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Navigation

Navigation. Martin La Rocque Member RSSC Institute of Navigation (ION) Associate Fellow Royal Institute of Navigation United States Power Squadron. Navigation. Dead Reckoning Compass Odometry GPS (Global Positioning System) Way-Point Calculation. Dead Reckoning (DR). Definition

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Navigation

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  1. Navigation • Martin La Rocque • Member RSSC • Institute of Navigation (ION) • Associate Fellow Royal Institute of Navigation • United States Power Squadron

  2. Navigation • Dead Reckoning • Compass • Odometry • GPS (Global Positioning System) • Way-Point Calculation

  3. Dead Reckoning (DR) • Definition • Etymology (Word Definition) • Animal Navigation • Marine Navigation • Air Navigation • Automotive Navigation • Differential Drive (DR)

  4. Dead Reckoning Definition • Dead Reckoning is the process of estimating a global position of a vehicle by advancing a known position using course, speed, time and distance to be traveled • In other words figuring out where you momentarily are or will be at a certain time if you hold speed, time and course you plan to travel

  5. Dead Reckoning (DR) • Dead Reckoning (DR) is a method of navigation used in ships, aircraft, trucks, cars, rail engines, construction site engines, and more recently mobile robots. • Essentially it is used to estimate an object’s position based on the distant traveled in its current direction from its previous position.

  6. Etymology (Word Derivation) • There is some controversy about the derivation of the phrase. • Deduced reckoning is not supported according to the Oxford English Dictionary, the phrase dead reckoning dates from Elizabethan times (1605 – 1615)

  7. Animal Navigation • Studies of animal navigation, dead reckoning is more commonly known as path integration, and animals use it to estimate their current location based on the movements they made since their last know position • Animals have also shown to continuously keep track of their location relative to start

  8. Marine Navigation • In Marine Navigation “dead” reckoning plot generally does not take into account the effect of currents or wind • Dead reckoning begins with a known position, or fix • Recorded on a chart • Heading, speed and time

  9. Marine Navigation (Con’t-1) • Speed can be determined by many methods • Was determined aboard ship using a chip log • Pit log referencing engine speed (rpm) against a table of total displacement • Dead reckoning positions are calculated at predetermined intervals, and are maintained between fixes

  10. Marine Navigation (Con’t-2) • Before the marine chronometer, dead reckoning was the primary method of determining longitude • Used by Christopher Columbus and John Cabot on their trans Atlantic voyages

  11. Air Navigation • Traditionally, in air navigation, displacement or position caused by wind were taken into account, using a tool called a wind triangle • Dead reckoning positions were calculated every 300 miles • Dead reckoning in traditional form rarely used

  12. Automotive Navigation • Dead reckoning is implemented in some high-end automotive systems in order to overcome the limitations of GNSS (Global Navigation Satellite System) • A vehicle with dead reckoning would have sensors that record wheel rotation and steering direction

  13. Differential Drive DR • Dead reckoning formulas for the coordinates (x and y), and heading (Ø) for a differential drive robot with encoders on both wheels • x = Rw cos(Ø)(T1 + T2)PI/Tr • y = Rw sin(Ø)(T1 + T2)PI/Tr • Ø = 2PI(T1 + T2)/Tr

  14. Differential Drive DR (Con’t) • Where T1 are the encoder ticks recorded on drive one, T2 are the encoder ticks recorded on drive two, Rw is the radius of each drive wheel, and Tr is the number of encoder ticks recorded in a full, in-place rotation

  15. Compass • Hand Held Magnetic Compass • Hand Bearing Magnetic Compass • Liquid Magnetic Compass • Electronic – Digital Compass • Magnetic Variation – World Wide • Compass Correction • Gyrocompass

  16. Hand Held Magnetic Compass • Floating needle points to Magnetic North • Hand held compass is still used by various outdoor enthusiasts • Some mounted on a grid to aid in determining bearing • Quite often used with a map

  17. Hand Bearing Magnetic Compass • Hand Bearing Magnetic Compass held with a handle • View the compass angle with a prism • Quite often used to determine the position of stars • Usually have a battery operated light for night time use • Valuable for use for celestial navigation

  18. Liquid Magnetic Compass • A Liquid Magnetic Compass is a design that uses a needle or card damped by a fluid • Flush mounted use on boats • Panel mounted often used on airplanes • Provision to correct compass reading

  19. Electronic – Digital Compass • Electronic and/or Digital Compass are solid state compasses • Usually have two or three magnetic field sensors that provide data to a microprocessor or computer • Output either digital or analog voltage proportional to its orientation

  20. Electronic – Digital Compass (Con’t - 1) • This signal is interpreted by a microprocessor or computer and used internally and/or sent to a display • The sensor uses highly calibrated internal electronics to measure the response of the device to the earth’s magnetic field • Point to magnetic North Pole

  21. Electronic – Digital Compass (Con’t – 2) • Small compasses found in clocks, mobile phones and other electronic devices are solid state compasses • The difference between the reading of a solid state compass that reads magnetic North and true North is referred to as variation

  22. Electronic – Digital Compass (Con’t – 3) • Variation in degrees E or W is noted on nautical charts for that area and is updated with chart revisions • Local variation is contained in the GPS (Global Positioning System) data sentence $GPRMC • GPS receivers with two or more antennas now achieve 0.5° in heading accuracy

