File content as of revision 1:ca4d8c044898:

#include "mpu6050.h"

int Gscale = GFS_250DPS;
int Ascale = AFS_2G;

I2C i2c(I2C_SDA, I2C_SCL);

float aRes, gRes;

int intPin = 12;

int16_t accelCount[3];  // Stores the 16-bit signed accelerometer sensor output
float ax, ay, az;       // Stores the real accel value in g's
int16_t gyroCount[3];   // Stores the 16-bit signed gyro sensor output
float gx, gy, gz;       // Stores the real gyro value in degrees per seconds
float gyroBias[3] = {0, 0, 0}, accelBias[3] = {0, 0, 0}; // Bias corrections for gyro and accelerometer
int16_t tempCount;   // Stores the real internal chip temperature in degrees Celsius
float temperature;
float SelfTest[6];

int delt_t = 0; // used to control display output rate
int count = 0;  // used to control display output rate

// parameters for 6 DoF sensor fusion calculations
//float PI = 3.14159265358979323846f;
float GyroMeasError = PI * (60.0f / 180.0f);     // gyroscope measurement error in rads/s (start at 60 deg/s), then reduce after ~10 s to 3
float beta = sqrt(3.0f / 4.0f) * GyroMeasError;  // compute beta
float GyroMeasDrift = PI * (1.0f / 180.0f);      // gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
float zeta = sqrt(3.0f / 4.0f) * GyroMeasDrift;  // compute zeta, the other free parameter in the Madgwick scheme usually set to a small or zero value
float pitch, yaw, roll;
float deltat = 0.0f;                              // integration interval for both filter schemes
int lastUpdate = 0, firstUpdate = 0, Now = 0;     // used to calculate integration interval                               // used to calculate integration interval
float q[4] = {1.0f, 0.0f, 0.0f, 0.0f};            // vector to hold quaternion

void mpu6050::writeByte(uint8_t address, uint8_t subAddress, uint8_t data){
    char data_write[2];
    data_write[0] = subAddress;
    data_write[1] = data;
    i2c.write(address, data_write, 2, 0);
}

char mpu6050::readByte(uint8_t address, uint8_t subAddress){
    char data[1]; // `data` will store the register data     
    char data_write[1];
    data_write[0] = subAddress;
    i2c.write(address, data_write, 1, 1); // no stop
    i2c.read(address, data, 1, 0); 
    return data[0]; 
}

void mpu6050::readBytes(uint8_t address, uint8_t subAddress, uint8_t count, uint8_t * dest){
    char data[14];
    char data_write[1];
    data_write[0] = subAddress;
    i2c.write(address, data_write, 1, 1); // no stop
    i2c.read(address, data, count, 0); 
    for(int ii = 0; ii < count; ii++) {
     dest[ii] = data[ii];
    }
}

void mpu6050::getGres() {
  switch (Gscale)
  {
    // Possible gyro scales (and their register bit settings) are:
    // 250 DPS (00), 500 DPS (01), 1000 DPS (10), and 2000 DPS  (11). 
        // Here's a bit of an algorith to calculate DPS/(ADC tick) based on that 2-bit value:
    case GFS_250DPS:
          gRes = 250.0/32768.0;
          break;
    case GFS_500DPS:
          gRes = 500.0/32768.0;
          break;
    case GFS_1000DPS:
          gRes = 1000.0/32768.0;
          break;
    case GFS_2000DPS:
          gRes = 2000.0/32768.0;
          break;
  }
}

void mpu6050::getAres() {
  switch (Ascale)
  {
    // Possible accelerometer scales (and their register bit settings) are:
    // 2 Gs (00), 4 Gs (01), 8 Gs (10), and 16 Gs  (11). 
        // Here's a bit of an algorith to calculate DPS/(ADC tick) based on that 2-bit value:
    case AFS_2G:
          aRes = 2.0/32768.0;
          break;
    case AFS_4G:
          aRes = 4.0/32768.0;
          break;
    case AFS_8G:
          aRes = 8.0/32768.0;
          break;
    case AFS_16G:
          aRes = 16.0/32768.0;
          break;
  }
}

