File content as of revision 3:907803d8be4d:

/*
FreeIMU.cpp - A libre and easy to use orientation sensing library for Arduino
Copyright (C) 2011-2012 Fabio Varesano <fabio at varesano dot net>

Development of this code has been supported by the Department of Computer Science,
Universita' degli Studi di Torino, Italy within the Piemonte Project
http://www.piemonte.di.unito.it/


This program is free software: you can redistribute it and/or modify
it under the terms of the version 3 GNU General Public License as
published by the Free Software Foundation.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.

02/20/2013 - Modified by Aloïs Wolff for MBED with MPU6050 only (wolffalois@gmail.com)
*/

//#include <inttypes.h>
//#include <stdint.h>
//#define DEBUG
#include "FreeIMU.h"
#define     M_PI 3.1415926535897932384626433832795

#ifdef DEBUG
 #define DEBUG_PRINT(x) Serial.println(x)
 #else
 #define DEBUG_PRINT(x)
 #endif
// #include "WireUtils.h"
//#include "DebugUtils.h"

//#include "vector_math.h"

FreeIMU::FreeIMU() {

    accgyro = MPU6050(0x69); // I2C

  // initialize quaternion
  q0 = 1.0f;
  q1 = 0.0f;
  q2 = 0.0f;
  q3 = 0.0f;
  exInt = 0.0;
  eyInt = 0.0;
  ezInt = 0.0;
  twoKp = twoKpDef;
  twoKi = twoKiDef;
  integralFBx = 0.0f,  integralFBy = 0.0f, integralFBz = 0.0f;
  
  
  update.start();
  int dt_us=0;
  /*
  lastUpdate = 0;
  now = 0;
  */
  #ifndef CALIBRATION_H
  // initialize scale factors to neutral values
  acc_scale_x = 1;
  acc_scale_y = 1;
  acc_scale_z = 1;
  magn_scale_x = 1;
  magn_scale_y = 1;
  magn_scale_z = 1;
  #else
  // get values from global variables of same name defined in calibration.h
  acc_off_x = ::acc_off_x;
  acc_off_y = ::acc_off_y;
  acc_off_z = ::acc_off_z;
  acc_scale_x = ::acc_scale_x;
  acc_scale_y = ::acc_scale_y;
  acc_scale_z = ::acc_scale_z;
  magn_off_x = ::magn_off_x;
  magn_off_y = ::magn_off_y;
  magn_off_z = ::magn_off_z;
  magn_scale_x = ::magn_scale_x;
  magn_scale_y = ::magn_scale_y;
  magn_scale_z = ::magn_scale_z;
  #endif
}

void FreeIMU::init() {

  init(FIMU_ACCGYRO_ADDR, false);

}

void FreeIMU::init(bool fastmode) {
 
  init(FIMU_ACCGYRO_ADDR, fastmode);
 
}


/**
 * Initialize the FreeIMU I2C bus, sensors and performs gyro offsets calibration
*/

void FreeIMU::init(int accgyro_addr, bool fastmode) {

  wait_ms(5);
  /*
  // disable internal pullups of the ATMEGA which Wire enable by default
  #if defined(__AVR_ATmega168__) || defined(__AVR_ATmega8__) || defined(__AVR_ATmega328P__)
    // deactivate internal pull-ups for twi
    // as per note from atmega8 manual pg167
    cbi(PORTC, 4);
    cbi(PORTC, 5);
  #else
    // deactivate internal pull-ups for twi
    // as per note from atmega128 manual pg204
    cbi(PORTD, 0);
    cbi(PORTD, 1);
  #endif
  */
  
  /*
  if(fastmode) { // switch to 400KHz I2C - eheheh
    TWBR = ((F_CPU / 400000L) - 16) / 2; // see twi_init in Wire/utility/twi.c
  }
*/
  //accgyro = MPU6050(false, accgyro_addr);
  accgyro = MPU6050(0x69);
  accgyro.initialize();
  accgyro.setI2CMasterModeEnabled(0);
  accgyro.setI2CBypassEnabled(1);
  accgyro.setFullScaleGyroRange(MPU6050_GYRO_FS_2000);
  wait_ms(5);

  
  // zero gyro
  zeroGyro();
  
