ECE 450 Introduction to Robotics

Section: 50883

Instructor: Linda A. Gee

10/14/99

Lecture 12

Lecture 12 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

Lecture 12 3

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

Lecture 12 4

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

• xn+1 = xn + D sin

• yn+1 = yn + Dcos

Lecture 12 5

Odometry Sensors

• Brush encoders• Potentiometers• Synchros• Resolves

• Optical encoders• Magnetic encoders• Inductive encoders• Capacitive encoders

Rotational displacement and velocity sensors

Lecture 12 6

Potentiometers

• Low cost rotational displacement sensors

• Easy sensors to integrate

• Apply voltage divider

• Disadvantage: poor reliability due to dust and dirt build up

Lecture 12 7

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

Lecture 12 8

Synchros cont’d

• Most widely used synchro:• 3-phase transmitter/receiver pair

• Synchro receiver is electrically identical to the transmitter

Lecture 12 9

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

Lecture 12 10

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

Lecture 12 11

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

Lecture 12 12

Absolute Encoders

• Used for slower rotational applications

• Infrequent rotations• steering angle

• Disadvantages• Not tolerant of power interruption

• Operational limitations with temperature

Lecture 12 13

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

Lecture 12 14

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

Lecture 12 15

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

Lecture 12 16

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

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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

Lecture 12 18

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

Lecture 12 19

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

Lecture 12 20

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

Lecture 12 21

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

Lecture 12 22

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

Lecture 12 23

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