void mpu6050::readAccelData(int16_t * destination)
{
  uint8_t rawData[6];  // x/y/z accel register data stored here
  readBytes(MPU6050_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]);  // Read the six raw data registers into data array
  destination[0] = (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ;  // Turn the MSB and LSB into a signed 16-bit value
  destination[1] = (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;  
  destination[2] = (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ; 
}

void mpu6050::readGyroData(int16_t * destination)
{
  uint8_t rawData[6];  // x/y/z gyro register data stored here
  readBytes(MPU6050_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]);  // Read the six raw data registers sequentially into data array
  destination[0] = (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ;  // Turn the MSB and LSB into a signed 16-bit value
  destination[1] = (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;  
  destination[2] = (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ; 
}

int16_t mpu6050::readTempData()
{
  uint8_t rawData[2];  // x/y/z gyro register data stored here
  readBytes(MPU6050_ADDRESS, TEMP_OUT_H, 2, &rawData[0]);  // Read the two raw data registers sequentially into data array 
  return (int16_t)(((int16_t)rawData[0]) << 8 | rawData[1]) ;  // Turn the MSB and LSB into a 16-bit value
}

// Configure the motion detection control for low power accelerometer mode
void mpu6050::lowPowerAccelOnly()
{

// The sensor has a high-pass filter necessary to invoke to allow the sensor motion detection algorithms work properly
// Motion detection occurs on free-fall (acceleration below a threshold for some time for all axes), motion (acceleration
// above a threshold for some time on at least one axis), and zero-motion toggle (acceleration on each axis less than a 
// threshold for some time sets this flag, motion above the threshold turns it off). The high-pass filter takes gravity out
// consideration for these threshold evaluations; otherwise, the flags would be set all the time!
  
  uint8_t c = readByte(MPU6050_ADDRESS, PWR_MGMT_1);
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, c & ~0x30); // Clear sleep and cycle bits [5:6]
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, c |  0x30); // Set sleep and cycle bits [5:6] to zero to make sure accelerometer is running

  c = readByte(MPU6050_ADDRESS, PWR_MGMT_2);
  writeByte(MPU6050_ADDRESS, PWR_MGMT_2, c & ~0x38); // Clear standby XA, YA, and ZA bits [3:5]
  writeByte(MPU6050_ADDRESS, PWR_MGMT_2, c |  0x00); // Set XA, YA, and ZA bits [3:5] to zero to make sure accelerometer is running
    
  c = readByte(MPU6050_ADDRESS, ACCEL_CONFIG);
  writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, c & ~0x07); // Clear high-pass filter bits [2:0]
// Set high-pass filter to 0) reset (disable), 1) 5 Hz, 2) 2.5 Hz, 3) 1.25 Hz, 4) 0.63 Hz, or 7) Hold
  writeByte(MPU6050_ADDRESS, ACCEL_CONFIG,  c | 0x00);  // Set ACCEL_HPF to 0; reset mode disbaling high-pass filter

  c = readByte(MPU6050_ADDRESS, CONFIG);
  writeByte(MPU6050_ADDRESS, CONFIG, c & ~0x07); // Clear low-pass filter bits [2:0]
  writeByte(MPU6050_ADDRESS, CONFIG, c |  0x00);  // Set DLPD_CFG to 0; 260 Hz bandwidth, 1 kHz rate
    
  c = readByte(MPU6050_ADDRESS, INT_ENABLE);
  writeByte(MPU6050_ADDRESS, INT_ENABLE, c & ~0xFF);  // Clear all interrupts
  writeByte(MPU6050_ADDRESS, INT_ENABLE, 0x40);  // Enable motion threshold (bits 5) interrupt only
  
