Dancing in the dark
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Slides used during "Dancing in the dark" lecture on basic principles of both Inertial Navigation and Navigation in general held during #balccon2k18 by Bogdan Doroslovac.
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Dancing in the dark
- 1. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 1 Dancing in the dark
- 2. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 2 Bogdan Doroslovac Advanced Software Engineer www.linkedin.com/in/bogdandoroslovac bogdan.doroslovac@zuehlke.com +381 69 210 9949 About me
- 3. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 4
- 4. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 5 Navigation /navɪˈɡeɪʃ(ə)n/ noun “The process or activity of accurately ascertaining one's position and planning and following a route.” Google
- 5. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 6 Inertial VS Other • Celestial Navigation • Radio Navigation • Radar Navigation • Satellite Navigation
- 6. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 7 Inertial VS Other Inertial navigation • Navigation based of inertial sensors ☺ • Dead reckoning • No external reference
- 7. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 8 Inertial Navigation PROS • Reliable and redundant • (Example ADIRU) • Nearly impossible to spoof • Self-reliant • No external reference • Typically high rates ( >500 Hz)
- 8. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 9 Inertial Navigation CONS • Error on time (actually 𝑡 𝑛 ) • Pricy (especially in critical applications) • No correction possible without external reference • Calibration non-trivial
- 9. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 10 Navigation 3 Degrees Of Freedom (3DOF) 𝐹 = 𝑚𝑎 - II Newton’s law (well … assuming m = const.) 𝐹 = 𝑚 𝑑𝑣 𝑑𝑡 𝐹 = 𝑚 𝑑𝑟 𝑑2 𝑡 𝑟 = 𝑚 ඵ 𝐹 + 𝑪
- 10. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 11 Accelerometer /əkˌsɛləˈrɒmɪtə/ noun “An instrument for measuring the acceleration of a moving or vibrating body.” Google • Sensor measuring specific force: ത𝐹 = ത𝑎 + ҧ𝑔 • Accelerometer in freefall: ത𝐹 = 0 • Accelerometer still on Earth: ത𝐹 = ҧ𝑔
- 11. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 12 XKCD -> 𝒈 𝒎 ഥ𝒈 ?
- 12. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 13 Earth Models • Flat Earth • Spherical Earth • Ellipsoid Earth • Alpeoid & Geoid • WGS84 • World Gravity Standard 84
- 13. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 14 Accelerometer Types • Mechanical / Potentiometric • Capacitive accelerometers • Piezoelectric accelerometers • Piezo-resistive accelerometers • Variable inductance accelerometers • Hall Effect accelerometers • Magnetoresistive accelerometers • FBG Based accelerometers • Heated Gas accelerometers • MEMS-Based Accelerometers
- 14. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 15 Reference frames
- 15. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 16 𝑋 𝐼 − Vernal Equinox 𝑍 𝐼 − True North [0,0,0] − Origin at Earth center of mass 𝑌 𝐼 − Completing Right Cartesian frame Reference frames Inertial
