406 lines
13 KiB
C
406 lines
13 KiB
C
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/*
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开源的AHRS算法。
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MadgwickAHRS
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*/
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#include "ahrs.h"
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#include <string.h>
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#include "user_math.h"
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#define BETA_IMU (0.033f)
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#define BETA_AHRS (0.041f)
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/* 2 * proportional gain (Kp) */
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static float beta = BETA_IMU;
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/**
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* @brief 不使用磁力计计算姿态
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*
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* @param ahrs 姿态解算主结构体
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* @param accl 加速度计数据
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* @param gyro 陀螺仪数据
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* @return int8_t 0对应没有错误
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*/
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static int8_t AHRS_UpdateIMU(AHRS_t *ahrs, const AHRS_Accl_t *accl,
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const AHRS_Gyro_t *gyro) {
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if (ahrs == NULL) return -1;
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if (accl == NULL) return -1;
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if (gyro == NULL) return -1;
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beta = BETA_IMU;
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float ax = accl->x;
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float ay = accl->y;
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float az = accl->z;
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float gx = gyro->x;
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float gy = gyro->y;
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float gz = gyro->z;
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float recip_norm;
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float s0, s1, s2, s3;
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float q_dot1, q_dot2, q_dot3, q_dot4;
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float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2, _8q1, _8q2, q0q0, q1q1, q2q2,
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q3q3;
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/* Rate of change of quaternion from gyroscope */
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q_dot1 = 0.5f * (-ahrs->quat.q1 * gx - ahrs->quat.q2 * gy -
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ahrs->quat.q3 * gz);
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q_dot2 = 0.5f * (ahrs->quat.q0 * gx + ahrs->quat.q2 * gz -
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ahrs->quat.q3 * gy);
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q_dot3 = 0.5f * (ahrs->quat.q0 * gy - ahrs->quat.q1 * gz +
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ahrs->quat.q3 * gx);
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q_dot4 = 0.5f * (ahrs->quat.q0 * gz + ahrs->quat.q1 * gy -
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ahrs->quat.q2 * gx);
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/* Compute feedback only if accelerometer measurement valid (avoids NaN in
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* accelerometer normalisation) */
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if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
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/* Normalise accelerometer measurement */
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recip_norm = InvSqrt(ax * ax + ay * ay + az * az);
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ax *= recip_norm;
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ay *= recip_norm;
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az *= recip_norm;
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/* Auxiliary variables to avoid repeated arithmetic */
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_2q0 = 2.0f * ahrs->quat.q0;
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_2q1 = 2.0f * ahrs->quat.q1;
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_2q2 = 2.0f * ahrs->quat.q2;
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_2q3 = 2.0f * ahrs->quat.q3;
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_4q0 = 4.0f * ahrs->quat.q0;
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_4q1 = 4.0f * ahrs->quat.q1;
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_4q2 = 4.0f * ahrs->quat.q2;
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_8q1 = 8.0f * ahrs->quat.q1;
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_8q2 = 8.0f * ahrs->quat.q2;
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q0q0 = ahrs->quat.q0 * ahrs->quat.q0;
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q1q1 = ahrs->quat.q1 * ahrs->quat.q1;
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q2q2 = ahrs->quat.q2 * ahrs->quat.q2;
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q3q3 = ahrs->quat.q3 * ahrs->quat.q3;
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/* Gradient decent algorithm corrective step */
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s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
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s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * ahrs->quat.q1 -
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_2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
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s2 = 4.0f * q0q0 * ahrs->quat.q2 + _2q0 * ax + _4q2 * q3q3 -
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_2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
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s3 = 4.0f * q1q1 * ahrs->quat.q3 - _2q1 * ax +
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4.0f * q2q2 * ahrs->quat.q3 - _2q2 * ay;
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/* normalise step magnitude */
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recip_norm = InvSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3);
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s0 *= recip_norm;
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s1 *= recip_norm;
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s2 *= recip_norm;
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s3 *= recip_norm;
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/* Apply feedback step */
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q_dot1 -= beta * s0;
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q_dot2 -= beta * s1;
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q_dot3 -= beta * s2;
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q_dot4 -= beta * s3;
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}
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/* Integrate rate of change of quaternion to yield quaternion */
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ahrs->quat.q0 += q_dot1 * ahrs->inv_sample_freq;
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ahrs->quat.q1 += q_dot2 * ahrs->inv_sample_freq;
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ahrs->quat.q2 += q_dot3 * ahrs->inv_sample_freq;
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ahrs->quat.q3 += q_dot4 * ahrs->inv_sample_freq;
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/* Normalise quaternion */
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recip_norm = InvSqrt(ahrs->quat.q0 * ahrs->quat.q0 +
