Guide to gyro and accelerometer with Arduino including Kalman filtering

tensa: i was able to implement the filter thanks for this guide it was really helpful...thank you very much but i dont know how to relate these values to motor's rpm of a quadcopter so i will stabilize, can anybody post links to guides like this?

You will need to use a PID controller to give roll,pitch,yaw outputs when the orientation deviates from 0,0,0. However, I have used these filters on a quadcopter and they suffer from the problem of linear acceleration affecting the pitch and roll. The filters are fast enough, smooth and very stable (calculation time was 80micros for twin Kalmans on an Arduino Due) but you'd probably be better off using Mahonys DCM or Madgwicks filter - they're less sensitive to linear acceleration but a bit more prone to noise (vibration from the motors).

You'll find plenty of links via Google for any of this stuff.

i want to work with MPU-6050-Triple Axis Accelerometer Gyro can it be done

i want the same guide for MPU-6050-Triple Axis Accelerometer Gyro

the same think , so my ,i'd like this idea and i would like someone to share us the GUIDE of IMU 6050 and arduino

Hi,

The setup is very similar just note that if you are using an Arduino running at 5V you might damage the IMU as it's only running at 3.3V, but some breakout boards have a logic level circuit built-in. If not use have to use a logic level converter like this one: https://www.sparkfun.com/products/8745.

To connect the Arduino with the MPU-6050, you need to connect it as it says in the following comment: https://www.sparkfun.com/products/11028#comment-50b3c165ce395f484d000000.

Hopes this helps you out for now, as I havn't got time to write a guide at the moment.

Regards Lauszus

Hi Lauszus, I make a little customisation of your source for digital IMUs so it can work with Minimu-9 board , hope you don't mind.But there is something wrong here is what i get:

....(the board is on the ground and i don't touch it the whole time)
X: 180.00   Y: 180.01   
X: 180.05   Y: 180.06   
X: 180.22   Y: 180.14   
X: 180.51   Y: 180.16   
X: 180.82   Y: 180.11   
X: 181.07   Y: 180.04   
X: 181.42   Y: 179.92   
X: 181.79   Y: 179.80   
X: 182.22   Y: 179.65   
X: 182.72   Y: 179.46   
X: 183.23   Y: 179.28   
X: 183.85   Y: 179.08   
X: 184.54   Y: 178.80   
X: 185.26   Y: 178.48   
X: 185.99   Y: 178.02   
X: 186.60   Y: 177.45   
X: 187.54   Y: 176.95   
X: 188.54   Y: 176.43   
X: 189.64   Y: 175.72   
X: 190.82   Y: 175.03   
X: 192.13   Y: 174.37   
......  
X: 280.48   Y: 86.86    
X: 280.43   Y: 86.66    
X: 280.32   Y: 86.91    
X: 280.19   Y: 87.02    
X: 280.09   Y: 87.10    
X: 279.97   Y: 87.32    
X: 279.81   Y: 87.84    
X: 279.71   Y: 87.88    
X: 279.60   Y: 88.26    
X: 279.51   Y: 88.09    
X: 279.38   Y: 88.20    
X: 279.27   Y: 88.09    
X: 279.10   Y: 88.24    
X: 278.96   Y: 88.26    
X: 278.80   Y: 88.56    
...(finally the X stopped growing and the Y stopped getting lower)
X: 278.61   Y: 89.11    
X: 278.44   Y: 89.23    
X: 278.29   Y: 89.41    
X: 278.25   Y: 88.81    
X: 278.07   Y: 89.24    
X: 277.85   Y: 89.62    
X: 277.68   Y: 89.88    
X: 277.53   Y: 90.03    
X: 277.36   Y: 90.22    
X: 277.24   Y: 90.48    
X: 277.12   Y: 90.17    
X: 276.99   Y: 90.08    
X: 276.90   Y: 89.87    
X: 276.76   Y: 89.84    
X: 276.61   Y: 89.97    
X: 276.44   Y: 90.35    
X: 276.26   Y: 90.62    
X: 276.12   Y: 90.84    
X: 276.02   Y: 90.76    
X: 275.78   Y: 91.38    
X: 275.67   Y: 91.39    
X: 275.47   Y: 91.74    
X: 275.32   Y: 91.92    
X: 275.16   Y: 92.18    
X: 275.07   Y: 92.02    
X: 274.95   Y: 92.17    
X: 274.83   Y: 92.30    
X: 274.68   Y: 92.31    
X: 274.52   Y: 92.53    
X: 274.43   Y: 92.53    
X: 274.27   Y: 92.90    
X: 274.18   Y: 92.90    
X: 274.03   Y: 92.95
..(and all over again)

and here is my source

 #include 
#include 
#include 

L3G gyro;
LSM303 compass;
double zeroValue[5] = {-200, 44, 660, -18.5, 52.3}; // Found by experimenting

