File content as of revision 0:62284d27d75e:

/*
MinIMU-9-mbed-AHRS
Pololu MinIMU-9 + mbed AHRS (Attitude and Heading Reference System)

Modified and ported to mbed environment by Michael Shimniok
http://www.bot-thoughts.com/

Basedd on MinIMU-9-Arduino-AHRS
Pololu MinIMU-9 + Arduino AHRS (Attitude and Heading Reference System)

Copyright (c) 2011 Pololu Corporation.
http://www.pololu.com/

MinIMU-9-Arduino-AHRS is based on sf9domahrs by Doug Weibel and Jose Julio:
http://code.google.com/p/sf9domahrs/

sf9domahrs is based on ArduIMU v1.5 by Jordi Munoz and William Premerlani, Jose
Julio and Doug Weibel:
http://code.google.com/p/ardu-imu/

MinIMU-9-Arduino-AHRS is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published by the
Free Software Foundation, either version 3 of the License, or (at your option)
any later version.

MinIMU-9-Arduino-AHRS 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 Lesser General Public License for
more details.

You should have received a copy of the GNU Lesser General Public License along
with MinIMU-9-Arduino-AHRS. If not, see <http://www.gnu.org/licenses/>.

*/
#include "DCM.h"
#include "Matrix.h"
#include "math.h"
#include "Sensors.h"

#define MAG_SKIP 2

float DCM::constrain(float x, float a, float b) 
{
    float result = x;
    
    if (x < a) result = a;
    if (x > b) result = b;

    return result;  
}


DCM::DCM(void):
    G_Dt(0.02), update_count(MAG_SKIP)
{
    for (int m=0; m < 3; m++) {
        Accel_Vector[m] = 0;
        Gyro_Vector[m] = 0;
        Omega_Vector[m] = 0;
        Omega_P[m] = 0;
        Omega_I[m] = 0;
        Omega[m] = 0;
        errorRollPitch[m] = 0; 
        errorYaw[m] = 0;
        for (int n=0; n < 3; n++) {
            dcm[m][n] = (m == n) ? 1 : 0; // dcm starts as identity matrix
        }
    }
    
}


/**************************************************/
void DCM::Normalize(void)
{
  float error=0;
  float temporary[3][3];
  float renorm=0;
  
  error= -Vector_Dot_Product(&dcm[0][0], &dcm[1][0])*.5; //eq.19

  Vector_Scale(&temporary[0][0], &dcm[1][0], error); //eq.19
  Vector_Scale(&temporary[1][0], &dcm[0][0], error); //eq.19
  
  Vector_Add(&temporary[0][0], &temporary[0][0], &dcm[0][0]);//eq.19
  Vector_Add(&temporary[1][0], &temporary[1][0], &dcm[1][0]);//eq.19
  
  Vector_Cross_Product(&temporary[2][0],&temporary[0][0],&temporary[1][0]); // c= a x b //eq.20
  
  renorm= .5 *(3 - Vector_Dot_Product(&temporary[0][0],&temporary[0][0])); //eq.21
  Vector_Scale(&dcm[0][0], &temporary[0][0], renorm);
  
  renorm= .5 *(3 - Vector_Dot_Product(&temporary[1][0],&temporary[1][0])); //eq.21
  Vector_Scale(&dcm[1][0], &temporary[1][0], renorm);
  
  renorm= .5 *(3 - Vector_Dot_Product(&temporary[2][0],&temporary[2][0])); //eq.21
  Vector_Scale(&dcm[2][0], &temporary[2][0], renorm);
}

/**************************************************/
void DCM::Drift_correction(void)
{
  float mag_heading_x;
  float mag_heading_y;
  float errorCourse;
  //Compensation the Roll, Pitch and Yaw drift. 
  static float Scaled_Omega_P[3];
  static float Scaled_Omega_I[3];
  float Accel_magnitude;
  float Accel_weight;
  