// Motion detection interrupt requires the absolute value of any axis to lie above the detection threshold
// for at least the counter duration
  writeByte(MPU6050_ADDRESS, MOT_THR, 0x80); // Set motion detection to 0.256 g; LSB = 2 mg
  writeByte(MPU6050_ADDRESS, MOT_DUR, 0x01); // Set motion detect duration to 1  ms; LSB is 1 ms @ 1 kHz rate
  
  wait(0.1);  // Add delay for accumulation of samples
  
  c = readByte(MPU6050_ADDRESS, ACCEL_CONFIG);
  writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, c & ~0x07); // Clear high-pass filter bits [2:0]
  writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, c |  0x07);  // Set ACCEL_HPF to 7; hold the initial accleration value as a referance
   
  c = readByte(MPU6050_ADDRESS, PWR_MGMT_2);
  writeByte(MPU6050_ADDRESS, PWR_MGMT_2, c & ~0xC7); // Clear standby XA, YA, and ZA bits [3:5] and LP_WAKE_CTRL bits [6:7]
  writeByte(MPU6050_ADDRESS, PWR_MGMT_2, c |  0x47); // Set wakeup frequency to 5 Hz, and disable XG, YG, and ZG gyros (bits [0:2])  

  c = readByte(MPU6050_ADDRESS, PWR_MGMT_1);
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, c & ~0x20); // Clear sleep and cycle bit 5
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, c |  0x20); // Set cycle bit 5 to begin low power accelerometer motion interrupts

}


void mpu6050::reset() {
  // reset device
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
  wait(0.1);
  }
  
  
void mpu6050::init()
{  
 // Initialize MPU6050 device
 // wake up device
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, 0x00); // Clear sleep mode bit (6), enable all sensors 
  wait(0.1); // Delay 100 ms for PLL to get established on x-axis gyro; should check for PLL ready interrupt  

 // get stable time source
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, 0x01);  // Set clock source to be PLL with x-axis gyroscope reference, bits 2:0 = 001

 // Configure Gyro and Accelerometer
 // Disable FSYNC and set accelerometer and gyro bandwidth to 44 and 42 Hz, respectively; 
 // DLPF_CFG = bits 2:0 = 010; this sets the sample rate at 1 kHz for both
 // Maximum delay is 4.9 ms which is just over a 200 Hz maximum rate
  writeByte(MPU6050_ADDRESS, CONFIG, 0x03);  
 
 // Set sample rate = gyroscope output rate/(1 + SMPLRT_DIV)
  writeByte(MPU6050_ADDRESS, SMPLRT_DIV, 0x04);  // Use a 200 Hz rate; the same rate set in CONFIG above
 
 // Set gyroscope full scale range
 // Range selects FS_SEL and AFS_SEL are 0 - 3, so 2-bit values are left-shifted into positions 4:3
  uint8_t c =  readByte(MPU6050_ADDRESS, GYRO_CONFIG);
  writeByte(MPU6050_ADDRESS, GYRO_CONFIG, c & ~0xE0); // Clear self-test bits [7:5] 
  writeByte(MPU6050_ADDRESS, GYRO_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
  writeByte(MPU6050_ADDRESS, GYRO_CONFIG, c | Gscale << 3); // Set full scale range for the gyro
   
 // Set accelerometer configuration
  c =  readByte(MPU6050_ADDRESS, ACCEL_CONFIG);
  writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, c & ~0xE0); // Clear self-test bits [7:5] 
  writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
  writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, c | Ascale << 3); // Set full scale range for the accelerometer 

  // Configure Interrupts and Bypass Enable
  // Set interrupt pin active high, push-pull, and clear on read of INT_STATUS, enable I2C_BYPASS_EN so additional chips 
  // can join the I2C bus and all can be controlled by the Arduino as master
   writeByte(MPU6050_ADDRESS, INT_PIN_CFG, 0x22);    
   writeByte(MPU6050_ADDRESS, INT_ENABLE, 0x01);  // Enable data ready (bit 0) interrupt
}

