From 2a8fc64d5edf67945ad75674a325315682ecc8d5 Mon Sep 17 00:00:00 2001 From: Kris Winer Date: Sat, 27 Dec 2014 01:03:23 -0800 Subject: [PATCH] Create quaternionFilters.ino --- quaternionFilters.ino | 194 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 194 insertions(+) create mode 100644 quaternionFilters.ino diff --git a/quaternionFilters.ino b/quaternionFilters.ino new file mode 100644 index 0000000..b347c43 --- /dev/null +++ b/quaternionFilters.ino @@ -0,0 +1,194 @@ + +// 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; + + }