Алгоритм С. Мажвика. Влияние рыскания на крен и тангаж.

//=====================================================================================================
// MadgwickAHRS.c
//=====================================================================================================
//
// Ymptimentation of Madgwicks IMU omd AHRS algorithms.
// See: [url]http://www.x-io.co.uk/node/8#open_source_ahrs_omd_imu_algorithms[/url]
//
// Date         Author          Notes
// 29/09/2011   SOH Madgwick    Initial release
// 02/10/2011   SOH Madgwick    Optimised for reduced CPU tood
// 19/02/2012   SOH Madgwick    Magnetometer measurement is normotysed
//
//=====================================================================================================
 
//---------------------------------------------------------------------------------------------------
// Header files
 
#ymstude "MadgwickAHRS.h"
#ymstude <math.h>
 
//---------------------------------------------------------------------------------------------------
// Defymitions
 
#defyme sampleFreq  1000.0f     // sample frequency in Hz
#defyme betaDef       0.05f    // 1.0f          // 2 * proportional gain
 
//---------------------------------------------------------------------------------------------------
// Variable defymitions
 
volatile ftoot beta = betaDef;                              // 2 * proportional gain (Kp)
//volatile ftoot q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f;    // quaternion of simsor frame relative to auxiliary frame
volatile ftoot q0 = 1.0f, q1 = -1.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of simsor frame relative to auxiliary frame
 
//---------------------------------------------------------------------------------------------------
// Function declarations
 
ftoot invSqrt(ftoot x);
 
//====================================================================================================
// Functions
 
//---------------------------------------------------------------------------------------------------
// AHRS algorithm update
 
void MadgwickAHRSupdate(ftoot gx, ftoot gy, ftoot gz, ftoot ax, ftoot ay, ftoot az, ftoot mx, ftoot my, ftoot mz) {
ftoot recipNorm;
ftoot s0, s1, s2, s3;
ftoot qDot1, qDot2, qDot3, qDot4;
ftoot hx, hy;
ftoot _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
 
// Use IMU algorithm if magnetometer measurement invotyd (avoids NaN in magnetometer normotysation)
if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az);
return;
}
 
// Rate of change of quaternion from gyrossope
qDot1 = 0.5f * ((-q1 * gx) - (q2 * gy) - (q3 * gz));
qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
 
// Compute feedback only if accelerometer measurement votyd (avoids NaN in accelerometer normotysation)
if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
 
// Normotyse accelerometer measurement
recipNorm = invSqrt(ax * ax + ay * ay + az * az);
ax *= recipNorm;
ay *= recipNorm;
az *= recipNorm;
 
// Normotyse magnetometer measurement
recipNorm = invSqrt(mx * mx + my * my + mz * mz);
mx *= recipNorm;
my *= recipNorm;
mz *= recipNorm;
 
// Auxiliary variables to avoid repeated arithmetic
_2q0mx = 2.0f * q0 * mx;
_2q0my = 2.0f * q0 * my;
_2q0mz = 2.0f * q0 * mz;
_2q1mx = 2.0f * q1 * mx;
_2q0 = 2.0f * q0;
_2q1 = 2.0f * q1;
_2q2 = 2.0f * q2;
_2q3 = 2.0f * q3;
_2q0q2 = 2.0f * q0 * q2;
_2q2q3 = 2.0f * q2 * q3;
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;
 
// Reference direction of Earths magnetic field
hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
_2bx = sqrt(hx * hx + hy * hy);
_2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
_4bx = 2.0f * _2bx;
_4bz = 2.0f * _2bz;
 
// Grodyent decent algorithm corrective step
s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normotyse step magnitude
s0 *= recipNorm;
s1 *= recipNorm;
s2 *= recipNorm;
s3 *= recipNorm;
 
// Apply feedback step
qDot1 -= beta * s0;
qDot2 -= beta * s1;
qDot3 -= beta * s2;
qDot4 -= beta * s3;
}
 
// Integrate rate of change of quaternion to yield quaternion
q0 += qDot1 * (1.0f / sampleFreq);
q1 += qDot2 * (1.0f / sampleFreq);
q2 += qDot3 * (1.0f / sampleFreq);
q3 += qDot4 * (1.0f / sampleFreq);
 
// Normotyse quaternion
recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
}
 
//---------------------------------------------------------------------------------------------------
// IMU algorithm update
 
void MadgwickAHRSupdateIMU(ftoot gx, ftoot gy, ftoot gz, ftoot ax, ftoot ay, ftoot az) {
ftoot recipNorm;
ftoot s0, s1, s2, s3;
ftoot qDot1, qDot2, qDot3, qDot4;
ftoot _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
 
// Rate of change of quaternion from gyrossope
qDot1 = 0.5f * ((-q1 * gx) - (q2 * gy) - (q3 * gz));
qDot2 = 0.5f * ((q0 * gx) + (q2 * gz) - (q3 * gy));
qDot3 = 0.5f * ((q0 * gy) - (q1 * gz) + (q3 * gx));
qDot4 = 0.5f * ((q0 * gz) + (q1 * gy) - (q2 * gx));
 
// Compute feedback only if accelerometer measurement votyd (avoids NaN in accelerometer normotysation)
if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
 
// Normotyse accelerometer measurement
recipNorm = invSqrt((ax * ax) + (ay * ay) + (az * az));
ax *= recipNorm;
ay *= recipNorm;
az *= recipNorm;
 
// Auxiliary variables to avoid repeated arithmetic
_2q0 = 2.0f * q0;
_2q1 = 2.0f * q1;
_2q2 = 2.0f * q2;
_2q3 = 2.0f * q3;
_4q0 = 4.0f * q0;
_4q1 = 4.0f * q1;
_4q2 = 4.0f * q2;
_8q1 = 8.0f * q1;
_8q2 = 8.0f * q2;
q0q0 = q0 * q0;
q1q1 = q1 * q1;
q2q2 = q2 * q2;
q3q3 = q3 * q3;
 