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ahrs->quat.q1 * ahrs->quat.q1 +
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ahrs->quat.q2 * ahrs->quat.q2 +
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ahrs->quat.q3 * ahrs->quat.q3);
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ahrs->quat.q0 *= recip_norm;
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ahrs->quat.q1 *= recip_norm;
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ahrs->quat.q2 *= recip_norm;
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ahrs->quat.q3 *= recip_norm;
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return 0;
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}
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/**
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* @brief 初始化姿态解算
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*
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* @param ahrs 姿态解算主结构体
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* @param magn 磁力计数据
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* @param sample_freq 采样频率
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* @return int8_t 0对应没有错误
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*/
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int8_t AHRS_Init(AHRS_t *ahrs, const AHRS_Magn_t *magn, float sample_freq) {
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if (ahrs == NULL) return -1;
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ahrs->inv_sample_freq = 1.0f / sample_freq;
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ahrs->quat.q0 = 1.0f;
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ahrs->quat.q1 = 0.0f;
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ahrs->quat.q2 = 0.0f;
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ahrs->quat.q3 = 0.0f;
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if (magn) {
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float yaw = -atan2(magn->y, magn->x);
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if ((magn->x == 0.0f) && (magn->y == 0.0f) && (magn->z == 0.0f)) {
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ahrs->quat.q0 = 0.800884545f;
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ahrs->quat.q1 = 0.00862364192f;
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ahrs->quat.q2 = -0.00283267116f;
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ahrs->quat.q3 = 0.598749936f;
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} else if ((yaw < (M_PI / 2.0f)) || (yaw > 0.0f)) {
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ahrs->quat.q0 = 0.997458339f;
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ahrs->quat.q1 = 0.000336312107f;
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ahrs->quat.q2 = -0.0057230792f;
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ahrs->quat.q3 = 0.0740156546;
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} else if ((yaw < M_PI) || (yaw > (M_PI / 2.0f))) {
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ahrs->quat.q0 = 0.800884545f;
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ahrs->quat.q1 = 0.00862364192f;
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ahrs->quat.q2 = -0.00283267116f;
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ahrs->quat.q3 = 0.598749936f;
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} else if ((yaw < 90.0f) || (yaw > M_PI)) {
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ahrs->quat.q0 = 0.800884545f;
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ahrs->quat.q1 = 0.00862364192f;
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ahrs->quat.q2 = -0.00283267116f;
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ahrs->quat.q3 = 0.598749936f;
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} else if ((yaw < 90.0f) || (yaw > 0.0f)) {
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ahrs->quat.q0 = 0.800884545f;
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ahrs->quat.q1 = 0.00862364192f;
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ahrs->quat.q2 = -0.00283267116f;
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ahrs->quat.q3 = 0.598749936f;
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}
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}
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return 0;
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}
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/**
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* @brief 姿态运算更新一次
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* @note 输入数据必须是NED(North East Down) 参考坐标系
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*
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* @param ahrs 姿态解算主结构体
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* @param accl 加速度计数据
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* @param gyro 陀螺仪数据
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* @param magn 磁力计数据
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* @return int8_t 0对应没有错误
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*/
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int8_t AHRS_Update(AHRS_t *ahrs, const AHRS_Accl_t *accl,
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const AHRS_Gyro_t *gyro, const AHRS_Magn_t *magn) {
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if (ahrs == NULL) return -1;
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if (accl == NULL) return -1;
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if (gyro == NULL) return -1;
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beta = BETA_AHRS;
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float recip_norm;
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float s0, s1, s2, s3;
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float q_dot1, q_dot2, q_dot3, q_dot4;
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float hx, hy;
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float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1,
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_2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3,
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q2q2, q2q3, q3q3;
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if (magn == NULL) return AHRS_UpdateIMU(ahrs, accl, gyro);
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float mx = magn->x;
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float my = magn->y;
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float mz = magn->z;
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/* Use IMU algorithm if magnetometer measurement invalid (avoids NaN in */
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/* magnetometer normalisation) */
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if ((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
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return AHRS_UpdateIMU(ahrs, accl, gyro);
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}
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float ax = accl->x;
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float ay = accl->y;
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float az = accl->z;
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float gx = gyro->x;
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float gy = gyro->y;
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float gz = gyro->z;
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/* Rate of change of quaternion from gyroscope */
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q_dot1 = 0.5f * (-ahrs->quat.q1 * gx - ahrs->quat.q2 * gy -
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ahrs->quat.q3 * gz);
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q_dot2 = 0.5f * (ahrs->quat.q0 * gx + ahrs->quat.q2 * gz -
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ahrs->quat.q3 * gy);
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q_dot3 = 0.5f * (ahrs->quat.q0 * gy - ahrs->quat.q1 * gz +
