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Lecture 23
Dimitar Stefanov
Wheelchair kinematics
Recapping
Rolling wheels
Instantaneous Centre of Curvature (ICC)
motion must be
consistent
Nonholonomic
constraint
Position Estimation
(xn+1, yn+1)
(xn, yn)
Basic position estimation equations are:
x n 1  x n  Dsin 
y n 1  y n  D cos 
where:
D = vehicle displacement along path;
Θ = vehicle orientation (heading).
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:
cot  i  cot  o 
d
l
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)
Θo
ΘSA
Θi
ΘSA = vehicle steering angle.
cot  SA 
d
 cot i
2l
cot  SA  cot i 
d
2l
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
Synchro Drive
Dead reckoning for synchro-drive:
The MECANUM wheel (concept)
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
TRC Beacon navigation System
Light guidance system, Dohi Lab, Japan