- 16. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 17 True north? There is more then one north • Magnetic North • Geomagnetic North • Rotational (True) North
- 17. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 18 𝑋 𝐸𝐶𝐸𝐹 − Greenwich x Equator 𝑍 𝐸𝐶𝐸𝐹 − True North [0,0,0] − Origin at Earth center of mass 𝑌 𝐸𝐶𝐸𝐹 − Completing Right Cartesian frame Reference frames ECEF Earth Centered Earth Fixed
- 18. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 19 Reference frames NED and ENU North East Down East North Up 𝑋 𝑁𝐸𝐷 − North 𝑌 𝑁𝐸𝐷 − East 𝑍 𝑁𝐸𝐷 − Down [0,0,0] − Origin at referent point 𝑋 𝐸𝑁𝑈 − East 𝑌 𝐸𝑁𝑈 − North 𝑍 𝐸𝑁𝑈 − Up [0,0,0] − Origin at referent point
- 19. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 20 Reference frames Body 𝑋 𝐵𝑜𝑑𝑦 − Dominant Body axis 𝑍 𝐵𝑜𝑑𝑦 − Down (correlated to gravity) [0,0,0] − Origin at center of mass 𝑌 𝐵𝑜𝑑𝑦 − Completing Right Cartesian frame
- 20. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 21 3DOF VS 6DOF
- 21. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 22 Transformation matrices (Euler Angle) 𝑇𝑥(Φ) = 1 0 0 0 cos(−Φ) sin(Φ) 0 sin(Φ) cos(Φ) 𝑇𝑌(Θ) = cos(−Θ) 0 sin(Θ) 0 1 0 sin(Θ) 0 cos(Θ) 𝑇𝑧(Ψ) = cos(−Ψ) sin(Ψ) 0 sin(Ψ) cos(Ψ) 0 0 0 1 𝑇𝑟𝑜𝑡 Ψ, Θ, Φ = 𝑇𝑧 Ψ 𝑇𝑌 Θ 𝑇𝑥(Φ) PITCH YAW ROLL
- 22. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 23 Rotation 3 Degrees Of Freedom (3DOF) τ = 𝐼α - Euler angular acc (well … assuming I = const.) τ = 𝐼 𝑑ω 𝑑𝑡 τ = 𝐼 𝑑φ 𝑑2 𝑡 φ = 𝐼 ඵ τ + 𝑪
- 23. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 24 Navigation 6 Degrees Of Freedom (6DOF) 𝐹 = 𝑚𝑎 - II Newton’s law τ = 𝐼α - Euler angular acc 𝐼 = 𝐼 𝑥𝑥 𝐼 𝑥𝑦 𝐼 𝑥𝑧 𝐼 𝑦𝑥 𝐼 𝑦𝑦 𝐼 𝑦𝑧 𝐼𝑧𝑥 𝐼𝑧𝑦 𝐼𝑧𝑧 = 𝐼 𝑥𝑥 𝐼 𝑦𝑦 𝐼𝑧𝑧 𝑚 = 𝑚 𝑡 𝐼 = 𝐼 𝑚 𝑡 = 𝐼(𝑡)
- 24. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 25 Navigation 6 Degrees Of Freedom (6DOF) 𝑟 = 𝑚 ඵ 𝐹 + 𝑪 φ = 𝐼 ඵ τ + 𝑪 𝐼𝑛𝑡𝑔𝑟𝑎𝑙: න 𝑑𝑥 ~ 𝑡=0 ∞ Δ𝑥 𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒: 𝑑𝑥 𝑑𝑡 ~ Δ𝑥 Δ𝑡
- 25. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 26 Gyroscope /əkˌsɛləˈrɒmɪtə/ noun “Glorified spinning top” “Device capable of persistent heading awareness” 2 Basics types: • Position • Rate MEMS Gyro DTG (Dynamically Tuned Gyro) RLG (Ring Laser Gyro) FOG (Fiber-Optic Gyro)
- 26. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 27 Gyroscope Types • MEMS Gyro • DTG (Dynamically Tuned Gyro) • RLG (Ring Laser Gyro) • FOG (Fiber-Optic Gyro) ADIRU (Air Data Inertial Reference Unit) ITAR (International Trafficking Arms Regulation) MTCR (Missile Technology Control Regime)
- 27. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 28 Errors, Quirks, Goblins and Gremlins • Noise (Signal to noise) • Drift • Bias • Nonlinearity • Error Accumulation ( E = f(t))
- 28. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 29 DEMO (https://github.com/baghatur/BalCCon2k18_Demo)
- 29. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 30 QUATERNION ROTATION Food For Thought
- 30. © Zühlke 2018Dancing in the dark | Bogdan Doroslovac 12. September 2018 Slide 31 Qestions & Answers