Self-balancing Part 2

In this part of the tutorial I will cover how to get the most performance out of the MPU-6050 Accelerometer and Gyroscope module, using the Motion Apps library. This library is really amazing as the author reverse engineered the MPU-6050 so that most of the processing is done through the DMP on the module itself, instead of by the micro-controller! I have found that reading the sensor through the Motion Apps Library is faster than doing the calculations manually, and the readings tend to be significantly more accurate.


Analysing the Output

Here is the code that I used to get the yaw, pitch and roll sensor data. It is based on the “Teapot” demonstration program which comes with the MPU-6050 Motion Apps library. Once again, you need to have the “MPU6050” and the “I2Cdev” libraries installed to use this code.

// I2C device class (I2Cdev) demonstration Arduino sketch for MPU6050 class 
// using DMP (MotionApps v2.0)
// 6/21/2012 by Jeff Rowberg <jeff@rowberg.net>

/* ============================================
I2Cdev device library code is placed under the MIT license
Copyright (c) 2012 Jeff Rowberg

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
===============================================
*/

// I2Cdev and MPU6050 must be installed as libraries, or else the .cpp/.h files
// for both classes must be in the include path of your project
#include "I2Cdev.h"

#include "MPU6050_6Axis_MotionApps20.h"

// Arduino Wire library is required if I2Cdev I2CDEV_ARDUINO_WIRE implementation
// is used in I2Cdev.h
#if I2CDEV_IMPLEMENTATION == I2CDEV_ARDUINO_WIRE
    #include "Wire.h"
#endif

// class default I2C address is 0x68
// specific I2C addresses may be passed as a parameter here
// AD0 low = 0x68 (default for SparkFun breakout and InvenSense evaluation board)
// AD0 high = 0x69
MPU6050 mpu;
//MPU6050 mpu(0x69); // <-- use for AD0 high

/* =========================================================================
   NOTE: In addition to connection 3.3v, GND, SDA, and SCL, this sketch
   depends on the MPU-6050's INT pin being connected to the Arduino's
   external interrupt #0 pin. On the Arduino Uno and Mega 2560, this is
   digital I/O pin 2.

   For the Galileo Gen1/2 Boards, there is no INT pin support. Therefore
   the INT pin does not need to be connected, but you should work on getting
   the timing of the program right, so that there is no buffer overflow.
 * ========================================================================= */

/* =========================================================================
   NOTE: Arduino v1.0.1 with the Leonardo board generates a compile error
   when using Serial.write(buf, len). The Teapot output uses this method.
   The solution requires a modification to the Arduino USBAPI.h file, which
   is fortunately simple, but annoying. This will be fixed in the next IDE
   release. For more info, see these links:

   http://arduino.cc/forum/index.php/topic,109987.0.html
   http://code.google.com/p/arduino/issues/detail?id=958
 * ========================================================================= */


#define OUTPUT_READABLE_YAWPITCHROLL

// Unccomment if you are using an Arduino-Style Board
// #define ARDUINO_BOARD

// Uncomment if you are using a Galileo Gen1 / 2 Board
#define GALILEO_BOARD

#define LED_PIN 13      // (Galileo/Arduino is 13)
bool blinkState = false;

// MPU control/status vars
bool dmpReady = false;  // set true if DMP init was successful
uint8_t mpuIntStatus;   // holds actual interrupt status byte from MPU
uint8_t devStatus;      // return status after each device operation (0 = success, !0 = error)
uint16_t packetSize;    // expected DMP packet size (default is 42 bytes)
uint16_t fifoCount;     // count of all bytes currently in FIFO
uint8_t fifoBuffer[64]; // FIFO storage buffer

// orientation/motion vars
VectorFloat gravity;    // [x, y, z]            gravity vector
Quaternion q;           // [w, x, y, z]         quaternion container
float euler[3];         // [psi, theta, phi]    Euler angle container
float ypr[3];           // [yaw, pitch, roll]   yaw/pitch/roll container and gravity vector



// ================================================================
// ===               INTERRUPT DETECTION ROUTINE                ===
// ================================================================

// This function is not required when using the Galileo 
volatile bool mpuInterrupt = false;     // indicates whether MPU interrupt pin has gone high
void dmpDataReady() {
    mpuInterrupt = true;
}



// ================================================================
// ===                      INITIAL SETUP                       ===
// ================================================================

void setup() {
    // join I2C bus (I2Cdev library doesn't do this automatically)
    #if I2CDEV_IMPLEMENTATION == I2CDEV_ARDUINO_WIRE
        Wire.begin();
        int TWBR = 24; // 400kHz I2C clock (200kHz if CPU is 8MHz)
    #elif I2CDEV_IMPLEMENTATION == I2CDEV_BUILTIN_FASTWIRE
        Fastwire::setup(400, true);
    #endif

