Post on 07-May-2018
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:
cossin
1
1
DyyDxx
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:
ld
oi 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 ld
cot2
cot
ld
iSA 2cotcot
• 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
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, continueLet’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.