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madgwick.ino
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float B_madgwick = 0.02; //Madgwick filter parameter
//float B_madgwick = 0.02*loop_freq/100.0; //Madgwick filter parameter
void Madgwick(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float invSampleFreq) {
//DESCRIPTION: Attitude estimation through sensor fusion - 9DOF
/*
This function fuses the accelerometer gyro, and magnetometer readings AccX, AccY, AccZ, GyroX, GyroY, GyroZ, MagX, MagY, and MagZ for attitude estimation.
Don't worry about the math. There is a tunable parameter B_madgwick in the user specified variable section which basically
adjusts the weight of gyro data in the state estimate. Higher beta leads to noisier estimate, lower
beta leads to slower to respond estimate. It is currently tuned for 2kHz loop rate. This function updates the roll,
pitch, and yaw variables which are in degrees. If magnetometer data is not available, this function calls Madgwick6DOF() instead.
*/
float recipNorm;
float s0, s1, s2, s3;
float q0 = q(0);
float q1 = q(1);
float q2 = q(2);
float q3 = q(3);
float qDot1, qDot2, qDot3, qDot4;
float hx, hy;
float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
float mholder;
//Use 6DOF algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
if ((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
Madgwick6DOF(gx, gy, gz, ax, ay, az, invSampleFreq);
return;
}
//Rate of change of quaternion from gyroscope
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 valid (avoids NaN in accelerometer normalisation)
if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
//Normalise accelerometer measurement
recipNorm = invSqrt(ax * ax + ay * ay + az * az);
ax *= recipNorm;
ay *= recipNorm;
az *= recipNorm;
//Normalise 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 Earth's 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 = sqrtf(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;
//Gradient 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); // normalise step magnitude
s0 *= recipNorm;
s1 *= recipNorm;
s2 *= recipNorm;
s3 *= recipNorm;
//Apply feedback step
qDot1 -= B_madgwick * s0;
qDot2 -= B_madgwick * s1;
qDot3 -= B_madgwick * s2;
qDot4 -= B_madgwick * s3;
}
//Integrate rate of change of quaternion to yield quaternion
q0 += qDot1 * invSampleFreq;
q1 += qDot2 * invSampleFreq;
q2 += qDot3 * invSampleFreq;
q3 += qDot4 * invSampleFreq;
//Normalise quaternion
recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
q(0) = q0;
q(1) = q1;
q(2) = q2;
q(3) = q3;
// //compute angles - NWU
// rpy(0) = atan2(q0 * q1 + q2 * q3, 0.5f - q1 * q1 - q2 * q2) * 57.29577951; //degrees
// rpy(1) = -asin(-2.0f * (q1 * q3 - q0 * q2)) * 57.29577951; //degrees
// rpy(2) = -atan2(q1 * q2 + q0 * q3, 0.5f - q2 * q2 - q3 * q3) * 57.29577951; //degrees
// //compute angles
// roll = atan2(2 * (q0 * q1 + q2 * q3), 1.0f - 2 * (q1 * q1 + q2 * q2)) * 57.29577951; //degrees
// pitch = asin(2.0f * (q0 * q2 - q3 * q1)) * 57.29577951; //degrees
// yaw = atan2(2 * (q1 * q2 + q0 * q3), 1.0f - 2 * (q2 * q2 + q3 * q3)) * 57.29577951; //degrees
}
void Madgwick6DOF(float gx, float gy, float gz, float ax, float ay, float az, float invSampleFreq) {
//DESCRIPTION: Attitude estimation through sensor fusion - 6DOF
/*
See description of Madgwick() for more information. This is a 6DOF implimentation for when magnetometer data is not
available (for example when using the recommended MPU6050 IMU for the default setup).