    Serial.begin(115200);
    while (!Serial);

    // initialize device
    Serial.println(F("Initializing I2C devices..."));
    mpu.initialize();

    // verify connection
    Serial.println(F("Testing device connections..."));
    Serial.println(F("MPU6050 connection "));
    Serial.print(mpu.testConnection() ? F("successful") : F("failed"));

    // wait for ready
    Serial.println(F("\nSend any character to begin DMP programming and demo: "));
    while (Serial.available() && Serial.read()); // empty buffer
    while (!Serial.available());                 // wait for data
    while (Serial.available() && Serial.read()); // empty buffer again

    // load and configure the DMP
    Serial.println(F("Initializing DMP..."));
    devStatus = mpu.dmpInitialize();

    // supply your own gyro offsets here, scaled for min sensitivity
    mpu.setXGyroOffset(220);
    mpu.setYGyroOffset(76);
    mpu.setZGyroOffset(-85);
    mpu.setZAccelOffset(1788); // 1688 factory default for my test chip

    // make sure it worked (returns 0 if so)
    if (devStatus == 0) {
        // turn on the DMP, now that it's ready
        Serial.println(F("Enabling DMP..."));
        mpu.setDMPEnabled(true);

        // enable Arduino interrupt detection
        Serial.println(F("Enabling interrupt detection (Arduino external interrupt 0)..."));
        attachInterrupt(0, dmpDataReady, RISING);
        mpuIntStatus = mpu.getIntStatus();

        // set our DMP Ready flag so the main loop() function knows it's okay to use it
        Serial.println(F("DMP ready! Waiting for first interrupt..."));
        dmpReady = true;

        // get expected DMP packet size for later comparison
        packetSize = mpu.dmpGetFIFOPacketSize();
    } else {
        // ERROR!
        // 1 = initial memory load failed
        // 2 = DMP configuration updates failed
        // (if it's going to break, usually the code will be 1)
        Serial.print(F("DMP Initialization failed (code "));
        Serial.print(devStatus);
        Serial.println(F(")"));
    }

    // configure LED for output
    pinMode(LED_PIN, OUTPUT);
}



// ================================================================
// ===                    MAIN PROGRAM LOOP                     ===
// ================================================================

void loop() {
    // if programming failed, don't try to do anything
    if (!dmpReady) return;

    // wait for MPU interrupt or extra packet(s) available

    #ifdef ARDUINO_BOARD
        while (!mpuInterrupt && fifoCount < packetSize) {
        }
    #endif

    #ifdef GALILEO_BOARD
        delay(10);
    #endif

    // reset interrupt flag and get INT_STATUS byte
    mpuInterrupt = false;
    mpuIntStatus = mpu.getIntStatus();

    // get current FIFO count
    fifoCount = mpu.getFIFOCount();

    // check for overflow (this should never happen unless our code is too inefficient)
    if ((mpuIntStatus & 0x10) || fifoCount == 1024) {
        // reset so we can continue cleanly
        mpu.resetFIFO();
        Serial.println(F("FIFO overflow!"));

    // otherwise, check for DMP data ready interrupt (this should happen frequently)
    } else if (mpuIntStatus & 0x02) {
        // wait for correct available data length, should be a VERY short wait
        while (fifoCount < packetSize) fifoCount = mpu.getFIFOCount();

        // read a packet from FIFO
        mpu.getFIFOBytes(fifoBuffer, packetSize);
        
        // track FIFO count here in case there is > 1 packet available
        // (this lets us immediately read more without waiting for an interrupt)
        fifoCount -= packetSize;


        #ifdef OUTPUT_READABLE_YAWPITCHROLL
            // display Euler angles in degrees
            mpu.dmpGetQuaternion(&q, fifoBuffer);
            mpu.dmpGetGravity(&gravity, &q);
            mpu.dmpGetYawPitchRoll(ypr, &q, &gravity);
            Serial.print("ypr\t");
            Serial.print(ypr[0] * 180/M_PI);
            Serial.print("\t");
            Serial.print(ypr[1] * 180/M_PI);
            Serial.print("\t");
            Serial.println(ypr[2] * 180/M_PI);
        #endif

        // blink LED to indicate activity
        blinkState = !blinkState;
        digitalWrite(LED_PIN, blinkState);
    }
}

From a number of trials, I noticed that the accelerometer-gyroscope module and the Motion Apps library seem to have some type of auto-calibration feature, which requires a couple of seconds to complete. Here is a graph of the output I got directly after initiating the sensor:

Output from the MPU-6050, using Motion Apps
Output from the MPU-6050, using Motion Apps

All of the values float a large amount at the start, especially the yaw data. This then stops after around 13 seconds, probably due to the completion of some auto-calibration process. I repeated this test a number of times and it seems that the sensor can take up to 40 seconds to complete its calibration, on some occasions. Therefore we should take this delay into account in our program. The robot should wait for around 40 seconds, before beginning to use the sensor and starting the main program.

