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Inertial Measurement Unit-Accelerometer and Gyroscope MPU6050
- 1. Vijay Kumar Professor Mechanical Engineering Chitkara University IMU Fundamental
- 2. Micro: Very small in size. Measured in micrometer(μm) 1 μm = 10-6 m Electro: MEMS have electrical components Mechanical: MEMS have moving parts Systems: Refers to integration of components. We find MEMS in Automobiles (Air bag sensors) Computer printers (Ink jet print heads) Cell phones (RF devices) Optical devices (Micromirrors) MEMS They have also found application in the healthcare domain in devices such as blood pressure monitors, pacemakers, ventilators, and respirators. Air bag crash sensors Active suspension systems Antilock brake systems Ride control systems V K Jadon, Prof., Mechanical Engineering, Chitkara University 2
- 3. Accelerometer 𝑥, 𝑎 𝑘 𝑚 𝑥, 𝑎 𝑘 𝑚 𝑥, 𝑎 −𝑘𝑥 = 𝑚𝑎 𝑘 𝑚 𝑚𝑎𝑠𝑠 𝑖𝑠 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑 𝑎 = − 𝑘 𝑚 𝑥 𝑎 = 𝑓(𝑥) External Force in the direction of displacement =mass×acceleration 𝑚 𝑘𝑥 𝑎 𝐶 = 𝑓(𝐴/𝑥) 𝐶 = 𝑓(𝐴/𝑎) Accelerometer measures linear acceleration Acceleration is opposite to the displacement 𝐶 = 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝐴 = surface area of capacitor plates V K Jadon, Prof., Mechanical Engineering, Chitkara University 3
- 4. Displacement of the frame changes the differential capacitance Capacitive accelerometers offer high sensitivities and are utilized for low-amplitude, low-frequency devices. Accelerometer 𝒙 𝒛 𝒚 Internal moveable assembly Proof mass Spring External Fixed assembly MPU6050 measures linear acceleration in terms of g force Usefulness of accelerometer in IMU will be discussed later V K Jadon, Prof., Mechanical Engineering, Chitkara University 4
- 5. VCC GND SCL SDA XDA XCL ADO INT X Y I2C ProtocolGyro Accelerometer MPU6050 Pinout Clock pulse for I2C Communication Data through I2C communication Data to external sensors Clock pulse to external sensors I2C Slave Address Interrupt digital output The SCL line is the clock signal which synchronize the data transfer between the devices on the I2C bus. Clock signal is generated by the master device.
- 6. The full scale range of the digital output can be adjusted to ±2g, ±4g, ±8g, or ±16g. Three-Axis MEMS Accelerometer with 16-bit ADCs and Signal Conditioning MPU6050: MEMS Accelerometer The MPU-60X0’s 3-Axis accelerometer uses separate proof masses for each axis. Acceleration along an axis induces displacement on the corresponding proof mass, and capacitive sensors detect the displacement differentially. When the device is placed on a flat surface, it will measure 0g on the X- and Y-axes and +1g on the Z-axis (upward). Each sensor has a dedicated ADC for providing digital outputs. V K Jadon, Prof., Mechanical Engineering, Chitkara University 6
