2012-03-03 00:49:38 -04:00
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/*
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AP_Quaternion code, based on quaternion code from Jeb Madgwick
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See http://www.x-io.co.uk/res/doc/madgwick_internal_report.pdf
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adapted to APM by Andrew Tridgell
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later
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version.
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*/
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#include <AP_Quaternion.h>
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#define ToRad(x) (x*0.01745329252) // *pi/180
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#define ToDeg(x) (x*57.2957795131) // *180/pi
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// this is the speed in cm/s above which we first get a yaw lock with
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// the GPS
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#define GPS_SPEED_MIN 300
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// this is the speed in cm/s at which we stop using drift correction
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// from the GPS and wait for the ground speed to get above GPS_SPEED_MIN
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#define GPS_SPEED_RESET 100
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void
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AP_Quaternion::set_compass(Compass *compass)
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{
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_compass = compass;
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}
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// Function to compute one quaternion iteration without magnetometer
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void AP_Quaternion::update_IMU(float deltat, Vector3f &gyro, Vector3f &accel)
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{
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// Local system variables
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float norm; // vector norm
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float SEqDot_omega_1, SEqDot_omega_2, SEqDot_omega_3, SEqDot_omega_4; // quaternion derrivative from gyroscopes elements
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float f_1, f_2, f_3; // objective function elements
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float J_11or24, J_12or23, J_13or22, J_14or21, J_32, J_33; // objective function Jacobian elements
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float SEqHatDot_1, SEqHatDot_2, SEqHatDot_3, SEqHatDot_4; // estimated direction of the gyroscope error
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// Axulirary variables to avoid reapeated calcualtions
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float halfSEq_1 = 0.5f * SEq_1;
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float halfSEq_2 = 0.5f * SEq_2;
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float halfSEq_3 = 0.5f * SEq_3;
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float halfSEq_4 = 0.5f * SEq_4;
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float twoSEq_1 = 2.0f * SEq_1;
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float twoSEq_2 = 2.0f * SEq_2;
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float twoSEq_3 = 2.0f * SEq_3;
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// estimated direction of the gyroscope error (radians)
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Vector3f w_err;
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// normalise accelerometer vector
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accel.normalize();
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// Compute the objective function and Jacobian
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f_1 = twoSEq_2 * SEq_4 - twoSEq_1 * SEq_3 - accel.x;
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f_2 = twoSEq_1 * SEq_2 + twoSEq_3 * SEq_4 - accel.y;
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f_3 = 1.0f - twoSEq_2 * SEq_2 - twoSEq_3 * SEq_3 - accel.z;
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J_11or24 = twoSEq_3; // J_11 negated in matrix multiplication
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J_12or23 = 2.0f * SEq_4;
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J_13or22 = twoSEq_1; // J_12 negated in matrix multiplication
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J_14or21 = twoSEq_2;
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J_32 = 2.0f * J_14or21; // negated in matrix multiplication
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J_33 = 2.0f * J_11or24; // negated in matrix multiplication
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// Compute the gradient (matrix multiplication)
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SEqHatDot_1 = J_14or21 * f_2 - J_11or24 * f_1;
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SEqHatDot_2 = J_12or23 * f_1 + J_13or22 * f_2 - J_32 * f_3;
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SEqHatDot_3 = J_12or23 * f_2 - J_33 * f_3 - J_13or22 * f_1;
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SEqHatDot_4 = J_14or21 * f_1 + J_11or24 * f_2;
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// Normalise the gradient
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norm = 1.0/sqrt(SEqHatDot_1 * SEqHatDot_1 + SEqHatDot_2 * SEqHatDot_2 + SEqHatDot_3 * SEqHatDot_3 + SEqHatDot_4 * SEqHatDot_4);
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if (!isinf(norm)) {
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SEqHatDot_1 *= norm;
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SEqHatDot_2 *= norm;
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SEqHatDot_3 *= norm;
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SEqHatDot_4 *= norm;
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}