Calibrating the Sensor

Just like any sensor, the MPU-6050 needs to be calibrated before it is used for the first time. What we want to do is remove the zero-error; this is where the sensor is totally level, but it thinks that it is angled slightly. Therefore we need to adjust the offsets in order to counteract this error. Fortunately I found a program that can calibrate the MPU-6050 for us! In order to use the program, all you have to do is to upload the sketch and then place the accel-gyro module in a flat and level position. The program will make an average of a few hundred readings and display the offsets required to remove zero error.

// Arduino sketch that returns calibration offsets for MPU6050 
//   Version 1.1  (31th January 2014)
// Done by Luis Ródenas <luisrodenaslorda@gmail.com>
// Based on the I2Cdev library and previous work by Jeff Rowberg <jeff@rowberg.net>
// Updates (of the library) should (hopefully) always be available at https://github.com/jrowberg/i2cdevlib

// These offsets were meant to calibrate MPU6050's internal DMP, but can be also useful for reading sensors. 
// The effect of temperature has not been taken into account so I can't promise that it will work if you 
// calibrate indoors and then use it outdoors. Best is to calibrate and use at the same room temperature.

/* ==========  LICENSE  ==================================
 I2Cdev device library code is placed under the MIT license
 Copyright (c) 2011 Jeff Rowberg
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
 in the Software without restriction, including without limitation the rights
 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the Software is
 furnished to do so, subject to the following conditions:
 
 The above copyright notice and this permission notice shall be included in
 all copies or substantial portions of the Software.
 
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 =========================================================
 */

// I2Cdev and MPU6050 must be installed as libraries
#include "I2Cdev.h"
#include "MPU6050.h"
#include "Wire.h"

///////////////////////////////////   CONFIGURATION   /////////////////////////////
//Change this 3 variables if you want to fine tune the skecth to your needs.
int buffersize=1000;     //Amount of readings used to average, make it higher to get more precision but sketch will be slower  (default:1000)
int acel_deadzone=8;     //Acelerometer error allowed, make it lower to get more precision, but sketch may not converge  (default:8)
int giro_deadzone=1;     //Giro error allowed, make it lower to get more precision, but sketch may not converge  (default:1)

// default I2C address is 0x68
// specific I2C addresses may be passed as a parameter here
// AD0 low = 0x68 (default for InvenSense evaluation board)
// AD0 high = 0x69
//MPU6050 accelgyro;
MPU6050 accelgyro(0x68); // <-- use for AD0 high

int16_t ax, ay, az,gx, gy, gz;

int mean_ax,mean_ay,mean_az,mean_gx,mean_gy,mean_gz,state=0;
int ax_offset,ay_offset,az_offset,gx_offset,gy_offset,gz_offset;

///////////////////////////////////   SETUP   ////////////////////////////////////
void setup() {
  // join I2C bus (I2Cdev library doesn't do this automatically)
  Wire.begin();
  // COMMENT NEXT LINE IF YOU ARE USING ARDUINO DUE
  TWBR = 24; // 400kHz I2C clock (200kHz if CPU is 8MHz). Leonardo measured 250kHz.

  // initialize serial communication
  Serial.begin(115200);

  // initialize device
  accelgyro.initialize();

  // wait for ready
  while (Serial.available() && Serial.read()); // empty buffer
  while (!Serial.available()){
    Serial.println(F("Send any character to start sketch.\n"));
    delay(1500);
  }                
  while (Serial.available() && Serial.read()); // empty buffer again

  // start message
  Serial.println("\nMPU6050 Calibration Sketch");
  delay(2000);
  Serial.println("\nYour MPU6050 should be placed in horizontal position, with package letters facing up. \nDon't touch it until you see a finish message.\n");
  delay(3000);
  // verify connection
  Serial.println(accelgyro.testConnection() ? "MPU6050 connection successful" : "MPU6050 connection failed");
  delay(1000);
  // reset offsets
  accelgyro.setXAccelOffset(0);
  accelgyro.setYAccelOffset(0);
  accelgyro.setZAccelOffset(0);
  accelgyro.setXGyroOffset(0);
  accelgyro.setYGyroOffset(0);
  accelgyro.setZGyroOffset(0);
}