// Function which accumulates gyro and accelerometer data after device initialization. It calculates the average
// of the at-rest readings and then loads the resulting offsets into accelerometer and gyro bias registers.
void mpu6050::calibrate(float * dest1, float * dest2)
{  
  uint8_t data[12]; // data array to hold accelerometer and gyro x, y, z, data
  uint16_t ii, packet_count, fifo_count;
  int32_t gyro_bias[3] = {0, 0, 0}, accel_bias[3] = {0, 0, 0};
  
// reset device, reset all registers, clear gyro and accelerometer bias registers
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
  wait(0.1);  
   
// get stable time source
// Set clock source to be PLL with x-axis gyroscope reference, bits 2:0 = 001
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, 0x01);  
  writeByte(MPU6050_ADDRESS, PWR_MGMT_2, 0x00); 
  wait(0.2);
  
// Configure device for bias calculation
  writeByte(MPU6050_ADDRESS, INT_ENABLE, 0x00);   // Disable all interrupts
  writeByte(MPU6050_ADDRESS, FIFO_EN, 0x00);      // Disable FIFO
  writeByte(MPU6050_ADDRESS, PWR_MGMT_1, 0x00);   // Turn on internal clock source
  writeByte(MPU6050_ADDRESS, I2C_MST_CTRL, 0x00); // Disable I2C master
  writeByte(MPU6050_ADDRESS, USER_CTRL, 0x00);    // Disable FIFO and I2C master modes
  writeByte(MPU6050_ADDRESS, USER_CTRL, 0x0C);    // Reset FIFO and DMP
  wait(0.015);
  
// Configure MPU6050 gyro and accelerometer for bias calculation
  writeByte(MPU6050_ADDRESS, CONFIG, 0x01);      // Set low-pass filter to 188 Hz
  writeByte(MPU6050_ADDRESS, SMPLRT_DIV, 0x00);  // Set sample rate to 1 kHz
  writeByte(MPU6050_ADDRESS, GYRO_CONFIG, 0x00);  // Set gyro full-scale to 250 degrees per second, maximum sensitivity
  writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, 0x00); // Set accelerometer full-scale to 2 g, maximum sensitivity
 
  uint16_t  gyrosensitivity  = 131;   // = 131 LSB/degrees/sec
  uint16_t  accelsensitivity = 16384;  // = 16384 LSB/g

// Configure FIFO to capture accelerometer and gyro data for bias calculation
  writeByte(MPU6050_ADDRESS, USER_CTRL, 0x40);   // Enable FIFO  
  writeByte(MPU6050_ADDRESS, FIFO_EN, 0x78);     // Enable gyro and accelerometer sensors for FIFO  (max size 1024 bytes in MPU-6050)
  wait(0.08); // accumulate 80 samples in 80 milliseconds = 960 bytes

// At end of sample accumulation, turn off FIFO sensor read
  writeByte(MPU6050_ADDRESS, FIFO_EN, 0x00);        // Disable gyro and accelerometer sensors for FIFO
  readBytes(MPU6050_ADDRESS, FIFO_COUNTH, 2, &data[0]); // read FIFO sample count
  fifo_count = ((uint16_t)data[0] << 8) | data[1];
  packet_count = fifo_count/12;// How many sets of full gyro and accelerometer data for averaging

  for (ii = 0; ii < packet_count; ii++) {
    int16_t accel_temp[3] = {0, 0, 0}, gyro_temp[3] = {0, 0, 0};
    readBytes(MPU6050_ADDRESS, FIFO_R_W, 12, &data[0]); // read data for averaging
    accel_temp[0] = (int16_t) (((int16_t)data[0] << 8) | data[1]  ) ;  // Form signed 16-bit integer for each sample in FIFO
    accel_temp[1] = (int16_t) (((int16_t)data[2] << 8) | data[3]  ) ;
    accel_temp[2] = (int16_t) (((int16_t)data[4] << 8) | data[5]  ) ;    
    gyro_temp[0]  = (int16_t) (((int16_t)data[6] << 8) | data[7]  ) ;
    gyro_temp[1]  = (int16_t) (((int16_t)data[8] << 8) | data[9]  ) ;
    gyro_temp[2]  = (int16_t) (((int16_t)data[10] << 8) | data[11]) ;
    
