ECE 450 Introduction to Robotics Section: 50883 Instructor: Linda A. Gee 10/14/99 Lecture 12.
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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
Lecture 12 17
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
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