/* All the angles start at 180 degrees */
double gyroXangle = 180;
double gyroYangle = 180;

double compAngleX = 180;
double compAngleY = 180;

unsigned long timer;
/* Kalman filter variables and constants */
const double Q_angleX = 0.001; // Process noise covariance for the accelerometer - Sw
const double Q_gyroX = 0.003; // Process noise covariance for the gyro - Sw
const double R_angleX = 0.03; // Measurement noise covariance - Sv

double angleX = 180; // The angle output from the Kalman filter
double biasX = 0; // The gyro bias calculated by the Kalman filter
double PX_00 = 0, PX_01 = 0, PX_10 = 0, PX_11 = 0;
double dtX, yX, SX;
double KX_0, KX_1;

double kalmanX(double newAngle, double newRate, double dtime) {
  // KasBot V2 - Kalman filter module - http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1284738418
  // See also http://www.x-firm.com/?page_id=145
  // with slightly modifications by Kristian Lauszus
  // See http://academic.csuohio.edu/simond/courses/eec644/kalman.pdf and
  // http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf for more information
  dtX = dtime / 1000000; // Convert from microseconds to seconds

  // Discrete Kalman filter time update equations - Time Update ("Predict")
  // Update xhat - Project the state ahead
  angleX += dtX * (newRate - biasX);

  // Update estimation error covariance - Project the error covariance ahead
  PX_00 += -dtX * (PX_10 + PX_01) + Q_angleX * dtX;
  PX_01 += -dtX * PX_11;
  PX_10 += -dtX * PX_11;
  PX_11 += +Q_gyroX * dtX;

  // Discrete Kalman filter measurement update equations - Measurement Update ("Correct")
  // Calculate Kalman gain - Compute the Kalman gain
  SX = PX_00 + R_angleX;
  KX_0 = PX_00 / SX;
  KX_1 = PX_10 / SX;

  // Calculate angle and resting rate - Update estimate with measurement zk
  yX = newAngle - angleX;
  angleX += KX_0 * yX;
  biasX += KX_1 * yX;

  // Calculate estimation error covariance - Update the error covariance
  PX_00 -= KX_0 * PX_00;
  PX_01 -= KX_0 * PX_01;
  PX_10 -= KX_1 * PX_00;
  PX_11 -= KX_1 * PX_01;

  return angleX;
}
/* Kalman filter variables and constants */
const double Q_angleY = 0.001; // Process noise covariance for the accelerometer - Sw
const double Q_gyroY = 0.003; // Process noise covariance for the gyro - Sw
const double R_angleY = 0.03; // Measurement noise covariance - Sv

double angleY = 180; // The angle output from the Kalman filter
double biasY = 0; // The gyro bias calculated by the Kalman filter
double PY_00 = 0, PY_01 = 0, PY_10 = 0, PY_11 = 0;
double dtY, yY, SY;
double KY_0, KY_1;

double kalmanY(double newAngle, double newRate, double dtime) {
  // KasBot V2 - Kalman filter module - http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1284738418
  // See also http://www.x-firm.com/?page_id=145
  // with slightly modifications by Kristian Lauszus
  // See http://academic.csuohio.edu/simond/courses/eec644/kalman.pdf and
  // http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf for more information
  dtY = dtime / 1000000; // Convert from microseconds to seconds

  // Discrete Kalman filter time update equations - Time Update ("Predict")
  // Update xhat - Project the state ahead
  angleY += dtY * (newRate - biasY);

  // Update estimation error covariance - Project the error covariance ahead
  PY_00 += -dtY * (PY_10 + PY_01) + Q_angleY * dtY;
  PY_01 += -dtY * PY_11;
  PY_10 += -dtY * PY_11;
  PY_11 += +Q_gyroY * dtY;

