Odometry

Odometry

Error Detection & Correction

- Sudhan Kanitkar

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

Ed = DR / DL

Uncertainty about wheelbase Eb = bactual / bnominal

Unidirectional square path test

Robot starts at a position x0,y0,θ0 labelled START

Then it moves along a square path to a return position εx,εy,εθ

εx = xabs – xcalc

εy = yabs – ycalc

εθ= εabs – εcalc

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

UMBmark test

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 εθ 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 |θtotal,cw| < |θnominal| AND |θtotal,ccw| < |θnominal|

Type B |θtotal,cw| < |θnominal| AND |θtotal,ccw| > |θnominal|

Computation for Diameters

α is the error in angle of rotation α = (xc.g,cw + xcg.,ccw)/(-4L)

β is the angle that the robot deviates β = (xc.g,cw - xcg.,ccw)/(-4L)

R is the radius curvature of curved path R = (L/2)/sin(β/2)

Ed = DR/DL = (R+b/2)/(R-b/2)

Computation for wheelbase

bactual/90 = bnominal/(90-α)

bactual = (90/(90-α)). Bnominal

Hence,Eb = 90/90-α

Corrections

To keep average diameter constant we get Da = (DR + DL)/2

Using this and the equation for Ed we get DL = 2.Da / (Ed + 1) DR = 2.Da / ((1/Ed) + 1)

Results

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

Le – line where A expects B to be

Lm – line where A actually finds B

Even if B hit a bump orientation error measurement wont be affected

Smart Encoder Trailer