    accel_bias[0] += (int32_t) accel_temp[0]; // Sum individual signed 16-bit biases to get accumulated signed 32-bit biases
    accel_bias[1] += (int32_t) accel_temp[1];
    accel_bias[2] += (int32_t) accel_temp[2];
    gyro_bias[0]  += (int32_t) gyro_temp[0];
    gyro_bias[1]  += (int32_t) gyro_temp[1];
    gyro_bias[2]  += (int32_t) gyro_temp[2];
            
}
    accel_bias[0] /= (int32_t) packet_count; // Normalize sums to get average count biases
    accel_bias[1] /= (int32_t) packet_count;
    accel_bias[2] /= (int32_t) packet_count;
    gyro_bias[0]  /= (int32_t) packet_count;
    gyro_bias[1]  /= (int32_t) packet_count;
    gyro_bias[2]  /= (int32_t) packet_count;
    
  if(accel_bias[2] > 0L) {accel_bias[2] -= (int32_t) accelsensitivity;}  // Remove gravity from the z-axis accelerometer bias calculation
  else {accel_bias[2] += (int32_t) accelsensitivity;}
 
// Construct the gyro biases for push to the hardware gyro bias registers, which are reset to zero upon device startup
  data[0] = (-gyro_bias[0]/4  >> 8) & 0xFF; // Divide by 4 to get 32.9 LSB per deg/s to conform to expected bias input format
  data[1] = (-gyro_bias[0]/4)       & 0xFF; // Biases are additive, so change sign on calculated average gyro biases
  data[2] = (-gyro_bias[1]/4  >> 8) & 0xFF;
  data[3] = (-gyro_bias[1]/4)       & 0xFF;
  data[4] = (-gyro_bias[2]/4  >> 8) & 0xFF;
  data[5] = (-gyro_bias[2]/4)       & 0xFF;

// Push gyro biases to hardware registers
  writeByte(MPU6050_ADDRESS, XG_OFFS_USRH, data[0]); 
  writeByte(MPU6050_ADDRESS, XG_OFFS_USRL, data[1]);
  writeByte(MPU6050_ADDRESS, YG_OFFS_USRH, data[2]);
  writeByte(MPU6050_ADDRESS, YG_OFFS_USRL, data[3]);
  writeByte(MPU6050_ADDRESS, ZG_OFFS_USRH, data[4]);
  writeByte(MPU6050_ADDRESS, ZG_OFFS_USRL, data[5]);

  dest1[0] = (float) gyro_bias[0]/(float) gyrosensitivity; // construct gyro bias in deg/s for later manual subtraction
  dest1[1] = (float) gyro_bias[1]/(float) gyrosensitivity;
  dest1[2] = (float) gyro_bias[2]/(float) gyrosensitivity;

// Construct the accelerometer biases for push to the hardware accelerometer bias registers. These registers contain
// factory trim values which must be added to the calculated accelerometer biases; on boot up these registers will hold
// non-zero values. In addition, bit 0 of the lower byte must be preserved since it is used for temperature
// compensation calculations. Accelerometer bias registers expect bias input as 2048 LSB per g, so that
// the accelerometer biases calculated above must be divided by 8.

