Papers & Documents “Where am I ?” Sensors & Methods for Mobile Robot Positioning Ch.5 J. Borenstein, H.R.Everett, L.Feng. Measurement and Correction of Systematic Odometry Errors In Mobile Robots J. 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 & Uses Fused with position measurements to provide better position estimation Increased accuracy can result in lesser absolute position updates In 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 Odometry Systematic Unequal wheel diameters Actual diameter different from nominal diameter Actual wheelbase different from nominal wheelbase Misaligned wheels Finite encoder resolution Finite encoder sampling rate
Errors in Odometry Non-Systematic Travel over uneven floor Travel over unexpected objects on floor Wheel slippage Slippery floor Overacceleration Fast turning Interaction with external bodies Internal forces(castor wheel) Non-point wheel contact with floor
Position Estimation Error Detect the uncertainty in the position Each position is surrounded by a characteristic error ellipse which indicates region of uncertainty These 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 Errors Borenstein & Feng established a simplified error model for Systematic errors. They considered two dominant causes of errors : Unequal wheel diameters E d = D R / D L Uncertainty about wheelbase E b = b actual / b nominal
Unidirectional square path test Robot starts at a position x 0,y 0, θ 0 labelled START Then it moves along a square path to a return position ε x,ε y,ε θ ε x = x abs – x calc ε y = y abs – y calc ε θ = ε abs – ε calc
Drawback It is not possible to determine whether unequal diameters or uncertainty about wheelbase is causing the error Not able to identify if two errors compensate each other
Bidirectional Square Path Test Overcomes the drawback of Unidirectional test Principle 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 Errors Some information can be derived from the spread of return position errors. This can be through the estimated standard deviation σ. 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 Parameter If 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 ε θ should be used.
Specifications about Bumps Bumps should resemble a cable of diameter 9 to 10 millimeters 10 bumps should be distributed as evenly as possible Bumps should be introduced during first segment of the square path along the wheel which faces inside of the square Effect is an orientation error in direction of the wheel which encountered the bump
Reduction of Odometry Errors Vehicles 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 accuracy The wheels used for odometry should be knife-edge thin and not compressible
Auxiliary Wheels Along with weight bearing wheels we also have steel wheels especially for encoding Feasible for Differential drive, tricycle drive and Ackerman vehicles
Basic Encoder Trailer Especially used with tracked vehicles because of large amount of slippage during turning A separate trailer is used for the purpose of encoding It can be used only when ground characteristics allow one to use it Trailer will be raised when crossing obstacles
Systematic Calibration Needs UMBtest. The error characteristics are meaningful only in context of UMBtest. Type A - Orientation error that reduces or increases in both directions Type B - Orientation error reduces in one direction but increases in other direction
Type A & Type B Errors
Determining Type A or B Type A | θ total,cw | < | θ nominal | AND | θ total,ccw | < | θ nominal | Type B | θ total,cw | | θ nominal |
Computation for Diameters α is the error in angle of rotation α = (x c.g,cw + x cg.,ccw )/(-4L) β is the angle that the robot deviates β = (x c.g,cw - x cg.,ccw )/(-4L) R is the radius curvature of curved path R = (L/2)/sin(β/2) E d = D R /D L = (R+b/2)/(R-b/2)
Computation for wheelbase b actual /90 = b nominal /(90-α) b actual = (90/(90-α)). B nominal Hence, E b = 90/90-α
Corrections To keep average diameter constant we get D a = (D R + D L )/2 Using this and the equation for E d we get D L = 2.D a / (E d + 1) D R = 2.D a / ((1/E d ) + 1)
Reduction of Non-Systematic Errors Mutual Referencing Use two robots that could measure positions mutually When one moves, other remains still and observes motion Thus one robot localizes with reference to fixed object Limits the efficiency of the robots
IPEC Internal position error correction This 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 accurately This has been implemented in CLAPPER
CLAPPER Compliant Linkage Autonomous Platform with Position Error Recovery Fast Growing Error Irregularity on floor will cause immediate orientation error Slow Growing Error Associated Lateral displacement Detect only the Fast growing errors relying on fact that lateral position errors were small
CLAPPER L e – line where A expects B to be L m – line where A actually finds B Even if B hit a bump orientation error measurement wont be affected