This document discusses various methods for estimating the position and orientation of a wheelchair using sensors and kinematic models. It begins by recapping concepts related to wheelchair kinematics like rolling wheels and the instantaneous center of curvature. It then describes using basic equations to estimate position based on displacement, orientation, and encoder readings from the wheels. It also discusses Ackerman steering modeling for outdoor vehicles. Additional sections cover synchro drive modeling, omnidirectional drive configurations, and beacon-based localization using trilateration or triangulation with active light sources.

1. Lecture 23
Dimitar Stefanov

2. Wheelchair kinematics
Recapping
Rolling wheels
Instantaneous Centre of Curvature (ICC)
motion must be
consistent
Nonholonomic
constraint

3. Position Estimation
(xn, yn)
(xn+1, yn+1)
Basic position estimation equations are:








cos
sin
1
1
D
y
y
D
x
x
n
n
n
n
where:
D = vehicle displacement along path;
Θ = vehicle orientation (heading).

4. 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.

5. Ackerman Steering (cont.1)
Θi
Θo
Ackerman equation:
l
d
o
i 


 cot
cot
where:
Θi = relative steering angle of inner wheel;
Θo = relative steering angle of outer wheel;
l = longitudinal wheel separation;
d = lateral wheel separation.

6. Ackerman Steering (cont.2)
Θo Θi
ΘSA
ΘSA = vehicle steering angle.
i
SA
l
d



 cot
2
cot
l
d
i
SA
2
cot
cot 




7. • 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

8. Synchro Drive
Dead reckoning for synchro-drive:

9. The MECANUM wheel (concept)

10. 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

11. 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.

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

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

14. 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.

15. 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.

16. 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.

17. 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.

18. Active rangefinder chip – an example
TRC Beacon navigation System

19. Light guidance system, Dohi Lab, Japan