- 7. UNO Arduino AREF GND 13 12 ~11 ~10 ~9 8 7 ~6 ~5 4 ~3 2 TX-1 RX-0 IOREF RESET 3.3V 5V GND GND Vin A0 A1 A2 A3 A4 A5 ON TX RX L Arduino Uno Pinout master out slave in master in slave out Serial Clock Slave Select V K Jadon, Prof., Mechanical Engineering, Chitkara University 7
- 8. UNO Arduino AREF GND 13 12 ~11 ~10 ~9 8 7 ~6 ~5 4 ~3 2 TX-1 RX-0 IOREF RESET 3.3V 5V GND GND Vin A0 A1 A2 A3 A4 A5 ON TX RX L MPU6050 Connection V K Jadon, Prof., Mechanical Engineering, Chitkara University 8
- 9. I2C Protocol
- 10. I2C Protocol V K Jadon, Prof., Mechanical Engineering, Chitkara University 10 • Begins with a start bit • 7 bit Address is transmitted • 1 control bit to indicate Master to Read from or write to slave • If communicated slave send ack bit to Master • Master to send 8 bit Internal Register Address • Slave send back ack bit • Master transmits data in 8 bits chunk • Write request – Slave sends ack bit to Master • Read request – Master sends ack bit to Slave I2C addresses are generally 7 bits, yielding an address between 0 and 127. The addresses from 0 to 7 are not used because are reserved. So, the first address that can be used is 8 S B6 B5 B4 B3 B2 B1 B0 R/W Ack B7 B6 B5 B4 B3 B2 B1 B0 Ack B7 B6 B5 B4 B3 B2 B1 B0 Ack S 7 bit Device Address sequence 8 bit internal Register Address sequence 8 bit data sequence • Ends with a stop bit
- 11. V K Jadon, Prof., Mechanical Engineering, Chitkara University 11 <Wire.h> Library Wire.begin(address) function initiates Wire library Wire.beginTransmission(address) begins transmission to the particular sensor Wire.beginTransmission(0b1101000) Wire.endTransmission(address) Transmits data in buffer and return a status byte, 0 for success. Wire.endTransmission(0b1101000) write() buffers data for sending Wire.write(value) Wire.write(string) Wire.write(data, length) value: a value to send as a single byte string: a string to send as a series of bytes data: an array of data to send as bytes length: the number of bytes to transmit write() will return the number of bytes written, though reading that number is optional address: the 7-bit slave address (optional); if not specified, join the bus as a master. Start condition to the slave device with the given address. It asks for data from the internal registers of the slave device S B6 B5 B4 B3 B2 B1 B0 R/W A B7 B6 B5 B4 B3 B2 B1 B0 A B7 B6 B5 B4 B3 B2 B1 B0 A S
