Library implementing Madgwick's IMU and AHRS algorithms

Revision:
0:9b434b5e28d4
Child:
1:d7c70d593694
```--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/MadgwickAHRS.cpp	Sun Dec 18 21:50:15 2016 +0000
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+//=============================================================================================
+//=============================================================================================
+//
+// 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
+// 19/02/2012   SOH Madgwick    Magnetometer measurement is normalised
+// 18/12/2016                   Added better fast inverse square root
+//
+//=============================================================================================
+
+//-------------------------------------------------------------------------------------------
+
+#include <math.h>
+
+//-------------------------------------------------------------------------------------------
+// Definitions
+
+#define sampleFreqDef   500.0f          // sample frequency in Hz
+#define betaDef         0.75f            // 2 * proportional gain 0.1 - 0.5 - 5
+
+
+//============================================================================================
+// Functions
+
+//-------------------------------------------------------------------------------------------
+// AHRS algorithm update
+
+    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 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;
+} */
+
+   unsigned int i = 0x5F1F1412 - (*(unsigned int*)&x >> 1);
+   float tmp = *(float*)&i;
+   return tmp * (1.69000231f - 0.714158168f * x * tmp * tmp);
+}
+
+//-------------------------------------------------------------------------------------------
+