ardupilot/ArducopterNG/DCM.pde

/*
 www.ArduCopter.com - www.DIYDrones.com
 Copyright (c) 2010.  All rights reserved.
 An Open Source Arduino based multicopter.
 
 File     : DCM.pde
 Version  : v1.0, Aug 27, 2010
 Author(s): ArduCopter Team
             Ted Carancho (aeroquad), Jose Julio, Jordi Muñoz,
             Jani Hirvinen, Ken McEwans, Roberto Navoni,          
             Sandro Benigno, Chris Anderson
 
 This program is free software: you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation, either version 3 of the License, or
 (at your option) any later version.
 
 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/>.

* ************************************************************** *
ChangeLog:


* ************************************************************** *
TODO:


* ************************************************************** */

/* ******************************************* */

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

  Vector_Scale(&temporary[0][0], &DCM_Matrix[1][0], error); //eq.19
  Vector_Scale(&temporary[1][0], &DCM_Matrix[0][0], error); //eq.19
  
  Vector_Add(&temporary[0][0], &temporary[0][0], &DCM_Matrix[0][0]);//eq.19
  Vector_Add(&temporary[1][0], &temporary[1][0], &DCM_Matrix[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_Matrix[0][0], &temporary[0][0], renorm);
  
  renorm= .5 *(3 - Vector_Dot_Product(&temporary[1][0],&temporary[1][0])); //eq.21
  Vector_Scale(&DCM_Matrix[1][0], &temporary[1][0], renorm);
  
  renorm= .5 *(3 - Vector_Dot_Product(&temporary[2][0],&temporary[2][0])); //eq.21
  Vector_Scale(&DCM_Matrix[2][0], &temporary[2][0], renorm);
}

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

  Vector_Cross_Product(&errorRollPitch[0],&Accel_Vector[0],&DCM_Matrix[2][0]); //adjust the ground of reference
  // errorRollPitch are in Accel ADC units
  // Limit max errorRollPitch to limit max Omega_P and Omega_I
  errorRollPitch[0] = constrain(errorRollPitch[0],-50,50);
  errorRollPitch[1] = constrain(errorRollPitch[1],-50,50);
  errorRollPitch[2] = constrain(errorRollPitch[2],-50,50);
  Vector_Scale(&Omega_P[0],&errorRollPitch[0],Kp_ROLLPITCH);
  
  Vector_Scale(&Scaled_Omega_I[0],&errorRollPitch[0],Ki_ROLLPITCH);
  Vector_Add(Omega_I,Omega_I,Scaled_Omega_I);
  
  //*****YAW***************
  // We make the gyro YAW drift correction based on compass magnetic heading 
  if (MAGNETOMETER == 1) {
    errorCourse= (DCM_Matrix[0][0]*AP_Compass.heading_y) - (DCM_Matrix[1][0]*AP_Compass.heading_x);  //Calculating YAW error
    Vector_Scale(errorYaw,&DCM_Matrix[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);
    Vector_Add(Omega_P,Omega_P,Scaled_Omega_P);//Adding  Proportional.
    
    // Limit max errorYaw to limit max Omega_I
    errorYaw[0] = constrain(errorYaw[0],-50,50);
    errorYaw[1] = constrain(errorYaw[1],-50,50);
    errorYaw[2] = constrain(errorYaw[2],-50,50);
  
    Vector_Scale(&Scaled_Omega_I[0],&errorYaw[0],Ki_YAW);
    Vector_Add(Omega_I,Omega_I,Scaled_Omega_I);//adding integrator to the Omega_I
  }

}
/**************************************************/
void 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
}
/**************************************************/

void Matrix_update(void)
{
  Gyro_Vector[0]=Gyro_Scaled_X(read_adc(0)); //gyro x roll
  Gyro_Vector[1]=Gyro_Scaled_Y(read_adc(1)); //gyro y pitch
  Gyro_Vector[2]=Gyro_Scaled_Z(read_adc(2)); //gyro Z yaw
  
  // Low pass filter on accelerometer data (to filter vibrations)
  Accel_Vector[0]=Accel_Vector[0]*0.6 + (float)read_adc(3)*0.4; // acc x
  Accel_Vector[1]=Accel_Vector[1]*0.6 + (float)read_adc(4)*0.4; // acc y
  Accel_Vector[2]=Accel_Vector[2]*0.6 + (float)read_adc(5)*0.4; // acc z
  
  Vector_Add(&Omega[0], &Gyro_Vector[0], &Omega_I[0]);//adding integrator
  Vector_Add(&Omega_Vector[0], &Omega[0], &Omega_P[0]);//adding proportional
  
  //Accel_adjust();//adjusting centrifugal acceleration. // Not used for quadcopter
  
 #if OUTPUTMODE==1 // corrected mode
  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;
  #endif
  #if OUTPUTMODE==0 // uncorrected data of the gyros (with drift)
  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(DCM_Matrix,Update_Matrix,Temporary_Matrix); //a*b=c

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

void Euler_angles(void)
{
  #if (OUTPUTMODE==2)         // Only accelerometer info (debugging purposes)
    roll = atan2(Accel_Vector[1],Accel_Vector[2]);   // atan2(acc_y,acc_z)
    pitch = -asin((Accel_Vector[0])/(float)GRAVITY); // asin(acc_x)
    yaw = 0;
  #else        // Euler angles from DCM matrix
    pitch = asin(-DCM_Matrix[2][0]);
    roll = atan2(DCM_Matrix[2][1],DCM_Matrix[2][2]);
    yaw = atan2(DCM_Matrix[1][0],DCM_Matrix[0][0]);
  #endif
}


// VECTOR FUNCTIONS
//Computes the dot product of two vectors
float Vector_Dot_Product(float vector1[3],float vector2[3])
{
  float op=0;
  
  for(int c=0; c<3; c++)
  {
  op+=vector1[c]*vector2[c];
  }
  
  return op; 
}

//Computes the cross product of two vectors
void Vector_Cross_Product(float vectorOut[3], float v1[3],float v2[3])
{
  vectorOut[0]= (v1[1]*v2[2]) - (v1[2]*v2[1]);
  vectorOut[1]= (v1[2]*v2[0]) - (v1[0]*v2[2]);
  vectorOut[2]= (v1[0]*v2[1]) - (v1[1]*v2[0]);
}

//Multiply the vector by a scalar. 
void Vector_Scale(float vectorOut[3],float vectorIn[3], float scale2)
{
  for(int c=0; c<3; c++)
  {
   vectorOut[c]=vectorIn[c]*scale2; 
  }
}

void Vector_Add(float vectorOut[3],float vectorIn1[3], float vectorIn2[3])
{
  for(int c=0; c<3; c++)
  {
     vectorOut[c]=vectorIn1[c]+vectorIn2[c];
  }
}

/********* MATRIX FUNCTIONS *****************************************/
//Multiply two 3x3 matrixs. This function developed by Jordi can be easily adapted to multiple n*n matrix's. (Pero me da flojera!). 
void Matrix_Multiply(float a[3][3], float b[3][3],float mat[3][3])
{
  float op[3]; 
  for(int x=0; x<3; x++)
  {
    for(int y=0; y<3; y++)
    {
      for(int w=0; w<3; w++)
      {
       op[w]=a[x][w]*b[w][y];
      } 
      mat[x][y]=0;
      mat[x][y]=op[0]+op[1]+op[2];
      
      float test=mat[x][y];
    }
  }
}