  int32_t accel_bias_reg[3] = {0, 0, 0}; // A place to hold the factory accelerometer trim biases
  readBytes(MPU6050_ADDRESS, XA_OFFSET_H, 2, &data[0]); // Read factory accelerometer trim values
  accel_bias_reg[0] = (int16_t) ((int16_t)data[0] << 8) | data[1];
  readBytes(MPU6050_ADDRESS, YA_OFFSET_H, 2, &data[0]);
  accel_bias_reg[1] = (int16_t) ((int16_t)data[0] << 8) | data[1];
  readBytes(MPU6050_ADDRESS, ZA_OFFSET_H, 2, &data[0]);
  accel_bias_reg[2] = (int16_t) ((int16_t)data[0] << 8) | data[1];
  
  uint32_t mask = 1uL; // Define mask for temperature compensation bit 0 of lower byte of accelerometer bias registers
  uint8_t mask_bit[3] = {0, 0, 0}; // Define array to hold mask bit for each accelerometer bias axis
  
  for(ii = 0; ii < 3; ii++) {
    if(accel_bias_reg[ii] & mask) mask_bit[ii] = 0x01; // If temperature compensation bit is set, record that fact in mask_bit
  }

  // Construct total accelerometer bias, including calculated average accelerometer bias from above
  accel_bias_reg[0] -= (accel_bias[0]/8); // Subtract calculated averaged accelerometer bias scaled to 2048 LSB/g (16 g full scale)
  accel_bias_reg[1] -= (accel_bias[1]/8);
  accel_bias_reg[2] -= (accel_bias[2]/8);
 
  data[0] = (accel_bias_reg[0] >> 8) & 0xFF;
  data[1] = (accel_bias_reg[0])      & 0xFF;
  data[1] = data[1] | mask_bit[0]; // preserve temperature compensation bit when writing back to accelerometer bias registers
  data[2] = (accel_bias_reg[1] >> 8) & 0xFF;
  data[3] = (accel_bias_reg[1])      & 0xFF;
  data[3] = data[3] | mask_bit[1]; // preserve temperature compensation bit when writing back to accelerometer bias registers
  data[4] = (accel_bias_reg[2] >> 8) & 0xFF;
  data[5] = (accel_bias_reg[2])      & 0xFF;
  data[5] = data[5] | mask_bit[2]; // preserve temperature compensation bit when writing back to accelerometer bias registers

  // Push accelerometer biases to hardware registers
//  writeByte(MPU6050_ADDRESS, XA_OFFSET_H, data[0]);  
//  writeByte(MPU6050_ADDRESS, XA_OFFSET_L_TC, data[1]);
//  writeByte(MPU6050_ADDRESS, YA_OFFSET_H, data[2]);
//  writeByte(MPU6050_ADDRESS, YA_OFFSET_L_TC, data[3]);  
//  writeByte(MPU6050_ADDRESS, ZA_OFFSET_H, data[4]);
//  writeByte(MPU6050_ADDRESS, ZA_OFFSET_L_TC, data[5]);

// Output scaled accelerometer biases for manual subtraction in the main program
   dest2[0] = (float)accel_bias[0]/(float)accelsensitivity; 
   dest2[1] = (float)accel_bias[1]/(float)accelsensitivity;
   dest2[2] = (float)accel_bias[2]/(float)accelsensitivity;
}


// Accelerometer and gyroscope self test; check calibration wrt factory settings
void mpu6050::selfTest(float * destination) // Should return percent deviation from factory trim values, +/- 14 or less deviation is a pass
{
   uint8_t rawData[4] = {0, 0, 0, 0};
   uint8_t selfTest[6];
   float factoryTrim[6];
   