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// Compute the quaternion derrivative measured by gyroscopes
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SEqDot_omega_1 = -halfSEq_2 * gyro.x - halfSEq_3 * gyro.y - halfSEq_4 * gyro.z;
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SEqDot_omega_2 = halfSEq_1 * gyro.x + halfSEq_3 * gyro.z - halfSEq_4 * gyro.y;
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SEqDot_omega_3 = halfSEq_1 * gyro.y - halfSEq_2 * gyro.z + halfSEq_4 * gyro.x;
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SEqDot_omega_4 = halfSEq_1 * gyro.z + halfSEq_2 * gyro.y - halfSEq_3 * gyro.x;
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// Compute then integrate the estimated quaternion derrivative
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SEq_1 += (SEqDot_omega_1 - (beta * SEqHatDot_1)) * deltat;
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SEq_2 += (SEqDot_omega_2 - (beta * SEqHatDot_2)) * deltat;
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SEq_3 += (SEqDot_omega_3 - (beta * SEqHatDot_3)) * deltat;
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SEq_4 += (SEqDot_omega_4 - (beta * SEqHatDot_4)) * deltat;
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// Normalise quaternion
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norm = 1.0/sqrt(SEq_1 * SEq_1 + SEq_2 * SEq_2 + SEq_3 * SEq_3 + SEq_4 * SEq_4);
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if (!isinf(norm)) {
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SEq_1 *= norm;
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SEq_2 *= norm;
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SEq_3 *= norm;
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SEq_4 *= norm;
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}
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}
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// Function to compute one quaternion iteration including magnetometer
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void AP_Quaternion::update_MARG(float deltat, Vector3f &gyro, Vector3f &accel, Vector3f &mag)
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{
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// local system variables
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float norm; // vector norm
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float SEqDot_omega_1, SEqDot_omega_2, SEqDot_omega_3, SEqDot_omega_4; // quaternion rate from gyroscopes elements
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float f_1, f_2, f_3, f_4, f_5, f_6; // objective function elements
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float J_11or24, J_12or23, J_13or22, J_14or21, J_32, J_33, // objective function Jacobian elements
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J_41, J_42, J_43, J_44, J_51, J_52, J_53, J_54, J_61, J_62, J_63, J_64; //
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float SEqHatDot_1, SEqHatDot_2, SEqHatDot_3, SEqHatDot_4; // estimated direction of the gyroscope error
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// computed flux in the earth frame
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Vector3f flux;
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// estimated direction of the gyroscope error (radians)
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Vector3f w_err;
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// normalise accelerometer vector
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accel.normalize();
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// normalise the magnetometer measurement
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mag.normalize();
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// auxiliary variables to avoid repeated calculations
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float halfSEq_1 = 0.5f * SEq_1;
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float halfSEq_2 = 0.5f * SEq_2;
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float halfSEq_3 = 0.5f * SEq_3;
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float halfSEq_4 = 0.5f * SEq_4;
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float twoSEq_1 = 2.0f * SEq_1;
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float twoSEq_2 = 2.0f * SEq_2;
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float twoSEq_3 = 2.0f * SEq_3;
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float twoSEq_4 = 2.0f * SEq_4;
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float twob_x = 2.0f * b_x;
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float twob_z = 2.0f * b_z;
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float twob_xSEq_1 = 2.0f * b_x * SEq_1;
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float twob_xSEq_2 = 2.0f * b_x * SEq_2;
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float twob_xSEq_3 = 2.0f * b_x * SEq_3;
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float twob_xSEq_4 = 2.0f * b_x * SEq_4;
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float twob_zSEq_1 = 2.0f * b_z * SEq_1;
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float twob_zSEq_2 = 2.0f * b_z * SEq_2;
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float twob_zSEq_3 = 2.0f * b_z * SEq_3;
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float twob_zSEq_4 = 2.0f * b_z * SEq_4;
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float SEq_1SEq_2;
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float SEq_1SEq_3 = SEq_1 * SEq_3;
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float SEq_1SEq_4;
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float SEq_2SEq_3;
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float SEq_2SEq_4 = SEq_2 * SEq_4;
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float SEq_3SEq_4;
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Vector3f twom = mag * 2.0;
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// compute the objective function and Jacobian
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f_1 = twoSEq_2 * SEq_4 - twoSEq_1 * SEq_3 - accel.x;