  #ifndef CALIBRATION_H
  // load calibration from eeprom
  calLoad();
  #endif
}
/*
#ifndef CALIBRATION_H

static uint8_t location; // assuming ordered reads

void eeprom_read_var(uint8_t size, byte * var) {
  for(uint8_t i = 0; i<size; i++) {
    var[i] = EEPROM.read(location + i);
  }
  location += size;
}
*/
void FreeIMU::calLoad() {
/*
  if(EEPROM.read(FREEIMU_EEPROM_BASE) == FREEIMU_EEPROM_SIGNATURE) { // check if signature is ok so we have good data
    location = FREEIMU_EEPROM_BASE + 1; // reset location
    
    eeprom_read_var(sizeof(acc_off_x), (byte *) &acc_off_x);
    eeprom_read_var(sizeof(acc_off_y), (byte *) &acc_off_y);
    eeprom_read_var(sizeof(acc_off_z), (byte *) &acc_off_z);
    
    eeprom_read_var(sizeof(magn_off_x), (byte *) &magn_off_x);
    eeprom_read_var(sizeof(magn_off_y), (byte *) &magn_off_y);
    eeprom_read_var(sizeof(magn_off_z), (byte *) &magn_off_z);
    
    eeprom_read_var(sizeof(acc_scale_x), (byte *) &acc_scale_x);
    eeprom_read_var(sizeof(acc_scale_y), (byte *) &acc_scale_y);
    eeprom_read_var(sizeof(acc_scale_z), (byte *) &acc_scale_z);
    
    eeprom_read_var(sizeof(magn_scale_x), (byte *) &magn_scale_x);
    eeprom_read_var(sizeof(magn_scale_y), (byte *) &magn_scale_y);
    eeprom_read_var(sizeof(magn_scale_z), (byte *) &magn_scale_z);
  }
  else {
  */
    acc_off_x = 0;
    acc_off_y = 0;
    acc_off_z = 0;
    acc_scale_x = 1;
    acc_scale_y = 1;
    acc_scale_z = 1;

    magn_off_x = 0;
    magn_off_y = 0;
    magn_off_z = 0;
    magn_scale_x = 1;
    magn_scale_y = 1;
    magn_scale_z = 1;
 // }
}
//#endif

/**
 * Populates raw_values with the raw_values from the sensors
*/
void FreeIMU::getRawValues(int16_t * raw_values) {

    accgyro.getMotion6(&raw_values[0], &raw_values[1], &raw_values[2], &raw_values[3], &raw_values[4], &raw_values[5]);

}


/**
 * Populates values with calibrated readings from the sensors
*/
void FreeIMU::getValues(float * values) {  

// MPU6050
    int16_t accgyroval[6];
    accgyro.getMotion6(&accgyroval[0], &accgyroval[1], &accgyroval[2], &accgyroval[3], &accgyroval[4], &accgyroval[5]);
    
    // remove offsets from the gyroscope
    accgyroval[3] = accgyroval[3] - gyro_off_x;
    accgyroval[4] = accgyroval[4] - gyro_off_y;
    accgyroval[5] = accgyroval[5] - gyro_off_z;

    for(int i = 0; i<6; i++) {
      if(i < 3) {
        values[i] = (float) accgyroval[i];
      }
      else {
        values[i] = ((float) accgyroval[i]) / 16.4f; // NOTE: this depends on the sensitivity chosen
      }
    }

  
  
  #warning Accelerometer calibration active: have you calibrated your device?
  // remove offsets and scale accelerometer (calibration)
  values[0] = (values[0] - acc_off_x) / acc_scale_x;
  values[1] = (values[1] - acc_off_y) / acc_scale_y;
  values[2] = (values[2] - acc_off_z) / acc_scale_z;
  
  
 
}


/**
 * Computes gyro offsets
*/
void FreeIMU::zeroGyro() {
  const int totSamples = 3;
  int16_t raw[11];
  float tmpOffsets[] = {0,0,0};
  
  for (int i = 0; i < totSamples; i++){
    getRawValues(raw);
    tmpOffsets[0] += raw[3];
    tmpOffsets[1] += raw[4];
    tmpOffsets[2] += raw[5];
  }
  
  gyro_off_x = tmpOffsets[0] / totSamples;
  gyro_off_y = tmpOffsets[1] / totSamples;
  gyro_off_z = tmpOffsets[2] / totSamples;
}