   // Configure the accelerometer for self-test
   writeByte(MPU6050_ADDRESS, ACCEL_CONFIG, 0xF0); // Enable self test on all three axes and set accelerometer range to +/- 8 g
   writeByte(MPU6050_ADDRESS, GYRO_CONFIG,  0xE0); // Enable self test on all three axes and set gyro range to +/- 250 degrees/s
   wait(0.25);  // Delay a while to let the device execute the self-test
   rawData[0] = readByte(MPU6050_ADDRESS, SELF_TEST_X); // X-axis self-test results
   rawData[1] = readByte(MPU6050_ADDRESS, SELF_TEST_Y); // Y-axis self-test results
   rawData[2] = readByte(MPU6050_ADDRESS, SELF_TEST_Z); // Z-axis self-test results
   rawData[3] = readByte(MPU6050_ADDRESS, SELF_TEST_A); // Mixed-axis self-test results
   // Extract the acceleration test results first
   selfTest[0] = (rawData[0] >> 3) | (rawData[3] & 0x30) >> 4 ; // XA_TEST result is a five-bit unsigned integer
   selfTest[1] = (rawData[1] >> 3) | (rawData[3] & 0x0C) >> 4 ; // YA_TEST result is a five-bit unsigned integer
   selfTest[2] = (rawData[2] >> 3) | (rawData[3] & 0x03) >> 4 ; // ZA_TEST result is a five-bit unsigned integer
   // Extract the gyration test results first
   selfTest[3] = rawData[0]  & 0x1F ; // XG_TEST result is a five-bit unsigned integer
   selfTest[4] = rawData[1]  & 0x1F ; // YG_TEST result is a five-bit unsigned integer
   selfTest[5] = rawData[2]  & 0x1F ; // ZG_TEST result is a five-bit unsigned integer   
   // Process results to allow final comparison with factory set values
   factoryTrim[0] = (4096.0f*0.34f)*(pow( (0.92f/0.34f) , ((selfTest[0] - 1.0f)/30.0f))); // FT[Xa] factory trim calculation
   factoryTrim[1] = (4096.0f*0.34f)*(pow( (0.92f/0.34f) , ((selfTest[1] - 1.0f)/30.0f))); // FT[Ya] factory trim calculation
   factoryTrim[2] = (4096.0f*0.34f)*(pow( (0.92f/0.34f) , ((selfTest[2] - 1.0f)/30.0f))); // FT[Za] factory trim calculation
   factoryTrim[3] =  ( 25.0f*131.0f)*(pow( 1.046f , (selfTest[3] - 1.0f) ));             // FT[Xg] factory trim calculation
   factoryTrim[4] =  (-25.0f*131.0f)*(pow( 1.046f , (selfTest[4] - 1.0f) ));             // FT[Yg] factory trim calculation
   factoryTrim[5] =  ( 25.0f*131.0f)*(pow( 1.046f , (selfTest[5] - 1.0f) ));             // FT[Zg] factory trim calculation
   
 //  Output self-test results and factory trim calculation if desired
 //  Serial.println(selfTest[0]); Serial.println(selfTest[1]); Serial.println(selfTest[2]);
 //  Serial.println(selfTest[3]); Serial.println(selfTest[4]); Serial.println(selfTest[5]);
 //  Serial.println(factoryTrim[0]); Serial.println(factoryTrim[1]); Serial.println(factoryTrim[2]);
 //  Serial.println(factoryTrim[3]); Serial.println(factoryTrim[4]); Serial.println(factoryTrim[5]);

 // Report results as a ratio of (STR - FT)/FT; the change from Factory Trim of the Self-Test Response
 // To get to percent, must multiply by 100 and subtract result from 100
   for (int i = 0; i < 6; i++) {
     destination[i] = 100.0f + 100.0f*(selfTest[i] - factoryTrim[i])/factoryTrim[i]; // Report percent differences
   }
   
}


// Implementation of Sebastian Madgwick's "...efficient orientation filter for... inertial/magnetic sensor arrays"
// (see http://www.x-io.co.uk/category/open-source/ for examples and more details)
// which fuses acceleration and rotation rate to produce a quaternion-based estimate of relative
// device orientation -- which can be converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc.
// The performance of the orientation filter is at least as good as conventional Kalman-based filtering algorithms
// but is much less computationally intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz!
        void mpu6050::MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz)
        {
            float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];         // short name local variable for readability
            float norm;                                               // vector norm
            float f1, f2, f3;                                         // objective funcyion elements
            float J_11or24, J_12or23, J_13or22, J_14or21, J_32, J_33; // objective function Jacobian elements
            float qDot1, qDot2, qDot3, qDot4;
            float hatDot1, hatDot2, hatDot3, hatDot4;
            float gerrx, gerry, gerrz, gbiasx, gbiasy, gbiasz;  // gyro bias error

