Lecture 23

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# Lecture 23 - PowerPoint PPT Presentation

Lecture 23. Dimitar Stefanov. Wheelchair kinematics. Recapping. Rolling wheels . Instantaneous Centre of Curvature (ICC). Nonholonomic constraint. motion must be consistent. Position Estimation. (x n+1 , y n+1 ). (x n , y n ). Basic position estimation equations are:. where:.

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### Lecture 23

Dimitar Stefanov

Wheelchair kinematics

Recapping

Rolling wheels

Instantaneous Centre of Curvature (ICC)

Nonholonomic constraint

motion must be consistent

Position Estimation

(xn+1, yn+1)

(xn, yn)

Basic position estimation equations are:

where:

D = vehicle displacement along path;

Ackerman 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)

Θo

Θi

Ackerman equation:

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)

ΘSA

Θo

Θi

ΘSA = vehicle steering angle.

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

Tricycle
• 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 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 Drives
• Minimum is a 3 wheel configuration.
• Each individual motor are driven independently, using velocity control.
Omni-Directional Drives, continue

Let’s note the velocity of the wheelchair platform in x and y direction with Vx and Vy respectively.

Beacon-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.
Triangulation
• 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.
Triangulation
• 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 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