Introduction to Inertial Measurement Units!
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1 !! Introduction to Inertial Measurement Units! Gordon Wetzstein! Stanford University! EE 267 Virtual Reality! Lecture 9! stanford.edu/class/ee267/! April 25, 2016!
2 Lecture Overview!! overview of inertial sensors: gyroscopes! accelerometers! magnetometers! specs of our prototype IMU! Arduino introduction, overview, short tutorial (more in lab)! coordinate systems (world, body/sensor, transforms)!
3 primary goal: track head orientation! inertial sensors required to determine yaw, pitch, roll! oculus.com!
4 yaw, pitch, roll angles are transform from body/ sensor coordinates to inertial coordinates! need to apply negative angle to go the other way! oculus.com!
5 from lecture 2:! vertex in clip space! vertex! v clip = M proj! M view! M model!v oculus.com!
6 from lecture 2:! vertex in clip space! vertex! v clip = M proj! M view! M model!v projection matrix! view matrix! model matrix! oculus.com!
7 from lecture 2:! vertex in clip space! vertex! v clip = M proj! M view! M model!v projection matrix! view matrix! model matrix! rotation! translation! ( ) M view = R!T T ("eye oculus.com!
8 from lecture 2:! vertex in clip space! vertex! v clip = M proj! M view! M model!v projection matrix! view matrix! model matrix! rotation! translation! ( ) M view = R!T T ("eye oculus.com! view matrix for stereo camera:! M stereo view = T! " # ± ipd 2,0,0 $ % & ' R 'T (eye ( )
9 from lecture 2:! vertex in clip space! vertex! v clip = M proj! M view! M model!v projection matrix! view matrix! model matrix! rotation! translation! ( ) M view = R!T T ("eye oculus.com! body/sensor frame! inertial frame!
10 from lecture 2:! vertex in clip space! vertex! v clip = M proj! M view! M model!v projection matrix! view matrix! model matrix! oculus.com! R = R z rotation! translation! ( ) M view = R!T T ("eye roll! pitch! yaw! (!" z )# R x (!" x )# R y!" y order of rotations! ( )
11 this is the orientation we want to track! oculus.com! R = R z roll! pitch! yaw! (!" z )# R x (!" x )# R y!" y order of rotations! ( )
12 ATTENTION!! yaw, pitch, roll (or Euler angles) determine orientation of head w.r.t. world! to integrate into graphics pipeline (i.e. view matrix), need to rotate world the other way around in front of HMD! oculus.com! R = R z roll! pitch! yaw! (!" z )# R x (!" x )# R y!" y order of rotations! ( )
13 What do Inertial Sensors Measure?! gyroscope measures angular velocity in degrees/sec! accelerometer measures linear acceleration in m/s 2! magnetometer measures magnetic field strength in ut (micro Tesla) or Gauss! 1 Gauss = 100 ut!!! a! m!
14
15 History of Gyroscopes! invented by Leon Foucault in 1852! wanted to demonstrate earth s rotation w.r.t. gyro! doesn t spin long enough for that experiment!
16 History of Gyroscopes! critical for inertial measurements in ballistic missiles, aircrafts, drones, the mars rover, pretty much anything that moves!! WWII era gyroscope used in the V2 rocket!
17 MEMS Gyroscopes! today, we use microelectromechanical systems (MEMS)! Coriolis Force! wikipedia! quora.com!
18
19 Gyroscopes! gyro model:!!! =! + b + "
20 gyro model:! Gyroscopes! ( )! 2! =! + b + "! ~ N 0," gyro true angular velocity! additive, zero-mean Gaussian noise! bias!
21 ! gyro model:! Gyroscopes! ( )! 2! =! + b + "! ~ N 0," gyro true angular velocity! additive, zero-mean Gaussian noise! bias! 3 DOF = 3 gyros measure 3 orthogonal axes, assume no crosstalk! oftentimes, bias is temperature-dependent and not static, but we ll model it as a quantity that doesn t change! also add additive noise to account for measurement errors!
22 ! Gyroscopes! from gyro measurements to orientation use Taylor expansion!! ( t + "t) #! ( t) +! ( t)"t + O ("t 2 )
23 ! Gyroscopes! from gyro measurements to orientation use Taylor expansion! have: angle at! last time step! have:! time step! ( ) #! ( t) +! t! t + "t want: angle at! current time step! ( ) ( )"t + O "t 2 =! approximation error! have: gyro measurement! (angular velocity)!
24 Gyro Integration: linear motion, no noise, no bias!
25 Gyro Integration: linear motion, noise, no bias!
26 Gyro Integration: linear motion, no noise, bias!
27 Gyro Integration: nonlinear motion, no noise, no bias!
28 Gyro Integration: nonlinear motion, noise, bias!
29 Gyro Integration! works well for linear motion, no noise, no bias = unrealistic! even if bias is know and noise is zero! drift (from integration)! bias & noise variance can be estimated, other sensor measurements used to correct for drift (sensor fusion)! accurate in short term, but not reliable in long term due to drift!
30 Gyro Advice! always be aware of what units you are working with:! degrees per second v radians per second!
31 Accelerometers! measure linear acceleration a = a g +a l! without motion: read gravity vector a = a g pointing UP! with magnitude 9.81 m/s2 = 1g! with motion: combined gravity vector a g and linear IMU acceleration a l!
32 chipworks!
33 capacitive! plates!
34
35 ! advantages:! points up on average! problem:! Accelerometers! accurate in long term because no drift and the earth s center of gravity (usually) doesn t move! noisy measurements! unreliable in short run due to motion (and noise)! complementary to gyro measurements!!