///////////////////////////////////   LOOP   ////////////////////////////////////
void loop() {
  if (state==0){
    Serial.println("\nReading sensors for first time...");
    meansensors();
    state++;
    delay(1000);
  }

  if (state==1) {
    Serial.println("\nCalculating offsets...");
    calibration();
    state++;
    delay(1000);
  }

  if (state==2) {
    meansensors();
    Serial.println("\nFINISHED!");
    Serial.print("\nSensor readings with offsets:\t");
    Serial.print(mean_ax); 
    Serial.print("\t");
    Serial.print(mean_ay); 
    Serial.print("\t");
    Serial.print(mean_az); 
    Serial.print("\t");
    Serial.print(mean_gx); 
    Serial.print("\t");
    Serial.print(mean_gy); 
    Serial.print("\t");
    Serial.println(mean_gz);
    Serial.print("Your offsets:\t");
    Serial.print(ax_offset); 
    Serial.print("\t");
    Serial.print(ay_offset); 
    Serial.print("\t");
    Serial.print(az_offset); 
    Serial.print("\t");
    Serial.print(gx_offset); 
    Serial.print("\t");
    Serial.print(gy_offset); 
    Serial.print("\t");
    Serial.println(gz_offset); 
    Serial.println("\nData is printed as: acelX acelY acelZ giroX giroY giroZ");
    Serial.println("Check that your sensor readings are close to 0 0 16384 0 0 0");
    Serial.println("If calibration was succesful write down your offsets so you can set them in your projects using something similar to mpu.setXAccelOffset(youroffset)");
    while (1);
  }
}

///////////////////////////////////   FUNCTIONS   ////////////////////////////////////
void meansensors(){
  long i=0,buff_ax=0,buff_ay=0,buff_az=0,buff_gx=0,buff_gy=0,buff_gz=0;

  while (i<(buffersize+101)){
    // read raw accel/gyro measurements from device
    accelgyro.getMotion6(&ax, &ay, &az, &gx, &gy, &gz);
    
    if (i>100 && i<=(buffersize+100)){ //First 100 measures are discarded
      buff_ax=buff_ax+ax;
      buff_ay=buff_ay+ay;
      buff_az=buff_az+az;
      buff_gx=buff_gx+gx;
      buff_gy=buff_gy+gy;
      buff_gz=buff_gz+gz;
    }
    if (i==(buffersize+100)){
      mean_ax=buff_ax/buffersize;
      mean_ay=buff_ay/buffersize;
      mean_az=buff_az/buffersize;
      mean_gx=buff_gx/buffersize;
      mean_gy=buff_gy/buffersize;
      mean_gz=buff_gz/buffersize;
    }
    i++;
    delay(2); //Needed so we don't get repeated measures
  }
}

void calibration(){
  ax_offset=-mean_ax/8;
  ay_offset=-mean_ay/8;
  az_offset=(16384-mean_az)/8;

  gx_offset=-mean_gx/4;
  gy_offset=-mean_gy/4;
  gz_offset=-mean_gz/4;
  while (1){
    int ready=0;
    accelgyro.setXAccelOffset(ax_offset);
    accelgyro.setYAccelOffset(ay_offset);
    accelgyro.setZAccelOffset(az_offset);

    accelgyro.setXGyroOffset(gx_offset);
    accelgyro.setYGyroOffset(gy_offset);
    accelgyro.setZGyroOffset(gz_offset);

    meansensors();
    Serial.println("...");

    if (abs(mean_ax)<=acel_deadzone) ready++;
    else ax_offset=ax_offset-mean_ax/acel_deadzone;

    if (abs(mean_ay)<=acel_deadzone) ready++;
    else ay_offset=ay_offset-mean_ay/acel_deadzone;

    if (abs(16384-mean_az)<=acel_deadzone) ready++;
    else az_offset=az_offset+(16384-mean_az)/acel_deadzone;

    if (abs(mean_gx)<=giro_deadzone) ready++;
    else gx_offset=gx_offset-mean_gx/(giro_deadzone+1);

    if (abs(mean_gy)<=giro_deadzone) ready++;
    else gy_offset=gy_offset-mean_gy/(giro_deadzone+1);

    if (abs(mean_gz)<=giro_deadzone) ready++;
    else gz_offset=gz_offset-mean_gz/(giro_deadzone+1);

    if (ready==6) break;
  }
}

The sketch outputs the required accelerometer and gyroscope offsets through the serial monitor. All you have to do is plug them into the initialisation code at the start of your program, and you are good to go! Please note that the required offsets vary significantly from sensor to sensor, so you have to repeat the calibration program above for each MPU-6050 sensor you are using.


That concludes the basic calibration of the MPU-6050; the sensor should now be more than accurate enough for most applications, such as self-balancing robots and quad-copters.

Part 4: The PID Controller

Updated: 23rd May 2019 – Reformatted post