Diff: sensor_fusion.h

Revision:

24:cbdf0f7d33bd

Child:

25:6e43bbe76aec

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/sensor_fusion.h	Tue Sep 20 04:18:34 2016 +0000
@@ -0,0 +1,211 @@
+#ifndef SENSOR_FUSION_H
+#define SENSOR_FUSION_H
+
+#include "mbed.h"
+
+// parameters for 6 DoF sensor fusion calculations
+float PI = 3.14159265358979323846f;
+float GyroMeasError = PI * (60.0f / 180.0f);     // gyroscope measurement error in rads/s (start at 60 deg/s), then reduce after ~10 s to 3
+float beta = sqrt(3.0f / 4.0f) * GyroMeasError;  // compute beta
+float GyroMeasDrift = PI * (1.0f / 180.0f);      // gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
+float zeta = sqrt(3.0f / 4.0f) * GyroMeasDrift;  // compute zeta, the other free parameter in the Madgwick scheme usually set to a small or zero value
+#define Kp 2.0f * 5.0f // these are the free parameters in the Mahony filter and fusion scheme, Kp for proportional feedback, Ki for integral
+#define Ki 0.0f
+
+
+float q[4] = {1.0f, 0.0f, 0.0f, 0.0f};           // vector to hold quaternion
+float eInt[3] = {0.0f, 0.0f, 0.0f};              // vector to hold integral error for Mahony method
+float pitch, yaw, roll;
+float deltat = 0.0f;                             // integration interval for both filter schemes
+int lastUpdate = 0, firstUpdate = 0, Now = 0;    // used to calculate integration interval
+
+// Implementation of Sebastian Madgwick's "...efficient orientation filter for... inertial/magnetic sensor arrays"
+// (see http://www.x-io.co.uk/category/open-source/ for examples and more details)
+// which fuses acceleration, rotation rate, and magnetic moments to produce a quaternion-based estimate of absolute
+// device orientation -- which can be converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc.
+// The performance of the orientation filter is at least as good as conventional Kalman-based filtering algorithms
+// but is much less computationally intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz!
+void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz)
+{
+    float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
+    float norm;
+    float hx, hy, _2bx, _2bz;
+    float s1, s2, s3, s4;
+    float qDot1, qDot2, qDot3, qDot4;
+
+    // Auxiliary variables to avoid repeated arithmetic
+    float _2q1mx;
+    float _2q1my;
+    float _2q1mz;
+    float _2q2mx;
+    float _4bx;
+    float _4bz;
+    float _2q1 = 2.0f * q1;
+    float _2q2 = 2.0f * q2;
+    float _2q3 = 2.0f * q3;
+    float _2q4 = 2.0f * q4;
+    float _2q1q3 = 2.0f * q1 * q3;
+    float _2q3q4 = 2.0f * q3 * q4;
+    float q1q1 = q1 * q1;
+    float q1q2 = q1 * q2;
+    float q1q3 = q1 * q3;
+    float q1q4 = q1 * q4;
+    float q2q2 = q2 * q2;
+    float q2q3 = q2 * q3;
+    float q2q4 = q2 * q4;
+    float q3q3 = q3 * q3;
+    float q3q4 = q3 * q4;
+    float q4q4 = q4 * q4;
+
+    // Normalise accelerometer measurement
+    norm = sqrt(ax * ax + ay * ay + az * az);
+    if (norm == 0.0f) return; // handle NaN
+    norm = 1.0f/norm;
+    ax *= norm;
+    ay *= norm;
+    az *= norm;
+
+    // Normalise magnetometer measurement
+    norm = sqrt(mx * mx + my * my + mz * mz);
+    if (norm == 0.0f) return; // handle NaN
+    norm = 1.0f/norm;
+    mx *= norm;
+    my *= norm;
+    mz *= norm;
+
+    // Reference direction of Earth's magnetic field
+    _2q1mx = 2.0f * q1 * mx;
+    _2q1my = 2.0f * q1 * my;
+    _2q1mz = 2.0f * q1 * mz;
+    _2q2mx = 2.0f * q2 * mx;
+    hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4;
+    hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4;
+    _2bx = sqrt(hx * hx + hy * hy);
+    _2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
+    _4bx = 2.0f * _2bx;
+    _4bz = 2.0f * _2bz;
+
+    // Gradient decent algorithm corrective step
+    s1 = -_2q3 * (2.0f * q2q4 - _2q1q3 - ax) + _2q2 * (2.0f * q1q2 + _2q3q4 - ay) - _2bz * q3 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q4 + _2bz * q2) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q3 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
+    s2 = _2q4 * (2.0f * q2q4 - _2q1q3 - ax) + _2q1 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q2 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + _2bz * q4 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q3 + _2bz * q1) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q4 - _4bz * q2) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