  
  //*****Roll and Pitch***************

  // Calculate the magnitude of the accelerometer vector
  Accel_magnitude = sqrt(Accel_Vector[0]*Accel_Vector[0] + Accel_Vector[1]*Accel_Vector[1] + Accel_Vector[2]*Accel_Vector[2]);
  Accel_magnitude = Accel_magnitude / GRAVITY; // Scale to gravity.
  // Dynamic weighting of accelerometer info (reliability filter)
  // Weight for accelerometer info (<0.5G = 0.0, 1G = 1.0 , >1.5G = 0.0)
  Accel_weight = constrain(1 - 2*abs(1 - Accel_magnitude),0,1);  //  

  Vector_Cross_Product(&errorRollPitch[0],&Accel_Vector[0],&dcm[2][0]); //adjust the ground of reference
  Vector_Scale(&Omega_P[0],&errorRollPitch[0],Kp_ROLLPITCH*Accel_weight);
  
  Vector_Scale(&Scaled_Omega_I[0],&errorRollPitch[0],Ki_ROLLPITCH*Accel_weight);
  Vector_Add(Omega_I,Omega_I,Scaled_Omega_I);     
  
  //*****YAW***************
  // We make the gyro YAW drift correction based on compass magnetic heading

  /* http://tinyurl.com/7bul438
   * William Premerlani:
   * 1. If you are treating the magnetometer as a tilt compensated compass, it will not work for pitch values near 90 degrees.
   *    A better way to do it is to use the magnetometer measurement as a reference vector instead. Use the direction cosine
   *    matrix to transform the magnetometer vector from body frame to earth frame, which works in any orientation, even with
   *    90 degree pitch. Then, extract the horizontal component of the magnetometer earth frame vector, and take the cross
   *    product of it with the known horizontal component of the earth's magnetic field. The result is a rotation error vector
   *    that you transform back into the body frame, and use it to compensate for gyro drift. That is technique we are using in
   *    MatrixPilot, it works for any orientation. A combination of two reference vectors (magnetometer and accelerometer) will
   *     provide a 3 axis lock.
   * 2. If you are using Euler angles to represent orientation, they do not work for 90 degree pitch. There is an effect known 
   *    as "gimbal lock" that throws off the roll. It is better to use either an angle and rotation axis representation, or
   *    quaternions.
   *
   * ummm... we're no actually calculating MAG_Heading anywhere... so it's zero...
   * mag_earth[3x1] = mag[3x1] dot dcm[3x3]
   * earth_rotation_error_vector = mag_earth[x and y] cross known_earth_mag[??]
   * gyro drift error aka body_rotation_error_vector = earth_rotation_error_Vector times dcm[3x3]
  float mag_earth[3], mag_sensor[3];
  mag_sensor[0] = magnetom_x;
  mag_sensor[1] = magnetom_y;
  mag_sensor[2] = magnetom_z;
  mag_earth[0] = VectorDotProduct( &dcm[0] , mag_sensor ) << 1;
  mag_earth[1] = VectorDotProduct( &dcm[1] , mag_sensor ) << 1;
  mag_earth[2] = VectorDotProduct( &dcm[2] , mag_sensor ) << 1;
  mag_error = 100 * VectorDotProduct( 2 , mag_earth , declinationVector ) ; // Dotgain = 1/2
  VectorScale( 3 , errorYawplane , &rmat[6] , mag_error ) ; // Scalegain = 1/2
   */
 
  mag_heading_x = cos(MAG_Heading);
  mag_heading_y = sin(MAG_Heading);
  errorCourse=(dcm[0][0]*mag_heading_y) - (dcm[1][0]*mag_heading_x);  //Calculating YAW error
  Vector_Scale(errorYaw,&dcm[2][0],errorCourse); //Applys the yaw correction to the XYZ rotation of the aircraft, depeding the position.
  
  Vector_Scale(&Scaled_Omega_P[0],&errorYaw[0],Kp_YAW);//.01proportional of YAW.
  Vector_Add(Omega_P,Omega_P,Scaled_Omega_P);//Adding  Proportional.
  