- 12. V K Jadon, Prof., Mechanical Engineering, Chitkara University 12 <Wire.h> Library requestFrom() Used by the master to request bytes from a slave device.. The default value is true. If true, requestFrom() sends a stop message after the request, releasing the I2C bus. If false, requestFrom() sends a restart message after the request. Wire.requestFrom(address, quantity) Wire.requestFrom(address, quantity, stop) If false, the bus will not be released, which prevents another master device from requesting between messages. This allows one master device to send multiple requests while in control. The Wire.available() function will return the number of bytes available for retrieval and if that number match with our requested bytes Wire.read() function we will read the bytes from the two registers of the X axis. I2C Scanner
- 14. UNO Arduino AREF GND 13 12 ~11 ~10 ~9 8 7 ~6 ~5 4 ~3 2 TX-1 RX-0 IOREF RESET 3.3V 5V GND GND Vin A0 A1 A2 A3 A4 A5 ON TX RX L MPU6050 Connection V K Jadon, Prof., Mechanical Engineering, Chitkara University 14
- 15. V K Jadon, Prof., Mechanical Engineering, Chitkara University 15 MPU6050 Setup Read Accelerometer data using Arduino Start I2C Communication ― Use Wire.begin() to initiate wire.h ― Wire.beginTransmission(SDA) Slave Device Address (SDA)=1101000 AD0=Low Slave Device Address (SDA)=1101001 AD0=High Reference – Product Specifications (Revision 3.4) Section 9.2 pp33 ― Wire.write(0x6B) Internal Register Address Sequence to access Power management register (0x6B) ― Wire.write(0b00000000) Data Transfer Bit Sequence to awake MPU ― Wire.endTransmission(1101000)
- 16. FS Range AFS_SEL Register Bit LSB Sensitivity ADC Bits ±2g 0 0b00000000 16384 LSB/g 15 bit ±4g 1 0b00001000 8192 LSB/g 14 bits ±8g 2 0b00010000 4096 LSB/g 13 bits ±16g 3 0b00011000 2048 LSB/g 12 bits 𝑥 ≈ 0 𝑦 ≈ 0 𝑧 ≈ 1𝑔 𝑦 ≈ 0 𝑧 ≈ 0 𝑥 ≈ 1𝑔 𝑧 ≈ 0 𝑥 ≈ 0 𝑦 ≈ 1𝑔 V K Jadon, Prof., Mechanical Engineering, Chitkara University 16 Accelerometer Setup The MPU-60X0 features three 16-bit ADCs for digitizing the accelerometer outputs. For precision tracking of both fast and slow motions, the parts feature a user- programmable accelerometer full-scale range of ±2g, ±4g, ±8g, and ±16g. Reference – Product Specifications (Revision 3.4) Section 6.2 pp13 ― Wire.beginTransmission(0b1101000) ― Wire.write(0b00000000) ― Wire.endTransmission(0b1101000) ― Wire.write(0x1C)Reference – Register Map and Description (Revision 4.2) Section 4.5 pp15 Reference – Product Specifications (Revision 3.4) Section 3.1 pp7
