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195 lines
9.2 KiB
195 lines
9.2 KiB
#include "Arduino.h" |
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// Implementation of Sebastian Madgwick's "...efficient orientation filter for... inertial/magnetic sensor arrays" |
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// (see http://www.x-io.co.uk/category/open-source/ for examples and more details) |
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// which fuses acceleration, rotation rate, and magnetic moments to produce a quaternion-based estimate of absolute |
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// device orientation -- which can be converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc. |
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// The performance of the orientation filter is at least as good as conventional Kalman-based filtering algorithms |
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// but is much less computationally intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz! |
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void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz) |
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{ |
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float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3]; // short name local variable for readability |
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float norm; |
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float hx, hy, _2bx, _2bz; |
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float s1, s2, s3, s4; |
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float qDot1, qDot2, qDot3, qDot4; |
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// Auxiliary variables to avoid repeated arithmetic |
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float _2q1mx; |
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float _2q1my; |
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float _2q1mz; |
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float _2q2mx; |
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float _4bx; |
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float _4bz; |
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float _2q1 = 2.0f * q1; |
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float _2q2 = 2.0f * q2; |
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float _2q3 = 2.0f * q3; |
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float _2q4 = 2.0f * q4; |
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float _2q1q3 = 2.0f * q1 * q3; |
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float _2q3q4 = 2.0f * q3 * q4; |
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float q1q1 = q1 * q1; |
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float q1q2 = q1 * q2; |
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float q1q3 = q1 * q3; |
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float q1q4 = q1 * q4; |
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float q2q2 = q2 * q2; |
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float q2q3 = q2 * q3; |
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float q2q4 = q2 * q4; |
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float q3q3 = q3 * q3; |
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float q3q4 = q3 * q4; |
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float q4q4 = q4 * q4; |
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// Normalise accelerometer measurement |
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norm = sqrt(ax * ax + ay * ay + az * az); |
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if (norm == 0.0f) return; // handle NaN |
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norm = 1.0f/norm; |
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ax *= norm; |
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ay *= norm; |
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az *= norm; |
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// Normalise magnetometer measurement |
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norm = sqrt(mx * mx + my * my + mz * mz); |
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if (norm == 0.0f) return; // handle NaN |
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norm = 1.0f/norm; |
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mx *= norm; |
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my *= norm; |
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mz *= norm; |
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// Reference direction of Earth's magnetic field |
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_2q1mx = 2.0f * q1 * mx; |
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_2q1my = 2.0f * q1 * my; |
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_2q1mz = 2.0f * q1 * mz; |
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_2q2mx = 2.0f * q2 * mx; |
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hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4; |
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hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4; |
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_2bx = sqrt(hx * hx + hy * hy); |
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_2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4; |
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_4bx = 2.0f * _2bx; |
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_4bz = 2.0f * _2bz; |
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// Gradient decent algorithm corrective step |
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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); |
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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); |
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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); |
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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); |
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norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4); // normalise step magnitude |
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norm = 1.0f/norm; |
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s1 *= norm; |
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s2 *= norm; |
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s3 *= norm; |
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s4 *= norm; |
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// Compute rate of change of quaternion |
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qDot1 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - beta * s1; |
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qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - beta * s2; |
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qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - beta * s3; |
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qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - beta * s4; |
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// Integrate to yield quaternion |
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q1 += qDot1 * deltat; |
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q2 += qDot2 * deltat; |
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q3 += qDot3 * deltat; |
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q4 += qDot4 * deltat; |
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norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4); // normalise quaternion |
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norm = 1.0f/norm; |
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q[0] = q1 * norm; |
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q[1] = q2 * norm; |
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q[2] = q3 * norm; |
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q[3] = q4 * norm; |
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} |
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// Similar to Madgwick scheme but uses proportional and integral filtering on the error between estimated reference vectors and |
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// measured ones. |
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void MahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz) |
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{ |
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float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3]; // short name local variable for readability |
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float norm; |
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float hx, hy, bx, bz; |
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float vx, vy, vz, wx, wy, wz; |
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float ex, ey, ez; |
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float pa, pb, pc; |
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// Auxiliary variables to avoid repeated arithmetic |
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float q1q1 = q1 * q1; |
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float q1q2 = q1 * q2; |
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float q1q3 = q1 * q3; |
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float q1q4 = q1 * q4; |
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float q2q2 = q2 * q2; |
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float q2q3 = q2 * q3; |
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float q2q4 = q2 * q4; |
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float q3q3 = q3 * q3; |
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float q3q4 = q3 * q4; |
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float q4q4 = q4 * q4; |
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// Normalise accelerometer measurement |
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norm = sqrt(ax * ax + ay * ay + az * az); |
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if (norm == 0.0f) return; // handle NaN |
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norm = 1.0f / norm; // use reciprocal for division |
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ax *= norm; |
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ay *= norm; |
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az *= norm; |
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// Normalise magnetometer measurement |
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norm = sqrt(mx * mx + my * my + mz * mz); |
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if (norm == 0.0f) return; // handle NaN |
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norm = 1.0f / norm; // use reciprocal for division |
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mx *= norm; |
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my *= norm; |
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mz *= norm; |
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// Reference direction of Earth's magnetic field |
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hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3); |
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hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2); |
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bx = sqrt((hx * hx) + (hy * hy)); |
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bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3); |
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// Estimated direction of gravity and magnetic field |
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vx = 2.0f * (q2q4 - q1q3); |
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vy = 2.0f * (q1q2 + q3q4); |
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vz = q1q1 - q2q2 - q3q3 + q4q4; |
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wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3); |
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wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4); |
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wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3); |
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// Error is cross product between estimated direction and measured direction of gravity |
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ex = (ay * vz - az * vy) + (my * wz - mz * wy); |
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ey = (az * vx - ax * vz) + (mz * wx - mx * wz); |
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ez = (ax * vy - ay * vx) + (mx * wy - my * wx); |
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if (Ki > 0.0f) |
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{ |
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eInt[0] += ex; // accumulate integral error |
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eInt[1] += ey; |
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eInt[2] += ez; |
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} |
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else |
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{ |
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eInt[0] = 0.0f; // prevent integral wind up |
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eInt[1] = 0.0f; |
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eInt[2] = 0.0f; |
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} |
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// Apply feedback terms |
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gx = gx + Kp * ex + Ki * eInt[0]; |
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gy = gy + Kp * ey + Ki * eInt[1]; |
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gz = gz + Kp * ez + Ki * eInt[2]; |
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// Integrate rate of change of quaternion |
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pa = q2; |
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pb = q3; |
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pc = q4; |
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q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * deltat); |
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q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * deltat); |
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q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * deltat); |
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q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * deltat); |
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// Normalise quaternion |
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norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4); |
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norm = 1.0f / norm; |
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q[0] = q1 * norm; |
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q[1] = q2 * norm; |
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q[2] = q3 * norm; |
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q[3] = q4 * norm; |
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}
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