+    s3 = -_2q1 * (2.0f * q2q4 - _2q1q3 - ax) + _2q4 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q3 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + (-_4bx * q3 - _2bz * q1) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q2 + _2bz * q4) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q1 - _4bz * q3) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
+    s4 = _2q2 * (2.0f * q2q4 - _2q1q3 - ax) + _2q3 * (2.0f * q1q2 + _2q3q4 - ay) + (-_4bx * q4 + _2bz * q2) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q1 + _2bz * q3) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q2 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
+    norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4);    // normalise step magnitude
+    norm = 1.0f/norm;
+    s1 *= norm;
+    s2 *= norm;
+    s3 *= norm;
+    s4 *= norm;
+
+    // Compute rate of change of quaternion
+    qDot1 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - beta * s1;
+    qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - beta * s2;
+    qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - beta * s3;
+    qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - beta * s4;
+
+    // Integrate to yield quaternion
+    q1 += qDot1 * deltat;
+    q2 += qDot2 * deltat;
+    q3 += qDot3 * deltat;
+    q4 += qDot4 * deltat;
+    norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);    // normalise quaternion
+    norm = 1.0f/norm;
+    q[0] = q1 * norm;
+    q[1] = q2 * norm;
+    q[2] = q3 * norm;
+    q[3] = q4 * norm;
+
+}
+
+// Similar to Madgwick scheme but uses proportional and integral filtering on the error between estimated reference vectors and
+// measured ones.
+void MahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz)
+{
+    float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
+    float norm;
+    float hx, hy, bx, bz;
+    float vx, vy, vz, wx, wy, wz;
+    float ex, ey, ez;
+    float pa, pb, pc;
+
+    // Auxiliary variables to avoid repeated arithmetic
+    float q1q1 = q1 * q1;
+    float q1q2 = q1 * q2;
+    float q1q3 = q1 * q3;
+    float q1q4 = q1 * q4;
+    float q2q2 = q2 * q2;
+    float q2q3 = q2 * q3;
+    float q2q4 = q2 * q4;
+    float q3q3 = q3 * q3;
+    float q3q4 = q3 * q4;
+    float q4q4 = q4 * q4;
+
+    // Normalise accelerometer measurement
+    norm = sqrt(ax * ax + ay * ay + az * az);
+    if (norm == 0.0f) return; // handle NaN
+    norm = 1.0f / norm;        // use reciprocal for division
+    ax *= norm;
+    ay *= norm;
+    az *= norm;
+
+    // Normalise magnetometer measurement
+    norm = sqrt(mx * mx + my * my + mz * mz);
+    if (norm == 0.0f) return; // handle NaN
+    norm = 1.0f / norm;        // use reciprocal for division
+    mx *= norm;
+    my *= norm;
+    mz *= norm;
+
+    // Reference direction of Earth's magnetic field
+    hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3);
+    hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2);
+    bx = sqrt((hx * hx) + (hy * hy));
+    bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3);
+
+    // Estimated direction of gravity and magnetic field
+    vx = 2.0f * (q2q4 - q1q3);
+    vy = 2.0f * (q1q2 + q3q4);
+    vz = q1q1 - q2q2 - q3q3 + q4q4;
+    wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3);
+    wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4);
+    wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3);
+
+    // Error is cross product between estimated direction and measured direction of gravity
+    ex = (ay * vz - az * vy) + (my * wz - mz * wy);
+    ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
+    ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
+    if (Ki > 0.0f) {
+        eInt[0] += ex;      // accumulate integral error
+        eInt[1] += ey;
+        eInt[2] += ez;
+    } else {
+        eInt[0] = 0.0f;     // prevent integral wind up
+        eInt[1] = 0.0f;
+        eInt[2] = 0.0f;
+    }
+
+    // Apply feedback terms
+    gx = gx + Kp * ex + Ki * eInt[0];
+    gy = gy + Kp * ey + Ki * eInt[1];
+    gz = gz + Kp * ez + Ki * eInt[2];
+
+    // Integrate rate of change of quaternion
+    pa = q2;
+    pb = q3;
+    pc = q4;
+    q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * deltat);
+    q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * deltat);
+    q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * deltat);
+    q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * deltat);
+
+    // Normalise quaternion
+    norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
+    norm = 1.0f / norm;
+    q[0] = q1 * norm;
+    q[1] = q2 * norm;
+    q[2] = q3 * norm;
+    q[3] = q4 * norm;
+
+}
+
+#endif
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