different from nominal wheelbaseMisaligned wheelsFinite encoder resolutionFinite encoder sampling rate
Errors in OdometryNon-Systematic Travel over uneven floorTravel over unexpected objects on floorWheel slippageSlippery floorOveraccelerationFast turningInteraction with external bodiesInternal forces(castor wheel)Non-point wheel contact with floor
Position Estimation ErrorDetect the uncertainty in the positionEach position is surrounded by a characteristic error ellipse which indicates region of uncertaintyThese ellipses grow in size with travel direction till absolute position measurement resets the size of error ellipse Only systematic errors are considered
Measurement of Odometry ErrorsBorenstein & Feng established a simplified error model for Systematic errors.They considered two dominant causes of errors :Unequal wheel diametersEd = DR / DLUncertainty about wheelbaseEb = bactual / bnominal
Unidirectional square path testRobot starts at a position x0,y0,0 labelled STARTThen it moves along a square path to a return position x,y,x = xabs xcalcy = yabs ycalc= abs calc
DrawbackIt is not possible to determine whether unequal diameters or uncertainty about wheelbase is causing the errorNot able to identify if two errors compensate each other
Bidirectional Square Path TestOvercomes the drawback of Unidirectional testPrinciple is that two dominant systematic errors which may compensate in each other in one direction add up in the opposite direction.
Bidirectional Square path
Measurement of Non-Systemic ErrorsSome information can be derived from the spread of return position errors.This can be through the estimated standard deviation .This depends on the robot & surface and might be different for different robots on the same floor.Hence its almost impossible to design test procedure for non-systematic errors.
Extended UMBmark Average Absolute Orientation Error
Measurable ParameterIf the bumps are concentrated at the beginning of first leg return position error will be small, conversely if they aare concentrated towards the end then the return error will be larger.Hence return position error is not a good choice.Instead the return orientation error should be used.
Specifications about BumpsBumps should resemble a cable of diameter 9 to 10 millimeters10 bumps should be distributed as evenly as possibleBumps should be introduced during first segment of the square path along the wheel which faces inside of the squareEffect is an orientation error in direction of the wheel which encountered the bump
Reduction of Odometry ErrorsVehicles with a small wheelbase are more prone to orientation errors.Castor wheels which bear significant portion of weight are likely to induce slippage.Synchro-drive design provides better odometric accuracyThe wheels used for odometry should be knife-edge thin and not compressible
Auxiliary WheelsAlong with weight bearing wheels we also have steel wheels especially for encodingFeasible for Differential drive, tricycle drive and Ackerman vehicles
Basic Encoder TrailerEspecially used with tracked vehicles because of large amount of slippage during turningA separate trailer is used for the purpose of encodingIt can be used only when ground characteristics allow one to use itTrailer will be raised when crossing obstacles
Systematic CalibrationNeeds UMBtest. The error characteristics are meaningful only in context of UMBtest.Type A - Orientation error that reduces or increases in both directionsType B - Orientation error reduces in one direction but increases in other direction
Type A & Type B Errors
Determining Type A or BType A|total,cw| < |nominal| AND |total,ccw| < |nominal|
Type B|total,cw| < |nominal| AND |total,ccw| > |nominal|
Computation for Diameters is the error in angle of rotation = (xc.g,cw + xcg.,ccw)/(-4L) is the angle that the robot deviates = (xc.g,cw - xcg.,ccw)/(-4L)R is the radius curvature of curved pathR = (L/2)/sin(/2)Ed = DR/DL = (R+b/2)/(R-b/2)
Computation for wheelbasebactual/90 = bnominal/(90-)
bactual = (90/(90-)). Bnominal
Hence,Eb = 90/90-
CorrectionsTo keep average diameter constant we getDa = (DR + DL)/2
Using this and the equation for Ed we getDL = 2.Da / (Ed + 1)DR = 2.Da / ((1/Ed) + 1)
Reduction of Non-Systematic ErrorsMutual ReferencingUse two robots that could measure positions mutuallyWhen one moves, other remains still and observes motionThus one robot localizes with reference to fixed objectLimits the efficiency of the robots
IPECInternal position error correctionThis method also uses two robots, except that the robots are in continuous motion.The robots should be able to measure their relative distance and bearing continuously and accuratelyThis has been implemented in CLAPPER
CLAPPERCompliant Linkage Autonomous Platform with Position Error RecoveryFast Growing ErrorIrregularity on floor will cause immediate orientation errorSlow Growing ErrorAssociated Lateral displacementDetect only the Fast growing errors relying on fact that lateral position errors were small
CLAPPERLe line where A expects B to beLm line where A actually finds B Even if B hit a bump orientation error measurement wont be affected
Smart Encoder Trailer