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f_2 = twoSEq_1 * SEq_2 + twoSEq_3 * SEq_4 - accel.y;
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f_3 = 1.0f - twoSEq_2 * SEq_2 - twoSEq_3 * SEq_3 - accel.z;
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f_4 = twob_x * (0.5f - SEq_3 * SEq_3 - SEq_4 * SEq_4) + twob_z * (SEq_2SEq_4 - SEq_1SEq_3) - mag.x;
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f_5 = twob_x * (SEq_2 * SEq_3 - SEq_1 * SEq_4) + twob_z * (SEq_1 * SEq_2 + SEq_3 * SEq_4) - mag.y;
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f_6 = twob_x * (SEq_1SEq_3 + SEq_2SEq_4) + twob_z * (0.5f - SEq_2 * SEq_2 - SEq_3 * SEq_3) - mag.z;
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J_11or24 = twoSEq_3; // J_11 negated in matrix multiplication
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J_12or23 = 2.0f * SEq_4;
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J_13or22 = twoSEq_1; // J_12 negated in matrix multiplication
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J_14or21 = twoSEq_2;
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J_32 = 2.0f * J_14or21; // negated in matrix multiplication
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J_33 = 2.0f * J_11or24; // negated in matrix multiplication
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J_41 = twob_zSEq_3; // negated in matrix multiplication
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J_42 = twob_zSEq_4;
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J_43 = 2.0f * twob_xSEq_3 + twob_zSEq_1; // negated in matrix multiplication
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J_44 = 2.0f * twob_xSEq_4 - twob_zSEq_2; // negated in matrix multiplication
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J_51 = twob_xSEq_4 - twob_zSEq_2; // negated in matrix multiplication
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J_52 = twob_xSEq_3 + twob_zSEq_1;
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J_53 = twob_xSEq_2 + twob_zSEq_4;
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J_54 = twob_xSEq_1 - twob_zSEq_3; // negated in matrix multiplication
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J_61 = twob_xSEq_3;
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J_62 = twob_xSEq_4 - 2.0f * twob_zSEq_2;
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J_63 = twob_xSEq_1 - 2.0f * twob_zSEq_3;
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J_64 = twob_xSEq_2;
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// compute the gradient (matrix multiplication)
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SEqHatDot_1 = J_14or21 * f_2 - J_11or24 * f_1 - J_41 * f_4 - J_51 * f_5 + J_61 * f_6;
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SEqHatDot_2 = J_12or23 * f_1 + J_13or22 * f_2 - J_32 * f_3 + J_42 * f_4 + J_52 * f_5 + J_62 * f_6;
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SEqHatDot_3 = J_12or23 * f_2 - J_33 * f_3 - J_13or22 * f_1 - J_43 * f_4 + J_53 * f_5 + J_63 * f_6;
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SEqHatDot_4 = J_14or21 * f_1 + J_11or24 * f_2 - J_44 * f_4 - J_54 * f_5 + J_64 * f_6;
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// normalise the gradient to estimate direction of the gyroscope error
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norm = 1.0 / sqrt(SEqHatDot_1 * SEqHatDot_1 + SEqHatDot_2 * SEqHatDot_2 + SEqHatDot_3 * SEqHatDot_3 + SEqHatDot_4 * SEqHatDot_4);
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SEqHatDot_1 *= norm;
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SEqHatDot_2 *= norm;
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SEqHatDot_3 *= norm;
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SEqHatDot_4 *= norm;
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// compute angular estimated direction of the gyroscope error
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w_err.x = twoSEq_1 * SEqHatDot_2 - twoSEq_2 * SEqHatDot_1 - twoSEq_3 * SEqHatDot_4 + twoSEq_4 * SEqHatDot_3;
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w_err.y = twoSEq_1 * SEqHatDot_3 + twoSEq_2 * SEqHatDot_4 - twoSEq_3 * SEqHatDot_1 - twoSEq_4 * SEqHatDot_2;
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w_err.z = twoSEq_1 * SEqHatDot_4 - twoSEq_2 * SEqHatDot_3 + twoSEq_3 * SEqHatDot_2 - twoSEq_4 * SEqHatDot_1;
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// compute and remove the gyroscope baises
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gyro_bias += w_err * (deltat * zeta);
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gyro -= gyro_bias;
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// compute the quaternion rate measured by gyroscopes
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SEqDot_omega_1 = -halfSEq_2 * gyro.x - halfSEq_3 * gyro.y - halfSEq_4 * gyro.z;
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SEqDot_omega_2 = halfSEq_1 * gyro.x + halfSEq_3 * gyro.z - halfSEq_4 * gyro.y;
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SEqDot_omega_3 = halfSEq_1 * gyro.y - halfSEq_2 * gyro.z + halfSEq_4 * gyro.x;
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SEqDot_omega_4 = halfSEq_1 * gyro.z + halfSEq_2 * gyro.y - halfSEq_3 * gyro.x;
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// compute then integrate the estimated quaternion rate
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SEq_1 += (SEqDot_omega_1 - (beta * SEqHatDot_1)) * deltat;
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SEq_2 += (SEqDot_omega_2 - (beta * SEqHatDot_2)) * deltat;
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SEq_3 += (SEqDot_omega_3 - (beta * SEqHatDot_3)) * deltat;
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SEq_4 += (SEqDot_omega_4 - (beta * SEqHatDot_4)) * deltat;
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// normalise quaternion
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norm = 1.0/sqrt(SEq_1 * SEq_1 + SEq_2 * SEq_2 + SEq_3 * SEq_3 + SEq_4 * SEq_4);
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if (!isinf(norm)) {
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SEq_1 *= norm;
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SEq_2 *= norm;