36 Accelerometers! fusing gyro and accelerometer data = 6 DOF sensor fusion! can correct tilt only no information about heading (know where down is, but don t know which direction)! sensor fusion can get little tricky, will discuss next lecture!
37 Positional Tracking with Accelerometers! why not double-integrate acceleration for positional tracking?! assume you can remove gravity vector (which is not trivial)! two ODEs to estimate linear velocity and position:! from accelerometer! x ( t +1)! x ( t) + x t ( )"t x( t + "t)! x( t) + x ( t)"t
38 Positional Tracking with Accelerometers! error grows quadratically!!
39 Magnetometers! lifescience.com! wikipedia!
40
41 Magnetometers! measure earth s magnetic field in Gauss or ut! 3 orthogonal axes = vector pointing along the magnetic field! actual direction depends on latitude and longitude!! distortions due to metal / electronics objects in the room or in HMD!
42 Magnetometers! measure earth s magnetic field in Gauss?! distortions due to metal / electronics objects in the room or in HMD!
43 Magnetometers! difficult to work with magnetometers without proper calibration! we will not use the magnetometer in the HW! LaValle et al.!
44 Magnetometers! advantages:! problems:! complementary to accelerometer - gives heading! affected by metal, distortions of magnetic field! need to know location, even when calibrated (e.g. GPS)! together with gyro + accelerometer = 9 DOF sensor fusion!
45 Ship Navigation with Compass! can measure north, ship s speed, and time! initial position known! map from game pirates!!
46 Ship Navigation with Compass! can measure north, ship s speed, and time! initial position known! dead reckoning same drift as in gyro integration! map from game pirates!!
47 Prototype IMU! 9 DOF IMU: InvenSense MPU-9255 = updated model of what was in the Oculus DK2! 3 axis gyro, 3 axis accelerometer, 3 axis magnetometer all on 1 chip (we ll only use gyro and acc, but we ll give you code to read mag if you want to use it in your project)! interface with I2C (serial bus) from Arduino!
48 Prototype IMU! to host:! serial via USB! I2C! Arduino Metro! InvenSense MPU-9255!
49 MPU-9255 Specs! multi-chip module: 1 die houses gyro & accelerometer, the other the magnetometer! magnetometer: Asahi Kasei Microdevices AK8963 ( 3 rd party device )! 9x 16 bit ADCs for digitizing 9DOF data!
50 MPU-9255 Specs!! gyro modes: ±250, ±500, ±1000, ±2000 /sec! accelerometer: ±2, ±4, ±8, ±16 g! magnetometer: ±4800 ut configure using registers (see specs) via I2C! also supports on-board Digital Motion Processing (DMP ) sorry, we don t have access! we ll provide starter code for Arduino in lab (easy to use for beginners, not consumer product grade!)!
51 MPU-9255 Specs!! gyro modes: ±250, ±500, ±1000, ±2000 /sec! accelerometer: ±2, ±4, ±8, ±16 g! magnetometer: ±4800 ut metric _ value = raw _ sensor _ value 2 15!1 "max_ range
52 MPU-9255 Coordinate Systems! gyro & accelerometer! magnetometer!
53 How to read data from IMU! I2C = serial interface with 2 cables (also see next lab)! microcontroller to read, we ll use Arduino Metro Mini! schematics - which pins to connect where! quick intro to Arduino! Wire library to stream out data via serial! serial client in C/C++!
54 How to read data from IMU!
55 How to read data from IMU! 3.3V! connect power & ground!
56 How to read data from IMU! 3.3V! connect power & ground! connect I2C clock (SCL,A5) and data (SDA,A4) lines!
57 How to read data from IMU! 3.3V! connect power & ground! connect I2C clock (SCL,A5) and data (SDA,A4) lines! connect micro USB for power and data transfer!
58 Introduction to Arduino! open source microcontroller hardware & software! directly interface with sensors (i.e. IMU) and process raw data! we will be working with Arduino Metro Mino (Adafruit.com)! use Arduino IDE for all software development, installed on all lab machines! if you want to install it on your laptop, make sure to get:! IDE: FTDI drivers: Wire library (for serial & I2C):
59 Introduction to Arduino (Random Test Program)! variable definition! setup function = initialization! loop function = runtime callback! connected to COM1 serial port!
60 Introduction to Arduino!! need to stream data from Arduino to host PC use Wire library for all serial & I2C communication! use provided C/C++ class to read from host PC (see lab)!
61 Introduction to Arduino! read from I2C (connected to IMU)! write to I2C (connected to IMU)! setup function = one time initialization! open serial connection to communicate with host PC! set registers to configure IMU!
62 Read Serial Data in Windows! serial ports called COMx (USB serial usually COM3-COM7)! 1.! establish connection to correct COM port (choose appropriate baud rate)! 2.! read incoming data (in a thread)!
63 ! Summary! coordinate systems (world, body/sensor, inertial, transforms)! overview of inertial sensors: gyroscopes, accelerometers, and magnetometers! specs of our prototype IMU! Arduino introduction, overview, short tutorial (more in lab)!
64 Next Lecture! IMU sensor fusion! 6 DOF tilt correction! rotations with quaternions! complementary filtering!
65 Additional Information! D. Sachs Sensor Fusion on Android Devices: A Revolution in Motion Processing, Google Tech Talks 2010, Video on youtube.com ( S. LaValle, A. Yershova, M. Katsev, M. Antonov Head Tracking for the Oculus Rift, Proc. ICRA 2014!
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