            // Auxiliary variables to avoid repeated arithmetic
            float _halfq1 = 0.5f * q1;
            float _halfq2 = 0.5f * q2;
            float _halfq3 = 0.5f * q3;
            float _halfq4 = 0.5f * q4;
            float _2q1 = 2.0f * q1;
            float _2q2 = 2.0f * q2;
            float _2q3 = 2.0f * q3;
            float _2q4 = 2.0f * q4;
//            float _2q1q3 = 2.0f * q1 * q3;
//            float _2q3q4 = 2.0f * q3 * q4;

            // Normalise accelerometer measurement
            norm = sqrt(ax * ax + ay * ay + az * az);
            if (norm == 0.0f) return; // handle NaN
            norm = 1.0f/norm;
            ax *= norm;
            ay *= norm;
            az *= norm;
            
            // Compute the objective function and Jacobian
            f1 = _2q2 * q4 - _2q1 * q3 - ax;
            f2 = _2q1 * q2 + _2q3 * q4 - ay;
            f3 = 1.0f - _2q2 * q2 - _2q3 * q3 - az;
            J_11or24 = _2q3;
            J_12or23 = _2q4;
            J_13or22 = _2q1;
            J_14or21 = _2q2;
            J_32 = 2.0f * J_14or21;
            J_33 = 2.0f * J_11or24;
          
            // Compute the gradient (matrix multiplication)
            hatDot1 = J_14or21 * f2 - J_11or24 * f1;
            hatDot2 = J_12or23 * f1 + J_13or22 * f2 - J_32 * f3;
            hatDot3 = J_12or23 * f2 - J_33 *f3 - J_13or22 * f1;
            hatDot4 = J_14or21 * f1 + J_11or24 * f2;
            
            // Normalize the gradient
            norm = sqrt(hatDot1 * hatDot1 + hatDot2 * hatDot2 + hatDot3 * hatDot3 + hatDot4 * hatDot4);
            hatDot1 /= norm;
            hatDot2 /= norm;
            hatDot3 /= norm;
            hatDot4 /= norm;
            
            // Compute estimated gyroscope biases
            gerrx = _2q1 * hatDot2 - _2q2 * hatDot1 - _2q3 * hatDot4 + _2q4 * hatDot3;
            gerry = _2q1 * hatDot3 + _2q2 * hatDot4 - _2q3 * hatDot1 - _2q4 * hatDot2;
            gerrz = _2q1 * hatDot4 - _2q2 * hatDot3 + _2q3 * hatDot2 - _2q4 * hatDot1;
            
            // Compute and remove gyroscope biases
            gbiasx += gerrx * deltat * zeta;
            gbiasy += gerry * deltat * zeta;
            gbiasz += gerrz * deltat * zeta;
 //           gx -= gbiasx;
 //           gy -= gbiasy;
 //           gz -= gbiasz;
            
            // Compute the quaternion derivative
            qDot1 = -_halfq2 * gx - _halfq3 * gy - _halfq4 * gz;
            qDot2 =  _halfq1 * gx + _halfq3 * gz - _halfq4 * gy;
            qDot3 =  _halfq1 * gy - _halfq2 * gz + _halfq4 * gx;
            qDot4 =  _halfq1 * gz + _halfq2 * gy - _halfq3 * gx;

            // Compute then integrate estimated quaternion derivative
            q1 += (qDot1 -(beta * hatDot1)) * deltat;
            q2 += (qDot2 -(beta * hatDot2)) * deltat;
            q3 += (qDot3 -(beta * hatDot3)) * deltat;
            q4 += (qDot4 -(beta * hatDot4)) * deltat;

            // Normalize the quaternion
            norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);    // normalise quaternion
            norm = 1.0f/norm;
            q[0] = q1 * norm;
            q[1] = q2 * norm;
            q[2] = q3 * norm;
            q[3] = q4 * norm;
            
        }