1. ECE 450 Introduction to Robotics Section: 50883 Instructor: Linda A. Gee 10/14/99 Lecture 12

2. 2 Dead Reckoning Term Dead Reckoning was derived from a former sailing term: Deduced Reckoning Mathematical procedure to determine present location of an object by advancing previous position through known course and velocity

3. Lecture 123 Dead Reckoning cont’d To calculate heading, the system counts the wheel rotations to obtain longitudinal displacement and uses frictional driven steering Implementations Odometry: instrumentation with optical encoders coupled with motor armatures or wheel axes Magnetic or Inductive proximity sensors with velocity feedback information

4. Lecture 124 Heading Function is derived from an onboard steering angle sensor Supplied by a magnetic compass or gyro Calculated from differential odometry incremental displacement along a path that is broken into x, y components in terms of elapsed time and distance traveled x n+1 = x n + D sin  y n+1 = y n + Dcos 

5. Lecture 125 Odometry Sensors Brush encoders Potentiometers Synchros Resolves Optical encoders Magnetic encoders Inductive encoders Capacitive encoders Rotational displacement and velocity sensors

6. Lecture 126 Potentiometers Low cost rotational displacement sensors Easy sensors to integrate Apply voltage divider Disadvantage: poor reliability due to dust and dirt build up

7. Lecture 127 Synchros Rotating electromagnetic device that transmits angular information electrically Forms a variable-coupling transformer Types of synchros transmitters, receivers differentials control transformers, linear transformers resolvers, differential resolvers transolvers

8. Lecture 128 Synchros cont’d Most widely used synchro: 3-phase transmitter/receiver pair Synchro receiver is electrically identical to the transmitter

9. Lecture 129 Resolver Special configuration of the synchro Gives voltages proportional to the sin and cos of the rotor angle Offers a rugged, reliable means for quantifying absolute angular position Advantages: accurate, low cost, small physical requirements

10. Lecture 1210 Optical Encoders Developed in the mid-1940s by the Baldwin Piano Company for electric organs to mimic the sound of other musical instruments Advantages: digital output, low cost, reliable, immune to noise Types of encoders incremental absolute

11. Lecture 1211 Incremental Encoders Easier to integrate than absolute encoders Example: –Single channel tachometer encoder uses square wave pulses for each shaft revolution Trade-off: resolution vs. rate Phase quadrature incremental encoders are immune to low speed instabilities due to the use of a second channel

12. Lecture 1212 Absolute Encoders Used for slower rotational applications Infrequent rotations steering angle Disadvantages Not tolerant of power interruption Operational limitations with temperature

13. Lecture 1213 Doppler and Inertial Navigation These techniques are employed to reduce the effects of slippage during navigation Doppler Navigation used in maritime and aeronautical applications to yield velocity measurements principle of operation: based on Doppler shift in frequency observed when radiated energy reflects from a surface that is moving with respect to the emitter

14. Lecture 1214 Doppler Navigation cont’d Other applications of Doppler Navigation include Maritime systems: acoustical energy is reflected from the ocean floor Airborne systems: sense microwave RF energy bouncing off the surface of the earth

15. Lecture 1215 Inertial Navigation Developed originally for the deployment of aircraft Technique later applied to missles and nuclear submarines Inertial Navigation Principle of operation: senses minute accelerations in each directional axes; integrating over time to derive velocity and position uses gyroscopes and accelerometers

16. Lecture 1216 Design Issues for Drive and Steering Configurations Maneuverability translate or change direction of motion with respect to the environment Controllability hardware, software to control mobility Traction minimize slippage under variable conditions Climbing traverse discontinuities in floor or ground surface

17. Lecture 1217 Design Issues cont’d Stability sufficient stability for the payload to address –safety, accleration, tilt, and roll Efficiency power consumption and conservation issues Maintenance ease of maintaining components functionally

18. Lecture 1218 Design Issues concluded Environmental impact drive and steering mechanisms do not impace the floor or ground Navigational considerations dead reckoning considerations with respect to the surroundings

19. Lecture 1219 Navigational Approaches Differential Steering consists of two individually controlled wheels –spin in place –maneuver through congested areas Ackerman Steering automotive industry uses this approach –inside front wheel rotates at a sharper angle than the outside wheel in a turn –reduces tire slippage –provides accurate dead reckoning –good choice for outdoor autonomous vehicles

20. Lecture 1220 Navigational Approaches cont’d Synchro Drive uses three or more wheels that are mechanically coupled wheels rotate in the same direction at the same speed offers reduced slippage since all wheels generate equal and parallel force vectors at all times three-point configuration works well for stability and traction use a steering angle encoder to address heading

21. Lecture 1221 Navigational Approaches cont’d Tricycle Drive uses a single driven front wheel two passive rear wheels center of gravity moves away from the front wheel when approaching an incline which leads to loss of traction

22. Lecture 1222 Navigational Approaches concluded Omni-Directional Drive Derive the position and velocity from the motor in terms of –tangential velocity of each wheel –rotational speed of each motor –rotational rate of the base –wheel radius

23. Lecture 1223 Internal Position Error Correction Uses absolute encoders to comprise a compliant linkage rotary encoders Compliant linkage addresses momentary controller errors without transferring any force eliminates wheel slippage Provides heading reference information in terms of world coordinates