  Vector_Scale(&Scaled_Omega_I[0],&errorYaw[0],Ki_YAW);//.00001Integrator
  Vector_Add(Omega_I,Omega_I,Scaled_Omega_I);//adding integrator to the Omega_I
}

/**************************************************/
void DCM::Accel_adjust(void)
{
 Accel_Vector[1] += Accel_Scale(speed_3d*Omega[2]);  // Centrifugal force on Acc_y = GPS_speed*GyroZ
 Accel_Vector[2] -= Accel_Scale(speed_3d*Omega[1]);  // Centrifugal force on Acc_z = GPS_speed*GyroY
 // Add linear (x-axis) acceleration correction here
 
// from MatrixPilot
// total (3D) airspeed in cm/sec is used to adjust for acceleration
//gplane[0]=gplane[0]- omegaSOG( omegaAccum[2] , air_speed_3DGPS ) ;
//gplane[2]=gplane[2]+ omegaSOG( omegaAccum[0] , air_speed_3DGPS ) ;
//gplane[1]=gplane[1]+ ((unsigned int)(ACCELSCALE))*forward_acceleration 
}

/**************************************************/
void DCM::Matrix_update(void)
{
  // TODO: Hardware-specific routines to convert gyro to units; this (probably) should be handled elsewhere

  Gyro_Vector[0]=Gyro_Scaled_X(gyro_x); //gyro x roll
  Gyro_Vector[1]=Gyro_Scaled_Y(gyro_y); //gyro y pitch
  Gyro_Vector[2]=Gyro_Scaled_Z(gyro_z); //gyro Z yaw
  
  // Why aren't we scaling accelerometer? I think the DCM paper talks a little about this... ??
  Accel_Vector[0]=accel_x;
  Accel_Vector[1]=accel_y;
  Accel_Vector[2]=accel_z;
    
  Vector_Add(&Omega[0], &Gyro_Vector[0], &Omega_I[0]);  //adding proportional term
  Vector_Add(&Omega_Vector[0], &Omega[0], &Omega_P[0]); //adding Integrator term

  // Remove centrifugal & linear acceleration.   
  Accel_adjust();    
  
 #if OUTPUTMODE==1         
  Update_Matrix[0][0]=0;
  Update_Matrix[0][1]=-G_Dt*Omega_Vector[2];//-z
  Update_Matrix[0][2]=G_Dt*Omega_Vector[1];//y
  Update_Matrix[1][0]=G_Dt*Omega_Vector[2];//z
  Update_Matrix[1][1]=0;
  Update_Matrix[1][2]=-G_Dt*Omega_Vector[0];//-x
  Update_Matrix[2][0]=-G_Dt*Omega_Vector[1];//-y
  Update_Matrix[2][1]=G_Dt*Omega_Vector[0];//x
  Update_Matrix[2][2]=0;
 #else                    // Uncorrected data (no drift correction)
  Update_Matrix[0][0]=0;
  Update_Matrix[0][1]=-G_Dt*Gyro_Vector[2];//-z
  Update_Matrix[0][2]=G_Dt*Gyro_Vector[1];//y
  Update_Matrix[1][0]=G_Dt*Gyro_Vector[2];//z
  Update_Matrix[1][1]=0;
  Update_Matrix[1][2]=-G_Dt*Gyro_Vector[0];
  Update_Matrix[2][0]=-G_Dt*Gyro_Vector[1];
  Update_Matrix[2][1]=G_Dt*Gyro_Vector[0];
  Update_Matrix[2][2]=0;
 #endif

  Matrix_Multiply(Temporary_Matrix, dcm, Update_Matrix); //c=a*b

// ???  Matrix_Add(dcm, dcm, Temporary_Matrix); ???
  for(int x=0; x<3; x++) { //Matrix Addition (update)
    for(int y=0; y<3; y++) {
      dcm[x][y] += Temporary_Matrix[x][y];
    } 
  }
}

void DCM::Euler_angles(void)
{
  pitch = -asin(dcm[2][0]);
  roll = atan2(dcm[2][1],dcm[2][2]);
  yaw = atan2(dcm[1][0],dcm[0][0]);
}

void DCM::Update_step()
{         
    Read_Gyro();
    Read_Accel();
    if (--update_count == 0) {
        Update_mag();
        update_count = MAG_SKIP;
    }
    Matrix_update();
    Normalize();
    Drift_correction();
    //Accel_adjust();
    Euler_angles();
}

void DCM::Update_mag()
{
    Read_Compass();
    Compass_Heading();
}