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Lecture 23

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

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  1. Lecture 23 Dimitar Stefanov

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

  3. Position Estimation (xn+1, yn+1) (xn, yn) Basic position estimation equations are: 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) 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.

  6. Ackerman Steering (cont.2) ΘSA Θo Θi ΘSA = vehicle steering angle.

  7. 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

  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

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