*/
float recipNorm;
float s0, s1, s2, s3;
float q0 = q(0);
float q1 = q(1);
float q2 = q(2);
float q3 = q(3);
float qDot1, qDot2, qDot3, qDot4;
float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 , _8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
//Rate of change of quaternion from gyroscope
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 valid (avoids NaN in accelerometer normalisation)
if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
//Normalise 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;
//Gradient 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); //normalise step magnitude
s0 *= recipNorm;
s1 *= recipNorm;
s2 *= recipNorm;
s3 *= recipNorm;
//Apply feedback step
qDot1 -= B_madgwick * s0;
qDot2 -= B_madgwick * s1;
qDot3 -= B_madgwick * s2;
qDot4 -= B_madgwick * s3;
}
//Integrate rate of change of quaternion to yield quaternion
q0 += qDot1 * invSampleFreq;
q1 += qDot2 * invSampleFreq;
q2 += qDot3 * invSampleFreq;
q3 += qDot4 * invSampleFreq;
//Normalise quaternion
recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
q(0) = q0;
q(1) = q1;
q(2) = q2;
q(3) = q3;
// //compute angles
// roll = atan2(q0 * q1 + q2 * q3, 0.5f - q1 * q1 - q2 * q2) * 57.29577951; //degrees
// pitch = -asin(-2.0f * (q1 * q3 - q0 * q2)) * 57.29577951; //degrees
// yaw = -atan2(q1 * q2 + q0 * q3, 0.5f - q2 * q2 - q3 * q3) * 57.29577951; //degrees
// //compute angles
// roll = atan2(2 * (q0 * q1 + q2 * q3), 1.0f - 2 * (q1 * q1 + q2 * q2)) * 57.29577951; //degrees
// pitch = asin(2.0f * (q0 * q2 - q3 * q1)) * 57.29577951; //degrees
// yaw = atan2(2 * (q1 * q2 + q0 * q3), 1.0f - 2 * (q2 * q2 + q3 * q3)) * 57.29577951; //degrees
}
float invSqrt(float x) {
//Fast inverse sqrt for madgwick filter
/*
float halfx = 0.5f * x;
float y = x;
long i = *(long*)&y;
i = 0x5f3759df - (i>>1);
y = *(float*)&i;
y = y * (1.5f - (halfx * y * y));
y = y * (1.5f - (halfx * y * y));
return y;
*/
//alternate form:
unsigned int i = 0x5F1F1412 - (*(unsigned int*)&x >> 1);
float tmp = *(float*)&i;
float y = tmp * (1.69000231f - 0.714158168f * x * tmp * tmp);
return y;
}
void printMadgwickRollPitchYaw(int print_rate) {
if ( (current_time - print_counter) * micros2secs > (1.0 / print_rate)) {
print_counter = micros();
SERIAL_PORT.print(F("roll: "));
SERIAL_PORT.print(rpy(0)*rad2deg);
SERIAL_PORT.print(F(" pitch: "));
SERIAL_PORT.print(rpy(1)*rad2deg);
SERIAL_PORT.print(F(" yaw: "));
SERIAL_PORT.print(rpy(2)*rad2deg);
}
}
void printVisualizationYawPitchRoll(int print_rate) {
if ( (current_time - print_counter) * micros2secs > (1.0 / print_rate)) {
print_counter = micros();
SERIAL_PORT.print("Orientation: ");
// SERIAL_PORT.print(F(" yaw: "));
SERIAL_PORT.print(rad2deg * rpy(2));
// SERIAL_PORT.print(F(" pitch: "));
SERIAL_PORT.print(" ");
SERIAL_PORT.print(rad2deg * rpy(1));
// SERIAL_PORT.print(F("roll: "));
SERIAL_PORT.print(" ");
SERIAL_PORT.print(rad2deg * rpy(0));
}
}
void printMadgwickQuaternions(int print_rate) {
if ( (current_time - print_counter) * micros2secs > (1.0 / print_rate)) {
print_counter = micros();
SERIAL_PORT.print(F("q(0): "));
SERIAL_PORT.print(q(0));
SERIAL_PORT.print(F(" q(1): "));
SERIAL_PORT.print(q(1));
SERIAL_PORT.print(F(" q(2): "));
SERIAL_PORT.print(q(2));
SERIAL_PORT.print(F(" q(3): "));
SERIAL_PORT.print(q(3));
}
}