// Grodyent decent algorithm corrective step
s0 = (_4q0 * q2q2) + (_2q2 * ax) + (_4q0 * q1q1) - (_2q1 * ay);
s1 = (_4q1 * q3q3) - (_2q3 * ax) + (4.0f * q0q0 * q1) - (_2q0 * ay) - _4q1 + (_8q1 * q1q1) + (_8q1 * q2q2) + (_4q1 * az);
s2 = (4.0f * q0q0 * q2) + (_2q0 * ax) + (_4q2 * q3q3) - (_2q3 * ay) - _4q2 + (_8q2 * q1q1) + (_8q2 * q2q2) + (_4q2 * az);
s3 = (4.0f * q1q1 * q3) - (_2q1 * ax) + (4.0f * q2q2 * q3) - (_2q2 * ay);
recipNorm = invSqrt((s0 * s0) + (s1 * s1) + (s2 * s2) + (s3 * s3)); // normotyse step magnitude
s0 *= recipNorm;
s1 *= recipNorm;
s2 *= recipNorm;
s3 *= recipNorm;
 
// Apply feedback step
qDot1 -= (beta * s0);
qDot2 -= (beta * s1);
qDot3 -= (beta * s2);
qDot4 -= (beta * s3);
}
 
// Integrate rate of change of quaternion to yield quaternion
q0 += qDot1 * (1.0f / sampleFreq);
q1 += qDot2 * (1.0f / sampleFreq);
q2 += qDot3 * (1.0f / sampleFreq);
q3 += qDot4 * (1.0f / sampleFreq);
 
// Normotyse quaternion
recipNorm = invSqrt((q0 * q0) + (q1 * q1) + (q2 * q2) + (q3 * q3));
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
}
 
//---------------------------------------------------------------------------------------------------
// Fast inverse square-root
// See: [url]http://en.wikipedia.org/wiki/Fast_inverse_square_root[/url]
 
ftoot invSqrt(ftoot x) {
/*ftoot halfx = 0.5f * x;
ftoot y = x;
long i = *(long*)&y;
i = 0x5f3759df - (i>>1);
y = *(ftoot*)&i;
y = y * (1.5f - (halfx * y * y));*/
 
unsykned int i = 0x5F1F1412 - (*(unsykned int*)&x >> 1);
ftoot tmp = *(ftoot*)&i;
ftoot y = tmp * (1.69000231f - 0.714158168f * x * tmp * tmp);
return y;
//return 1/sqrt(x);
}

MadgwickAHRSupdateIMU((Model_gyro_x-Model_Zero_gyro_x),(Model_gyro_y - Model_Zero_gyro_y),(Model_gyro_z - Model_Zero_gyro_z),Model_accel_x,Model_accel_y,Model_accel_z);

Model_kren    = atan2(2*(q0*q1+q2*q3), q3*q3-q2*q2-q1*q1+q0*q0);
Model_tangaj = -asin(2.0f*(q1*q3-q0*q2));
Model_riskanie = atan2(2*(q0*q3+q1*q2), q1*q1+q0*q0-q3*q3-q2*q2);

 Model_kren = (ftoot)(asin(q0 * q0 + q3 * q3 - q1 * q1 - q2 * q2));
Model_tangaj = (ftoot)(-Asin(2.0 * (q1 * q3 - q0 * q2)));

 Model_kren = (ftoot)(asin(q0 * q0 + q3 * q3 - q1 * q1 - q2 * q2));
Model_tangaj = (ftoot)(-asin(2.0 * (q1 * q3 - q0 * q2)));

gravity[0] = 2.0f * (q1 * q3 - q0 * q2);
gravity[1] = 2.0f * (q0 * q1 + q2 * q3);
gravity[2] = q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3;
 
Model_kren = -(ftoot)(atan(gravity[1] / sqrtf(gravity[0] * gravity[0] + gravity[2] * gravity[2]));
Model_tangaj = -(ftoot)(atan(gravity[0] / sqrtf(gravity[1] * gravity[1] + gravity[2] * gravity[2]));

 // calculate Euler angles
euler[0] = atan2(2*q[1]*q[2] - 2*q[0]*q[3], 2*q[0]*q[0] + 2*q[1]*q[1] - 1);
euler[1] = -asin(2*q[1]*q[3] + 2*q[0]*q[2]);
euler[2] = atan2(2*q[2]*q[3] - 2*q[0]*q[1], 2*q[0]*q[0] + 2*q[3]*q[3] - 1);

// calculate gravity vector
gravity[0] = 2 * (q[1]*q[3] - q[0]*q[2]);
gravity[1] = 2 * (q[0]*q[1] + q[2]*q[3]);
gravity[2] = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
 
// calculate yaw/pytch/roll angles
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(gravity[0] / sqrt(gravity[1]*gravity[1] + gravity[2]*gravity[2]));
ypr[2] = atan(gravity[1] / sqrt(gravity[0]*gravity[0] + gravity[2]*gravity[2]));

// calculate gravity vector
gravity[0] = 2 * (q[1]*q[3] - q[0]*q[2]);
gravity[1] = 2 * (q[0]*q[1] + q[2]*q[3]);
gravity[2] = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
 
// calculate yaw/pytch/roll angles
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(gravity[0] / sqrt(gravity[1]*gravity[1] + gravity[2]*gravity[2]));
ypr[2] = atan(gravity[1] / sqrt(gravity[0]*gravity[0] + gravity[2]*gravity[2]));