  23. Magnetic Variation – World Wide Chart

  24. Compass Correction • T – True North • V - Variation in degrees E or W from true N • M - Magnetic Heading • D - Deviation – local magnetic influence • C – Compass Heading (With no deviation this would be equal to Magnetic Heading)

  25. Compass Correction (Con’t-1) • True The true heading from the chart (where 0 degrees is the true north pole) • Virgins The magnetic variation that applies in the area where you are • Make The magnetic heading (after you have allowed for variation) • Dull The compass deviation that applies to the magnetic heading • Company The actual compass heading you will have to steer so that after allowing for variation and deviation you will be heading on your true course

  26. Compass Correction (Con’t-2) • Liquid Compasses used on boats and planes have small magnets on the periphery to compensate for local magnetic deviation • Electronic - Digital compasses do not have the small magnets for compensation, • Some can be partially calibrated by 360° rotation when installed • A deviation table of degrees of difference between compass heading and magnetic heading is required

  27. Deviation Table

  28. Compass Correction (Con’t-3)Deviation Table Small Robot • Preparation a Deviation Table • Prepare a Compass Rose • Align the Compass Rose with a magnetic compass to Magnetic North • Place robot in middle of Compass Rose with a method to rotate the Compass Rose

  29. Compass Correction (Con’t-4) Deviation Table Small Robot • Turn on power to robot and perform a test with wheel power on and note compass heading (Use of a readout is mandatory) • Rotate Compass Rose in 15° increments and note reading – calculate E or W difference • Continue for a full circle of 360° • Use deviation table data to correct the compass heading to magnetic heading

  30. Compass Rose – Deviation Table • Photo of a Compass Rose with Hand Held Compass • Photo of a Compass Rose with Hand Bearing Compass

  31. Compass Correction (Con’t-5) Deviation Table Magnetic Heading • 000 ____ 090 ____ 180 ____ 270 ____ • 015 ____ 105 ____ 195 ____ 285 ____ • 030 ____ 120 ____ 210 ____ 300 ____ • 045 ____ 135 ____ 225 ____ 315 ____ • 060 ____ 150 ____ 240 ____ 330 ____ • 075 ____ 165 ____ 255 ____ 345 ____ • Read compass and subtract if reading greater and enter E - if less add value and enter W

  32. Gyrocompass • A Gyrocompass is similar to a gyroscope • It is a non-magnetic compass that finds true north by using an (electronically powered) fast-spinning wheel and friction forces in order to exploit the rotation of the earth • Used widely on ships as they find true north • Not effected by ferrous metal in ship hull

  33. Odometry • Odometry is the use of data from the movement of encoders to estimate change in position over time • Odometry is used by some robots, whether they are legged or wheeled, to estimate their position relative to a starting position • Some motors have an encoder directly connected – provides for a readout from each motor • Some drive systems with single motor require an encoder to be added – not as accurate as individual encoders on each wheel drive motor

  34. Odometry (Con’t-1) Encoders • Odometry requires a method for accurately counting the rotation of the wheels – optical shaft encoders are commonalty used • Simplest method of location calculation is for a differentially steered robot with a pair of drive wheels and caster tail or nose wheel • Rombass Vacuum a sample

  35. Odometry (Con’t-2) Math • For a differentially steered robot, the location is updated using the following formulas • (1) distance = (left_encoder + right_encoder) /2.0 • (2) theta = (left_encoder – right_encoder) / wheel_base • Where wheel_base is the distance between the differential drive wheels

  36. Holonomic vs Non-Holonomic Robots • Two types of mobile robots • Non-Holonomic robots are ones that cannot instantaneously move in any direction, such as a car • Holonomic robots can instantaneously move in any direction

  37. GPS is a U.S. space-based global radio navigation system that provides reliable positioning, navigation and timing services to military and civilian users on a continuous basis • Anyone with a GPS receiver, the system provides accurate location and time, in any weather and anywhere in the world

  38. Global Positioning System (GPS) • GPS is a U.S. space-based global radio navigation system that provides reliable positioning, navigation and timing services to military and civilian users on a continous basis • Anyone with a GPS receiver, the system provides accurate location and time, in any weather and anywhere in the world

  39. GPS (Con’t-1) • GPS is made up of three parts: • (1) 24 – 32 Satellites orbiting the earth • (2) Control and Monitoring stations on earth • (3) GPS receivers owned by the users • Satellites broadcast signals from space are picked up and identified by GPS receivers. Each receiver then provides three dimensional location (latitude, longitude and altitude) and time.

  40. GPS (Cont-2) • GPS accuracy is approximately 10 meters or less • Quite often this accuracy is better, depending on the location and number of satellites in view • A localize correction system called WAAS (Wide Area Augmentation System) developed by the FAA to improve accuracy • Measurements from reference stations are sent as correction to a synchronous satellite for transmission back to earth • WAAS enabled GPS receivers have accuracy improved to approximately 3 meters

  41. GPS (Con’t-3) • Most GPS receivers have a serial output that is either proprietor and/or NMEA (National Marine Electronic Association) format • LORAN (Long Range Navigation) used prior to GPS had a serial output as does many other marine electronic devices • The baud rate of the data being outputted varies from 4800 baud to 38400 baud

  42. GPS (Con’t-4) • The recommended Minimum Specific GPS/TRANSIT Data (RMC) • Serial output data sentence from a Garmin 17HVS GPC: • $GPRMC,201931,A,4531.3677,N,12257.2458,W,000.0,000.0,160618,013.4,E*65<CR><LF> • Other sentences are outputted

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