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:

cos

sin

1

1

Dyy

Dxx

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:

l

doi 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 l

d cot

2cot

l

diSA 2

cotcot

• 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, continue

Let’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