  // Discrete Kalman filter measurement update equations - Measurement Update ("Correct")
  // Calculate Kalman gain - Compute the Kalman gain
  SY = PY_00 + R_angleY;
  KY_0 = PY_00 / SY;
  KY_1 = PY_10 / SY;

  // Calculate angle and resting rate - Update estimate with measurement zk
  yY = newAngle - angleY;
  angleY += KY_0 * yY;
  biasY += KY_1 * yY;

  // Calculate estimation error covariance - Update the error covariance
  PY_00 -= KY_0 * PY_00;
  PY_01 -= KY_0 * PY_01;
  PY_10 -= KY_1 * PY_00;
  PY_11 -= KY_1 * PY_01;

  return angleY;
}
int readGyroX(void) {
  int data;
  data =gyro.g.x;

  return data;
}
int readGyroY(void) {
  int data;
  data = gyro.g.y;

  return data;
}
double getXangle() {
  double accXval = (double)readAccX()-zeroValue[0];
  double accZval = (double)readAccZ()-zeroValue[2];
  double angle = (atan2(accXval,accZval)+PI)*RAD_TO_DEG;
  return angle;
}
double getYangle() {
  double accYval = (double)readAccY()-zeroValue[1];
  double accZval = (double)readAccZ()-zeroValue[2];
  double angle = (atan2(accYval,accZval)+PI)*RAD_TO_DEG;
  return angle;
}
int readAccX(void) {
  int data;
  data = compass.a.x;
  return data;
}
int readAccY(void) {
  int data;
  data = compass.a.y;
  return data;
}
int readAccZ(void) {
  int data;
  data =compass.a.z;
  return data;

}


void setup() {
  Serial.begin(9600);
  Wire.begin();
  
  if (!gyro.init())
  {
    Serial.println("Failed to autodetect gyro type!");
    while (1);
  }

  gyro.enableDefault();
   compass.init();
  compass.enableDefault();
    timer = micros();
}

void loop() {
  gyro.read();
 compass.read();

  double gyroXrate = (((double)readGyroX()-zeroValue[3])/14.375);
  gyroXangle += gyroXrate*((double)(micros()-timer)/1000000); // Without any filter
  
  double gyroYrate = -(((double)readGyroY()-zeroValue[4])/14.375);
  gyroYangle += gyroYrate*((double)(micros()-timer)/1000000); // Without any filter
  
  double accXangle = getXangle();
  double accYangle = getYangle();


  compAngleX = (0.93*(compAngleX+(gyroXrate*(double)(micros()-timer)/1000000)))+(0.07*accXangle);
  compAngleY = (0.93*(compAngleY+(gyroYrate*(double)(micros()-timer)/1000000)))+(0.07*accYangle);
  
  double xAngle = kalmanX(accXangle, gyroXrate, (double)(micros() - timer)); // calculate the angle using a Kalman filter
  double yAngle = kalmanY(accYangle, gyroYrate, (double)(micros() - timer)); // calculate the angle using a Kalman filter
  
  timer = micros();
  

  Serial.print("X: ");Serial.print(xAngle);Serial.print("\t");
  Serial.print("Y: ");Serial.print(yAngle);Serial.print("\t");
   
  Serial.print("\n");
  
  delay(10);


}

Could you please take a look of my source and tell me what I am doing wrong.I want to thank you in advance for your time. Stanislav.

@stunito0o0 It looks like you are reading the magnetometer (compass) and not the accelerometer. Btw the newest version of the code can be found here: https://github.com/TKJElectronics/KalmanFilter.

Lauszus: @stunito0o0 It looks like you are reading the magnetometer (compass) and not the accelerometer. Btw the newest version of the code can be found here: https://github.com/TKJElectronics/KalmanFilter.

