You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
287 lines
9.7 KiB
287 lines
9.7 KiB
//============================================================================================= |
|
// MadgwickAHRS.c |
|
//============================================================================================= |
|
// |
|
// Implementation of Madgwick's IMU and AHRS algorithms. |
|
// See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/ |
|
// |
|
// From the x-io website "Open-source resources available on this website are |
|
// provided under the GNU General Public Licence unless an alternative licence |
|
// is provided in source." |
|
// |
|
// Date Author Notes |
|
// 29/09/2011 SOH Madgwick Initial release |
|
// 02/10/2011 SOH Madgwick Optimised for reduced CPU load |
|
// 19/02/2012 SOH Madgwick Magnetometer measurement is normalised |
|
// |
|
//============================================================================================= |
|
|
|
//------------------------------------------------------------------------------------------- |
|
// Header files |
|
|
|
#include "MadgwickAHRS.h" |
|
#include <math.h> |
|
|
|
//------------------------------------------------------------------------------------------- |
|
// Definitions |
|
|
|
#define sampleFreqDef 512.0f // sample frequency in Hz |
|
#define betaDef 0.1f // 2 * proportional gain |
|
|
|
//============================================================================================ |
|
// Functions |
|
|
|
//------------------------------------------------------------------------------------------- |
|
// AHRS algorithm update |
|
|
|
Madgwick::Madgwick() { |
|
beta = betaDef; |
|
q0 = 1.0f; |
|
q1 = 0.0f; |
|
q2 = 0.0f; |
|
q3 = 0.0f; |
|
invSampleFreq = 1.0f / sampleFreqDef; |
|
anglesComputed = 0; |
|
} |
|
|
|
void Madgwick::update(float gx, float gy, float gz, float ax, float ay, |
|
float az, float mx, float my, float mz) { |
|
float recipNorm; |
|
float s0, s1, s2, s3; |
|
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; |
|
|
|
// Use IMU algorithm if magnetometer measurement invalid (avoids NaN in |
|
// magnetometer normalisation) |
|
if ((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) { |
|
updateIMU(gx, gy, gz, ax, ay, az); |
|
return; |
|
} |
|
|
|
// Convert gyroscope degrees/sec to radians/sec |
|
gx *= 0.0174533f; |
|
gy *= 0.0174533f; |
|
gz *= 0.0174533f; |
|
|
|
// 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 -= beta * s0; |
|
qDot2 -= beta * s1; |
|
qDot3 -= beta * s2; |
|
qDot4 -= beta * 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; |
|
anglesComputed = 0; |
|
} |
|
|
|
//------------------------------------------------------------------------------------------- |
|
// IMU algorithm update |
|
|
|
void Madgwick::updateIMU(float gx, float gy, float gz, float ax, float ay, |
|
float az) { |
|
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; |
|
|
|
// Convert gyroscope degrees/sec to radians/sec |
|
gx *= 0.0174533f; |
|
gy *= 0.0174533f; |
|
gz *= 0.0174533f; |
|
|
|
// 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 * 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; |
|
anglesComputed = 0; |
|
} |
|
|
|
//------------------------------------------------------------------------------------------- |
|
// Fast inverse square-root |
|
// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root |
|
|
|
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::computeAngles() { |
|
roll = atan2f(q0 * q1 + q2 * q3, 0.5f - q1 * q1 - q2 * q2); |
|
pitch = asinf(-2.0f * (q1 * q3 - q0 * q2)); |
|
yaw = atan2f(q1 * q2 + q0 * q3, 0.5f - q2 * q2 - q3 * q3); |
|
anglesComputed = 1; |
|
}
|
|
|