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Madgwick.cpp
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Madgwick.cpp
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#include "Madgwick.h"
#define Kp 2.0f * 5.0f
#define Ki 0.0f
float Madgwick::invSqrt(float x) {
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;
}
void Madgwick::Update(float ax, float ay, float az, float gx, float gy,
float gz, float deltat) {
float q0 = q[0], q1 = q[1], q2 = q[2], q3 = q[3];
float recipNorm;
float s0, s1, s2, s3;
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 -= beta * s0;
qDot2 -= beta * s1;
qDot3 -= beta * s2;
qDot4 -= beta * s3;
}
// Integrate rate of change of quaternion to yield quaternion
q0 += qDot1 * deltat;
q1 += qDot2 * deltat;
q2 += qDot3 * deltat;
q3 += qDot4 * deltat;
// Normalise quaternion
recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
// 補正
q0 += 0.000021;
q1 += 0.000018;
q2 += 0.000152;
q3 += 0.000177;
q[0] = q0;
q[1] = q1;
q[2] = q2;
q[3] = q3;
float w = q[0];
float x = q[1];
float y = q[2];
float z = q[3];
r[0] = w * w + x * x - y * y - z * z;
r[1] = 2.0 * x * y - 2.0 * w * z;
r[2] = 2.0 * x * z + 2.0 * w * y;
r[3] = 2.0 * x * y + 2.0 * w * z;
r[4] = w * w - x * x + y * y - z * z;
r[5] = 2.0 * y * z - 2.0 * w * x;
r[6] = 2.0 * x * z - 2.0 * w * y;
r[7] = 2.0 * y * z + 2.0 * w * x;
r[8] = w * w - x * x - y * y + z * z;
// for (int i = 0; i < 4; ++i) Serial.printf("q[%d] = %f\r\n", i, q[i]);
}
const float* Madgwick::getR2() { return r; }