/**
 * Quaternion implementation of the 'DCM filter' [Mayhony et al].  Incorporates the magnetic distortion
 * compensation algorithms from Sebastian Madgwick's filter which eliminates the need for a reference
 * direction of flux (bx bz) to be predefined and limits the effect of magnetic distortions to yaw
 * axis only.
 * 
 * @see: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
*/

void  FreeIMU::AHRSupdate(float gx, float gy, float gz, float ax, float ay, float az) {

  float recipNorm;
  float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
  float halfex = 0.0f, halfey = 0.0f, halfez = 0.0f;
  float qa, qb, qc;

  // Auxiliary variables to avoid repeated arithmetic
  q0q0 = q0 * q0;
  q0q1 = q0 * q1;
  q0q2 = q0 * q2;
  q0q3 = q0 * q3;
  q1q1 = q1 * q1;
  q1q2 = q1 * q2;
  q1q3 = q1 * q3;
  q2q2 = q2 * q2;
  q2q3 = q2 * q3;
  q3q3 = q3 * q3;
  
  

  // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
  if((ax != 0.0f) && (ay != 0.0f) && (az != 0.0f)) {
    float halfvx, halfvy, halfvz;
    
    // Normalise accelerometer measurement
    recipNorm = invSqrt(ax * ax + ay * ay + az * az);
    ax *= recipNorm;
    ay *= recipNorm;
    az *= recipNorm;
    
    // Estimated direction of gravity
    halfvx = q1q3 - q0q2;
    halfvy = q0q1 + q2q3;
    halfvz = q0q0 - 0.5f + q3q3;
  
    // Error is sum of cross product between estimated direction and measured direction of field vectors
    halfex += (ay * halfvz - az * halfvy);
    halfey += (az * halfvx - ax * halfvz);
    halfez += (ax * halfvy - ay * halfvx);
  }

  // Apply feedback only when valid data has been gathered from the accelerometer or magnetometer
  if(halfex != 0.0f && halfey != 0.0f && halfez != 0.0f) {
    // Compute and apply integral feedback if enabled
    if(twoKi > 0.0f) {
      integralFBx += twoKi * halfex * (1.0f / sampleFreq);  // integral error scaled by Ki
      integralFBy += twoKi * halfey * (1.0f / sampleFreq);
      integralFBz += twoKi * halfez * (1.0f / sampleFreq);
      gx += integralFBx;  // apply integral feedback
      gy += integralFBy;
      gz += integralFBz;
    }
    else {
      integralFBx = 0.0f; // prevent integral windup
      integralFBy = 0.0f;
      integralFBz = 0.0f;
    }

    // Apply proportional feedback
    gx += twoKp * halfex;
    gy += twoKp * halfey;
    gz += twoKp * halfez;
  }
  
  // Integrate rate of change of quaternion
  gx *= (0.5f * (1.0f / sampleFreq));   // pre-multiply common factors
  gy *= (0.5f * (1.0f / sampleFreq));
  gz *= (0.5f * (1.0f / sampleFreq));
  qa = q0;
  qb = q1;
  qc = q2;
  q0 += (-qb * gx - qc * gy - q3 * gz);
  q1 += (qa * gx + qc * gz - q3 * gy);
  q2 += (qa * gy - qb * gz + q3 * gx);
  q3 += (qa * gz + qb * gy - qc * gx);
  
  // Normalise quaternion
  recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
  q0 *= recipNorm;
  q1 *= recipNorm;
  q2 *= recipNorm;
  q3 *= recipNorm;
}


/**
 * Populates array q with a quaternion representing the IMU orientation with respect to the Earth
 * 
 * @param q the quaternion to populate
*/
void FreeIMU::getQ(float * q) {
  float val[9];
  getValues(val);
  
  DEBUG_PRINT(val[3] * M_PI/180);
  DEBUG_PRINT(val[4] * M_PI/180);
  DEBUG_PRINT(val[5] * M_PI/180);
  DEBUG_PRINT(val[0]);
  DEBUG_PRINT(val[1]);
  DEBUG_PRINT(val[2]);
  DEBUG_PRINT(val[6]);
  DEBUG_PRINT(val[7]);
  DEBUG_PRINT(val[8]);
  
  //now = micros();
  dt_us=update.read_us();
  sampleFreq = 1.0 / ((dt_us) / 1000000.0);
  update.reset();
 // lastUpdate = now;
  // gyro values are expressed in deg/sec, the * M_PI/180 will convert it to radians/sec

