Dimitar Stefanov

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Lecture 23

• Dimitar Stefanov

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Wheelchair kinematics
Recapping
Rolling wheels
Instantaneous Centre of Curvature (ICC)
Nonholonomic constraint
motion must be consistent
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Position Estimation
(xn1, yn1)
(xn, yn)
Basic position estimation equations are
where
D vehicle displacement along path T vehicle
orientation (heading).
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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.

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Ackerman Steering (cont.1)
Ti
To
Ackerman equation
where
Ti relative steering angle of inner wheel To
relative steering angle of outer wheel l
longitudinal wheel separation d lateral wheel
separation.
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Ackerman Steering (cont.2)
TSA
To
Ti
TSA vehicle steering angle.
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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.
• Improved dead reckoning.
• Synchro drives use belt, chain or gear drives.
• Problems in steering accuracy with wear/tear

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Synchro Drive
Dead reckoning for synchro-drive
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The MECANUM wheel (concept)
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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

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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.

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Omni-Directional Drives

• Minimum is a 3 wheel configuration.
• Each individual motor are driven independently,
  using velocity control.

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Omni-Directional Drives, continue
Lets note the velocity of the wheelchair
platform in x and y direction with Vx and Vy
respectively.
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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.
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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.

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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.

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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.
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Active rangefinder chip an example
TRC Beacon navigation System
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Light guidance system, Dohi Lab, Japan