- 17. V K Jadon, Prof., Mechanical Engineering, Chitkara University 17 Read Accelerometer Data Reference – Register Map (Revision 4.2) Section 3 pp7 Wire.beginTransmission(0b1101000) 3B and 3C stores Acceleration data along x-axis 3D and 3E stores Acceleration data along y-axis 3F and 40 stores Acceleration data along z-axis We should give starting Internal Register Address to access all Read only registers after that. To transmit all acceleration data, we should write to 0x3B register. ― Wire.write(0x3B) Slave device transmit data in 8 bits(1 byte) Master store integers in 16 bits. ― Wire.endTransmission(0b1101000)
- 18. V K Jadon, Prof., Mechanical Engineering, Chitkara University 18 Read Accelerometer Data For getting hold of the data available in buffer, master has to request using Wire.requestFrom(address, quantity) Wire.requestFrom(0b1101000, 6)Check availability of the data requested by the master Wire.available() It returns the number of received bytes from receive-buffer. Reads a byte that was transmitted from a slave device to a master after a call to requestFrom() using Wire.read() function. The each acceleration data is stored in two register (2 bytes) The data read is to be stored in one variable of int datatype. Every repeated Wire.read() gives the next byte available. accel_rawX = Wire.read()<<8|Wire.read(); 00001010 00001111 00001010-00000000 00001010-00001111 00001010
- 19. V K Jadon, Prof., Mechanical Engineering, Chitkara University 19 Arduino Pseudo Code Set-Up MPU6050 Configure Accelerometer Read Accelerometer Data Every task starts with beginning communication with slave device and ends with terminating communication with slave device begin communication – Slave device address sequence access power management register – internal register address sequence Update power management register to disable SLEEP mode – data transfer sequence terminate communication – stop bit (one time execution) (one time execution) begin communication – Slave device address sequence access accelerometer configure register – internal register address sequence update accelerometer register to set full scale range – data transfer sequence terminate communication – stop bit (data needed continuously) Disable SLEEP mode Set Full Scale range Read accelerometer data
- 20. V K Jadon, Prof., Mechanical Engineering, Chitkara University 20 Arduino Pseudo Code Set-Up MPU6050 Configure Accelerometer Read Accelerometer Data Every task starts with beginning communication with slave device and ends with terminating communication with slave device (data needed continuously) Disable SLEEP mode Set Full Scale range Access Register Read Data begin communication stop communication access accelerometer first data register Read accelerometer data begin communication stop communication Request data Check availability Read 8 bits and store in 16 bits data