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SEq_3 *= norm;
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SEq_4 *= norm;
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}
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// compute flux in the earth frame
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// recompute axulirary variables
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SEq_1SEq_2 = SEq_1 * SEq_2;
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SEq_1SEq_3 = SEq_1 * SEq_3;
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SEq_1SEq_4 = SEq_1 * SEq_4;
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SEq_3SEq_4 = SEq_3 * SEq_4;
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SEq_2SEq_3 = SEq_2 * SEq_3;
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SEq_2SEq_4 = SEq_2 * SEq_4;
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flux.x = twom.x * (0.5f - SEq_3 * SEq_3 - SEq_4 * SEq_4) + twom.y * (SEq_2SEq_3 - SEq_1SEq_4) + twom.z * (SEq_2SEq_4 + SEq_1SEq_3);
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flux.y = twom.x * (SEq_2SEq_3 + SEq_1SEq_4) + twom.y * (0.5f - SEq_2 * SEq_2 - SEq_4 * SEq_4) + twom.z * (SEq_3SEq_4 - SEq_1SEq_2);
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flux.z = twom.x * (SEq_2SEq_4 - SEq_1SEq_3) + twom.y * (SEq_3SEq_4 + SEq_1SEq_2) + twom.z * (0.5f - SEq_2 * SEq_2 - SEq_3 * SEq_3);
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// normalise the flux vector to have only components in the x and z
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b_x = sqrt((flux.x * flux.x) + (flux.y * flux.y));
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b_z = flux.z;
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}
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// Function to compute one quaternion iteration
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2012-03-03 01:00:57 -04:00
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void AP_Quaternion::update(void)
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2012-03-03 00:49:38 -04:00
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{
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Vector3f gyro, accel;
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2012-03-03 01:00:57 -04:00
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float deltat;
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2012-03-03 00:49:38 -04:00
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_imu->update();
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2012-03-03 01:00:57 -04:00
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delta_t = _imu->get_delta_time();
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2012-03-03 00:49:38 -04:00
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// get current IMU state
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gyro = _imu->get_gyro();
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gyro.x = -gyro.x;
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gyro.y = -gyro.y;
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accel = _imu->get_accel();
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accel.z = -accel.z;
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if (_compass == NULL) {
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update_IMU(deltat, gyro, accel);
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} else {
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Vector3f mag = Vector3f(_compass->mag_x, _compass->mag_y, - _compass->mag_z);
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update_MARG(deltat, gyro, accel, mag);
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}
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// compute the Eulers
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float test = (SEq_1*SEq_3 - SEq_4*SEq_2);
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const float singularity = 0.499; // 86.3 degrees?
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if (test > singularity) {
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// singularity at south pole
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// this one is ok..
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yaw = 2.0 * atan2(SEq_4, SEq_1);
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pitch = ToRad(-90.0);
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roll = 0.0;
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} else if (test < -singularity) {
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// singularity at north pole
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// this one is invalid :( .. fix it.
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yaw = -2.0 * atan2(SEq_4, SEq_1);
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pitch = ToRad(90.0);
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roll = 0.0;
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} else {
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roll = -(atan2(2.0*(SEq_1*SEq_2 + SEq_3*SEq_4),
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1 - 2.0*(SEq_2*SEq_2 + SEq_3*SEq_3)));
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pitch = -safe_asin(2.0*test);
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yaw = atan2(2.0*(SEq_1*SEq_4 + SEq_2*SEq_3),
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1 - 2.0*(SEq_3*SEq_3 + SEq_4*SEq_4));
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}
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|
// and integer Eulers
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|
roll_sensor = 100 * ToDeg(roll);
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pitch_sensor = 100 * ToDeg(pitch);
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|
yaw_sensor = 100 * ToDeg(yaw);
|
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|
if (yaw_sensor < 0) {
|
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|
yaw_sensor += 36000;
|
|
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|
}
|
|
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|
}
|
