[PPT]No Slide Title - Creating Web Pages in your Account ...web.cecs.pdx.edu/~mperkows/Rehabilitation_Robots/lecture... · Web viewLecture 23 Dimitar Stefanov Position Estimation

Lecture 23Lecture 23

Dimitar Stefanov

Wheelchair kinematicsRecapping

Rolling wheels Instantaneous Centre of Curvature (ICC)

motion must be consistent

Nonholonomic constraint

Position EstimationPosition Estimation

(xn, yn)

(xn+1, yn+1)

Basic position estimation equations are:

cossin

1

1

DyyDxx

nn

nn

where:D = vehicle displacement along path;Θ = vehicle orientation (heading).

Ackerman SteeringAckerman Steering

• The inside front wheel is rotated slightly sharper than the outside wheel (reduces tire slippage).

• Ackerman steering provides a fairly accurate dead-reckoning solution while supporting traction and ground clearance.

• Generally the method of choice for outdoor autonomous vehicles.

Ackerman Steering (cont.1)Ackerman Steering (cont.1)ΘiΘo

Ackerman equation:

ld

oi cotcot

where:Θi = relative steering angle of inner wheel;Θo = relative steering angle of outer wheel;l = longitudinal wheel separation;d = lateral wheel separation.

Ackerman Steering (cont.2)Ackerman Steering (cont.2)Θo Θi

ΘSA

ΘSA = vehicle steering angle.

iSA ld

cot2

cot

ld

iSA 2cotcot

• Three or more wheels are mechanically coupled. All wheels have one and the same orientation and rotate in the same direction at the same speed.

• Improved dead reckoning.• Synchro drives use belt, chain or gear drives.• Problems in steering accuracy with wear/tear

Synchro DriveSynchro Drive

Synchro DriveSynchro Drive

Dead reckoning for synchro-drive:

The MECANUM wheel (concept)The MECANUM wheel (concept)

TricycleTricycle• If a steerable drive wheel and encoder is used,

then we can use the Ackerman steering model.• Otherwise use we the differential odometry mode

Tricycle ProblemsTricycle Problems

• When going uphill the center of gravity of the wheelchair tends to move away from driven wheel. Causing loss of traction.

• As Ackerman-steered design causes surface damage.

Omni-Directional DrivesOmni-Directional Drives• Minimum is a 3 wheel configuration.• Each individual motor are driven

independently, using velocity control.

Omni-Directional Drives, continueOmni-Directional Drives, continueLet’s note the velocity of the wheelchair platform in x and y direction with Vx and Vy respectively.

Beacon-based LocalizationBeacon-based Localization• Trilateration

– Determine wheelchair position from distance measurements to 3 or more known beacons.

• Triangulation

– Determine wheelchair position for angular measurements to 3 or more known beacons.

TriangulationTriangulation•Solution to constraint equations relating the pose of an observer to the positions of a set of landmarks.

•Usually, the problem is considered in the 2D case.

TriangulationTriangulation

•Passive•Active

Active triangulation (AT):-A controlled light source (such as a laser) is positioned at point P1.-A imaging detector is placed at P2.-The distance A is preliminary known.-The image detector measures the angle position of the reflected-light beam.

•AT requires one camera or one position sensitive detector;•AT does not depend on the ambient lighting of the object.

Active triangulationActive triangulation

Photo detector– one- or two-dimensional array detector such as a CCD camera or photosensitive line.

Calibration – signals are measured on two preliminary known distances between the sensors and the object.

Active rangefinder chip – an example

TRC Beacon navigation System

Light guidance system, Dohi Lab, Japan