- 21. V K Jadon, Prof., Mechanical Engineering, Chitkara University 21 Angle Measurement 𝐹𝑥 𝒙 𝒚 𝒛 𝐹𝑦 𝐹𝑧 𝐹𝑥 2 + 𝐹𝑦 2 + 𝐹𝑧 2 𝐹𝑥 2 + 𝐹𝑦 2 𝐹𝑦 2 + 𝐹𝑧 2 𝐹𝑥 2 + 𝐹𝑧 2 𝒙 𝒚 𝒛 𝐹𝑥 2 + 𝐹𝑦 2 𝐹𝑦 2 + 𝐹𝑧 2 𝐹𝑥 2 + 𝐹𝑧 2
- 22. V K Jadon, Prof., Mechanical Engineering, Chitkara University 22 There are six possible orderings of these three rotation matrices and, in principle, all are equally valid Angle Measurement 𝜓, ∅, 𝜃 are called as Roll, Pitch, and Yaw Angles 𝑅 𝑥 = 1 0 0 0 𝑐𝑜𝑠𝜓 −𝑠𝑖𝑛𝜓 0 𝑠𝑖𝑛𝜓 𝑐𝑜𝑠𝜓 𝑅 𝑦 = 𝑐𝑜𝑠∅ 0 𝑠𝑖𝑛∅ 0 1 0 −𝑠𝑖𝑛∅ 0 𝑐𝑜𝑠∅ 𝑅 𝑧 = 𝑐𝑜𝑠𝜃 −𝑠𝑖𝑛𝜃 0 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃 0 0 0 1 Initial force vector= 0 0 1 𝑮 𝒑 = 𝑮 𝒑𝒙 𝑮 𝒑𝒚 𝑮 𝒑𝒛 = 𝑹 0 0 1 𝑹 𝒙𝒚𝒛 0 0 1 = 𝑹 𝒙(𝜓)𝑹 𝒚(∅) 𝑹 𝒛(𝜃) 0 0 1 𝑹 𝒚𝒛𝒙 0 0 1 = 𝑹 𝒚(∅) 𝑹 𝒛(𝜃)𝑹 𝒙(𝜓) 0 0 1 𝑹 𝒚𝒙𝒛 0 0 1 = 𝑹 𝒚(∅) 𝑹 𝒙(𝜓)𝑹 𝒛(𝜃) 0 0 1 𝑹 𝒛𝒙𝒚 0 0 1 = 𝑹 𝒛(𝜃)𝑹 𝒙(𝜓)𝑹 𝒚(∅) 0 0 1 𝑹 𝒙𝒛𝒚 0 0 1 = 𝑹 𝒙(𝜓)𝑹 𝒛(𝜃)𝑹 𝒚(∅) 0 0 1 𝑹 𝒛𝒚𝒙 0 0 1 = 𝑹 𝒛(𝜃)𝑹 𝒚(∅)𝑹 𝒙(𝜓) 0 0 1
- 23. V K Jadon, Prof., Mechanical Engineering, Chitkara University 23 The last four rotation sequences result in the accelerometer output being function of all three rotation angles and cannot therefore be solved. It is conventional therefore to select either the rotation sequence 𝑅 𝑥𝑦𝑧 or the sequence 𝑅 𝑦𝑥𝑧 to eliminate the yaw rotation ψ and allow solution for the roll φ and pitch θ angles. Angle Measurement 𝑮 𝒑 = 𝑮 𝒑𝒙 𝑮 𝒑𝒚 𝑮 𝒑𝒛 = 𝟏 𝐺 𝑝𝑥 2 + 𝐺 𝑝𝑦 2 + 𝐺 𝑝𝑧 2 𝐺 𝑝𝑥 𝐺 𝑝𝑦 𝐺 𝑝𝑧 = 𝐺 𝑝𝑥 𝐺 𝑝𝑦 𝐺 𝑝𝑧 𝑅 𝑥𝑦𝑧 0 0 1 = 𝑅 𝑥(𝜓)𝑅 𝑦(∅) 𝑅 𝑧(𝜃) 0 0 1 𝑅 𝑥𝑦𝑧 = 𝑐𝑜𝑠∅𝑐𝑜𝑠𝜃 𝑐𝑜𝑠∅𝑠𝑖𝑛𝜃 −𝑠𝑖𝑛∅ 𝑐𝑜𝑠𝜃𝑠𝑖𝑛∅𝑠𝑖𝑛𝜓 − 𝑐𝑜𝑠𝜓𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜓𝑐𝑜𝑠𝜃 + 𝑠𝑖𝑛∅𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜃 𝑐𝑜𝑠∅𝑠𝑖𝑛𝜓 𝑐𝑜𝑠𝜓𝑐𝑜𝑠𝜃𝑠𝑖𝑛∅ + 𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜓𝑠𝑖𝑛∅𝑠𝑖𝑛𝜃 − 𝑐𝑜𝑠∅𝑠𝑖𝑛𝜓 𝑐𝑜𝑠∅𝑐𝑜𝑠𝜓 𝑅 𝑥𝑦𝑧 = −𝑠𝑖𝑛∅ 𝑐𝑜𝑠∅𝑠𝑖𝑛𝜓 𝑐𝑜𝑠∅𝑐𝑜𝑠𝜓 𝑅 𝑦𝑥𝑧 = 𝑅 𝑦(∅) 𝑅 𝑥(𝜓)𝑅 𝑧(𝜃) 0 0 1 = −𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜃 𝑠𝑖𝑛𝜓 𝑐𝑜𝑠∅𝑐𝑜𝑠𝜓 𝑅 𝑥𝑧𝑦 = 𝑅 𝑥(𝜓)𝑅 𝑧(𝜃)𝑅 𝑦(∅) 0 0 1 = −𝑐𝑜𝑠𝜃𝑠𝑖𝑛∅ 𝑐𝑜𝑠∅𝑠𝑖𝑛𝜓 + 𝑐𝑜𝑠𝜓𝑠𝑖𝑛∅𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜓𝑐𝑜𝑠∅ − 𝑠𝑖𝑛∅𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜃 𝑅 𝑥𝑧𝑦 = 𝑅 𝑥(𝜓)𝑅 𝑧(𝜃)𝑅 𝑦(∅) 0 0 1 = 𝑐𝑜𝑠∅𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜃 − 𝑐𝑜𝑠𝜓𝑠𝑖𝑛∅ 𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜓 𝑐𝑜𝑠∅𝑐𝑜𝑠𝜓 + 𝑠𝑖𝑛∅𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜃 𝑅 𝑧𝑦𝑥 = 𝑅 𝑧(𝜃)𝑅 𝑦(∅)𝑅 𝑥(𝜓) 0 0 1 = 𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜃 − 𝑐𝑜𝑠𝜓𝑐𝑜𝑠𝜃𝑠𝑖𝑛∅ 𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜓 + 𝑐𝑜𝑠𝜓𝑠𝑖𝑛𝜃𝑠𝑖𝑛∅ 𝑐𝑜𝑠∅𝑐𝑜𝑠𝜓 𝑅 𝑧𝑥𝑦 = 𝑅 𝑧(𝜃) 𝑅 𝑥(𝜓)𝑅 𝑦(∅) 0 0 1 = 𝑐𝑜𝑠∅𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜃 − 𝑐𝑜𝑠𝜃𝑠𝑖𝑛∅ 𝑐𝑜𝑠𝜃𝑐𝑜𝑠∅𝑠𝑖𝑛𝜓 + 𝑠𝑖𝑛∅𝑐𝑜𝑠𝜃 𝑐𝑜𝑠∅𝑐𝑜𝑠𝜓 Accelerometer Readings