    AHRSupdate(val[3] * M_PI/180, val[4] * M_PI/180, val[5] * M_PI/180, val[0], val[1], val[2]);

  
  q[0] = q0;
  q[1] = q1;
  q[2] = q2;
  q[3] = q3;
}



/**
 * Returns the Euler angles in radians defined in the Aerospace sequence.
 * See Sebastian O.H. Madwick report "An efficient orientation filter for 
 * inertial and intertial/magnetic sensor arrays" Chapter 2 Quaternion representation
 * 
 * @param angles three floats array which will be populated by the Euler angles in radians
*/
void FreeIMU::getEulerRad(float * angles) {
  float q[4]; // quaternion
  getQ(q);
  angles[0] = atan2(2 * q[1] * q[2] - 2 * q[0] * q[3], 2 * q[0]*q[0] + 2 * q[1] * q[1] - 1); // psi
  angles[1] = -asin(2 * q[1] * q[3] + 2 * q[0] * q[2]); // theta
  angles[2] = atan2(2 * q[2] * q[3] - 2 * q[0] * q[1], 2 * q[0] * q[0] + 2 * q[3] * q[3] - 1); // phi
}


/**
 * Returns the Euler angles in degrees defined with the Aerospace sequence.
 * See Sebastian O.H. Madwick report "An efficient orientation filter for 
 * inertial and intertial/magnetic sensor arrays" Chapter 2 Quaternion representation
 * 
 * @param angles three floats array which will be populated by the Euler angles in degrees
*/
void FreeIMU::getEuler(float * angles) {
  getEulerRad(angles);
  arr3_rad_to_deg(angles);
}


/**
 * Returns the yaw pitch and roll angles, respectively defined as the angles in radians between
 * the Earth North and the IMU X axis (yaw), the Earth ground plane and the IMU X axis (pitch)
 * and the Earth ground plane and the IMU Y axis.
 * 
 * @note This is not an Euler representation: the rotations aren't consecutive rotations but only
 * angles from Earth and the IMU. For Euler representation Yaw, Pitch and Roll see FreeIMU::getEuler
 * 
 * @param ypr three floats array which will be populated by Yaw, Pitch and Roll angles in radians
*/
void FreeIMU::getYawPitchRollRad(float * ypr) {
  float q[4]; // quaternion
  float gx, gy, gz; // estimated gravity direction
  getQ(q);
  
  gx = 2 * (q[1]*q[3] - q[0]*q[2]);
  gy = 2 * (q[0]*q[1] + q[2]*q[3]);
  gz = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
  
  ypr[0] = atan2(2 * q[1] * q[2] - 2 * q[0] * q[3], 2 * q[0]*q[0] + 2 * q[1] * q[1] - 1);
  ypr[1] = atan(gx / sqrt(gy*gy + gz*gz));
  ypr[2] = atan(gy / sqrt(gx*gx + gz*gz));
}


/**
 * Returns the yaw pitch and roll angles, respectively defined as the angles in degrees between
 * the Earth North and the IMU X axis (yaw), the Earth ground plane and the IMU X axis (pitch)
 * and the Earth ground plane and the IMU Y axis.
 * 
 * @note This is not an Euler representation: the rotations aren't consecutive rotations but only
 * angles from Earth and the IMU. For Euler representation Yaw, Pitch and Roll see FreeIMU::getEuler
 * 
 * @param ypr three floats array which will be populated by Yaw, Pitch and Roll angles in degrees
*/
void FreeIMU::getYawPitchRoll(float * ypr) {
  getYawPitchRollRad(ypr);
  arr3_rad_to_deg(ypr);
}


/**
 * Converts a 3 elements array arr of angles expressed in radians into degrees
*/
void arr3_rad_to_deg(float * arr) {
  arr[0] *= 180/M_PI;
  arr[1] *= 180/M_PI;
  arr[2] *= 180/M_PI;
}


/**
 * Fast inverse square root implementation
 * @see http://en.wikipedia.org/wiki/Fast_inverse_square_root
*/
float invSqrt(float number) {
  volatile long i;
  volatile float x, y;
  volatile const float f = 1.5F;

  x = number * 0.5F;
  y = number;
  i = * ( long * ) &y;
  i = 0x5f375a86 - ( i >> 1 );
  y = * ( float * ) &i;
  y = y * ( f - ( x * y * y ) );
  return y;
}