Hi again, :) I thought too that it might be the compass data I am reading so i opened the example for the "LSM303.h" libraly and here is the source:

#include 
#include 

LSM303 compass;

void setup() {
  Serial.begin(9600);
  Wire.begin();
  compass.init();
  compass.enableDefault();
}

void loop() {
  compass.read();

  Serial.print("A ");
  Serial.print("X: ");
  Serial.print((int)compass.a.x);
  Serial.print(" Y: ");
  Serial.print((int)compass.a.y);
  Serial.print(" Z: ");
  Serial.print((int)compass.a.z);

  Serial.print(" M ");  
  Serial.print("X: ");
  Serial.print((int)compass.m.x);
  Serial.print(" Y: ");
  Serial.print((int)compass.m.y);
  Serial.print(" Z: ");
  Serial.println((int)compass.m.z);

  
  delay(100);
}

According to the example "compass.a.x","compass.a.y" and "compass.a.z" are for reading the acc data.I will really appreciate if you take another look of my code.I think that when i was customising your source i might have deleted something important.Thank you again for your time. :) P.S. Now i rememberd that i deleted part of the source for getting the data of acc and gyro.For example "readAccX" function was something like this:

int readAccX(void) {
  int data;
  data = i2cRead(adxlAddress, 0x32);
  data |= i2cRead(adxlAddress,0x33)<<8;
  return data;
}

and i didn't understand what "data |= i2cRead(adxlAddress,0x33)<<8;" is for so i deleted it. now it looks like this:

int readAccX(void) {
  int data;
  data = compass.a.x;
  return data;
}

Sorry I was in a hurry when I wrote the first reply. First of all I think it will be easier for you to if you modify this example: https://github.com/pololu/LSM303/blob/master/LSM303/examples/Serial/Serial.ino to your needs.

First of all you should NOT subtract the zeroValues, as they are specific for the IMU used in the example. I think you can use your values directly, so you don't even have to subtract any zeroValue. Take a look at this example: https://github.com/TKJElectronics/Example-Sketch-for-IMU-including-Kalman-filter/blob/master/IMU6DOF/MPU6050/MPU6050.ino

Also you assume that the gyro has the same sensitivity as the one used in the example which is most likely not the case (take a look at your datasheet)!

Hi again Lauzurus , :) Thank you verry much for your answer ,but i am afraid that I won't need your source anymore.I just found out this link it is a source for Arduino and MinIMU-9 board wich is exactly what i have.Once again I am really sorry for wasting your time. :) I hope you that you won't get angry at me. :)

No problem. I'm just glad you got it working :)

Hey Lauszus!

I was hoping to learn something about using IMU effectively with the help of Kalman filtering as I came across this wonderful tutorial. The only problem I have is I have 2 separate gyro and accelerometer modules (L3G4200D and ADXL 335). How do I combine and use them according to your pin config.

gyro has pins GND, VIN, SCL, SDA, SDD, INT1, INT2 and accelerometer pins are VCC, GND,X,Y,Z,ST. Where do these pins go?

Thanks!

@psyoptica The gyroscope is a digital gyroscope so you need to connect it to the SDA and SCL on the Arduino. See the following page for more information: http://arduino.cc/en/Reference/Wire. Then connect VIN to 3.3V and GND to GND on the Arduino.

Your accelerometer is a analog one, so you need to connect X, Y, and Z to your analog inputs. And yet again connect VIN to 3.3V and GND to GND on the Arduino.

Thanks! this really helps but aren't A4 and A5 analog input pins?

@psyoptica Yes they are, but pins can have several capabilities.

For instance you can also use any analog pin as a digital pin like so:

pinMode(A0,OUTPUT);
digitalWrite(A0,HIGH);

You can read more about it in the datasheet: http://www.atmel.com/Images/Atmel-8271-8-bit-AVR-Microcontroller-ATmega48A-48PA-88A-88PA-168A-168PA-328-328P_datasheet.pdf.

Tell me if I have configured it correctly

Acc_Gyro Arduino 3.3V <—> 3.3V GND <—> GND X <—> AN0 Y <—> AN1 Z <—> AN2 SDA <—> AN4 SCL <—> AN5

@psyoptica Yes that looks correct. But beware that if there is no logic level circuit on your breakout board, you might damage the IC. So get a logic level converter if you need to use if on the long run: https://www.sparkfun.com/products/8745.

I don't think there is a need for any logic level converter device since the arduino I'm using already gives a 3.3V signal.

Thanks for the quick responses. Really hope I learn something from this tutorial.

@psyoptica You are using an Arduino Uno, right? Then there is need for a logic level converter! Since the ATmega328P is running at 5V.

Thanks for clearing it up. Will definitely have to get a converter circuit then…