- 24. V K Jadon, Prof., Mechanical Engineering, Chitkara University 24 Angle Measurement Solving 𝑅 𝑥𝑦𝑧 for the Roll (𝜓) and Pitch (∅) Angles The rotation sequence 𝑅 𝑥𝑦𝑧 is widely used in the aerospace industry and is termed the 'aerospace rotation sequence‘. 𝐺 𝑝𝑥 𝐺 𝑝𝑦 𝐺 𝑝𝑧 = −𝑠𝑖𝑛∅ 𝑐𝑜𝑠∅𝑠𝑖𝑛𝜓 𝑐𝑜𝑠∅𝑐𝑜𝑠𝜓 𝐺 𝑝𝑥 = −𝑠𝑖𝑛∅ 𝐺 𝑝𝑦 = 𝑐𝑜𝑠∅𝑠𝑖𝑛𝜓 𝐺 𝑝𝑧 = 𝑐𝑜𝑠∅𝑐𝑜𝑠𝜓 tan 𝜓 𝑥𝑦𝑧 = 𝐺 𝑝𝑦 𝐺 𝑝𝑧 tan ∅ 𝑥𝑦𝑧 = −𝐺 𝑝𝑥 𝐺 𝑝𝑦 2 + 𝐺 𝑝𝑧 2 𝜋 4 − 3𝜋 4 𝑠𝑖𝑛 𝜋 4 = 1 2 𝑐𝑜𝑠 𝜋 4 = 1 2 𝑡𝑎𝑛 𝜋 4 = 1 𝑠𝑖𝑛 − 3𝜋 4 = − 1 2 𝑐𝑜𝑠 − 3𝜋 4 = − 1 2 𝑡𝑎𝑛 − 3𝜋 4 = 1 𝑡𝑎𝑛−1 1 1 = 𝑡𝑎𝑛−1 −1 −1 atan function does not distinguish between opposite angles atan2 function takes into account the ratio and sign of 𝑦 and 𝑥 𝑎𝑡𝑎𝑛2 1, 1 = 𝜋 4 𝑎𝑡𝑎𝑛2 −1, −1 = − 3𝜋 4
- 25. Gyroscope
- 26. 𝝎 𝑿𝒁 𝒀 MEMS gyroscopes measure the angular rate of rotation of one or more axes V K Jadon, Prof., Mechanical Engineering, Chitkara University Gyroscope 𝒗 𝑨 = 𝝎 × 𝒓 𝑨 𝝎 𝒙 𝒛 𝒚 Path of the ball as seen by an observer moving with table Path of the ball as seen from fixed frame 𝒗 𝑪 𝒙 𝒛 𝒚 Position of ball after some time ∆𝑡 𝒗 𝑩 𝑩 𝑩 Point B after time∆𝑡 𝒗 𝑨 𝒗 𝒃𝒂𝒍𝒍
- 27. Ball has two velocities V K Jadon, Prof., Mechanical Engineering, Chitkara University Gyroscope 𝒗 𝑨 = 𝝎 × 𝒓 𝑨 𝒗 𝒃𝒂𝒍𝒍 𝝎 𝒙 𝒛 𝒚 𝝎 𝒗 𝒃𝒂𝒍𝒍 MEMS gyroscopes use vibrating mechanical elements (proof-mass) to sense rotation caused by Coriolis acceleration.
- 28. The ADC sample rate is programmable from 8,000 samples per second, down to 3.9 samples per second, and user-selectable low-pass filters enable a wide range of cut-off frequencies. Three-Axis MEMS Gyroscope with 16-bit ADCs and Signal Conditioning Gyroscope Setup-MPU6050 V K Jadon, Prof., Mechanical Engineering, Chitkara University 28 The MPU-60X0 consists of three independent vibratory MEMS rate gyroscopes, which detect rotation about the X-, Y-, and Z- Axes. When the gyros are rotated about any of the sense axes, the Coriolis Effect causes a vibration that is detected by a capacitive pickoff. The signal is amplified, demodulated, and filtered to produce a voltage that is proportional to the angular rate. This voltage is digitized using individual on-chip 16-bit Analog-to- Digital Converters (ADCs) to sample each axis. The full-scale range of the gyro sensors may be digitally programmed to ±250, ±500, ±1000, or ±2000 degrees per second (dps).
- 29. 𝑟𝑝𝑚 = 𝑟𝑎𝑛𝑔𝑒(°/𝑠) 360 × 60 Range Condition 𝒅𝒆𝒕𝒆𝒄𝒕𝒂𝒃𝒍𝒆 𝒓𝒑𝒎 Register Bit ±250 0 41.67 0x00000000 ±500 1 83.33 0x00001000 ±1000 2 166.7 0x00010000 ±2000 3 333.3 0x00011000 Gyroscope Setup V K Jadon, Prof., Mechanical Engineering, Chitkara University 29
- 30. V K Jadon, Prof., Mechanical Engineering, Chitkara University For a FS_SEL =1 LSB Sensitivity = 65.5 Register Bit = 0x00001000 𝜔(𝑦𝑎𝑤 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛) = 1 0 𝑠 𝑔𝑦𝑟𝑜 𝑧 = 65.5 𝜔(𝑦𝑎𝑤 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛) = 5 0 𝑠 𝑔𝑦𝑟𝑜 𝑧 = 327.5 At any particular time To convert Gyro values into instantaneous angular rate 𝑖𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑟𝑎𝑡𝑒 = 𝑔𝑦𝑟𝑜 𝑥,𝑦,𝑧 𝐿𝑆𝐵 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 = 327.5 65.5 = 5 0 𝑠 To measure total angle travelled add all instantaneous angles obtained for small time duration, ∆𝑡 𝜔 = 𝑑𝜃 𝑑𝑡 𝑑𝜃 = 𝜔𝑑𝑡 𝜃 = 𝑡1 𝑡2 𝜔𝑑𝑡 Gyroscope Data
- 31. V K Jadon, Prof., Mechanical Engineering, Chitkara University 𝜃 = 𝑡1 𝑡2 𝜔𝑑𝑡 𝜔 𝑡 𝜔 𝑡 ∆𝑒 Drift error Drift error is gradual divergence between the true orientation and estimated orientation by gyro due to error in measurement. 𝑒 𝑡 Use other sensors to bring down the drift error to zero. Take angles with reference to world frame. Gradually apply corrections. • These correction are to be fast enough to fully compensate the drift error. • Slow enough to avoid jerky compensations Tilt Error or (roll and pitch angle error) Yaw Error Linear accelerometer Magnetometer The noise part is also integrated
- 32. V K Jadon, Prof., Mechanical Engineering, Chitkara University gyro_pitch_angle=gyro_pitch_angle+ gyro_roll_angle * sin(gyro_z) gyro_roll_angle=gyro_roll_angle- gyro_pitch_angle * sin(gyro_z) Transfer of Yaw angles
- 33. V K Jadon, Prof., Mechanical Engineering, Chitkara University The gyroscope drift is mainly due to the integration of two components: a slow changing, near-dc variable called bias instability and a higher frequency noise variable called angular random walk (ARW). The yaw axis is most sensitive to this drift. A good portion of the pitch (attitude) and roll axis gyroscope drift can be removed within an IMU through the use of accelerometer feedback to monitor position relative to gravity. Ideally, two references are needed to correct for gyroscope drift on all axes. An IMU with nine degrees of freedom typically provides additional magnetometer sensors - about 3 axes. A magnetometer senses field strength relative to the Earth’s magnetic North. These sensors can be used together with accelerometer data, as another external reference, to mitigate the impact of gyroscope drift error on the yaw axis.
- 34. V K Jadon, Prof., Mechanical Engineering, Chitkara University However, design of proper spatial magnetometers can be a less reliable vector than an accelerometer, as there are many things that create magnetic fields within the same order of magnitude as that of the Earth. Another one of the more effective methods for cancelling long-term drift is to implement a zero angular velocity update to the gyroscope. Any time the device is known to be completely stationary, the gyroscope offset can be nulled to zero for that respective axis. This opportunity can vary wildly depending on the application. But any instance that the system is at a recurring resting state can be used for nulling, such as an idling car, a stationary autonomous robot, or the time between human foot steps. Of course, using a state-of-the-art IMU that has minimal bias instability within the design at the onset may offer the most immediate impact on gyroscope drift. The constant bias error of a gyroscope can be measured by taking the average of the output over a long period of time while the device is not rotating.
- 35. Thanks V K Jadon, Prof., Mechanical Engineering, Chitkara University 35