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ahrs->quat.q3 * gx);
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q_dot4 = 0.5f * (ahrs->quat.q0 * gz + ahrs->quat.q1 * gy -
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ahrs->quat.q2 * gx);
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/* Compute feedback only if accelerometer measurement valid (avoids NaN in
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* accelerometer normalisation) */
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if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
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/* Normalise accelerometer measurement */
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recip_norm = InvSqrt(ax * ax + ay * ay + az * az);
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ax *= recip_norm;
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ay *= recip_norm;
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az *= recip_norm;
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/* Normalise magnetometer measurement */
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recip_norm = InvSqrt(mx * mx + my * my + mz * mz);
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mx *= recip_norm;
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my *= recip_norm;
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mz *= recip_norm;
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/* Auxiliary variables to avoid repeated arithmetic */
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_2q0mx = 2.0f * ahrs->quat.q0 * mx;
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_2q0my = 2.0f * ahrs->quat.q0 * my;
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_2q0mz = 2.0f * ahrs->quat.q0 * mz;
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_2q1mx = 2.0f * ahrs->quat.q1 * mx;
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_2q0 = 2.0f * ahrs->quat.q0;
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_2q1 = 2.0f * ahrs->quat.q1;
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_2q2 = 2.0f * ahrs->quat.q2;
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_2q3 = 2.0f * ahrs->quat.q3;
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_2q0q2 = 2.0f * ahrs->quat.q0 * ahrs->quat.q2;
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_2q2q3 = 2.0f * ahrs->quat.q2 * ahrs->quat.q3;
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q0q0 = ahrs->quat.q0 * ahrs->quat.q0;
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q0q1 = ahrs->quat.q0 * ahrs->quat.q1;
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q0q2 = ahrs->quat.q0 * ahrs->quat.q2;
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q0q3 = ahrs->quat.q0 * ahrs->quat.q3;
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q1q1 = ahrs->quat.q1 * ahrs->quat.q1;
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q1q2 = ahrs->quat.q1 * ahrs->quat.q2;
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q1q3 = ahrs->quat.q1 * ahrs->quat.q3;
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q2q2 = ahrs->quat.q2 * ahrs->quat.q2;
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q2q3 = ahrs->quat.q2 * ahrs->quat.q3;
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q3q3 = ahrs->quat.q3 * ahrs->quat.q3;
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/* Reference direction of Earth's magnetic field */
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hx = mx * q0q0 - _2q0my * ahrs->quat.q3 +
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_2q0mz * ahrs->quat.q2 + mx * q1q1 +
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_2q1 * my * ahrs->quat.q2 + _2q1 * mz * ahrs->quat.q3 -
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mx * q2q2 - mx * q3q3;
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hy = _2q0mx * ahrs->quat.q3 + my * q0q0 -
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_2q0mz * ahrs->quat.q1 + _2q1mx * ahrs->quat.q2 -
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my * q1q1 + my * q2q2 + _2q2 * mz * ahrs->quat.q3 - my * q3q3;
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// _2bx = sqrtf(hx * hx + hy * hy);
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// 改为invsqrt
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_2bx = 1.f / InvSqrt(hx * hx + hy * hy);
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_2bz = -_2q0mx * ahrs->quat.q2 + _2q0my * ahrs->quat.q1 +
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mz * q0q0 + _2q1mx * ahrs->quat.q3 - mz * q1q1 +
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_2q2 * my * ahrs->quat.q3 - mz * q2q2 + mz * q3q3;
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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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s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) +
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_2q1 * (2.0f * q0q1 + _2q2q3 - ay) -
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_2bz * ahrs->quat.q2 *
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(_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
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(-_2bx * ahrs->quat.q3 + _2bz * ahrs->quat.q1) *
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(_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
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_2bx * ahrs->quat.q2 *
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(_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
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s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) +
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_2q0 * (2.0f * q0q1 + _2q2q3 - ay) -
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4.0f * ahrs->quat.q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) +
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_2bz * ahrs->quat.q3 *
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(_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
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(_2bx * ahrs->quat.q2 + _2bz * ahrs->quat.q0) *
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(_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
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(_2bx * ahrs->quat.q3 - _4bz * ahrs->quat.q1) *
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(_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
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s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) +
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_2q3 * (2.0f * q0q1 + _2q2q3 - ay) -
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4.0f * ahrs->quat.q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) +
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(-_4bx * ahrs->quat.q2 - _2bz * ahrs->quat.q0) *
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(_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
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(_2bx * ahrs->quat.q1 + _2bz * ahrs->quat.q3) *
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(_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
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(_2bx * ahrs->quat.q0 - _4bz * ahrs->quat.q2) *
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(_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
|
||
|
s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) +
|
||
|
_2q2 * (2.0f * q0q1 + _2q2q3 - ay) +
|
||
|
(-_4bx * ahrs->quat.q3 + _2bz * ahrs->quat.q1) *
|
||
|
(_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
|
||
|
(-_2bx * ahrs->quat.q0 + _2bz * ahrs->quat.q2) *
|
||
|
(_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
|
||
|
_2bx * ahrs->quat.q1 *
|
||
|
(_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
|
||
|
/* normalise step magnitude */
|
||
|
recip_norm = InvSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3);
|
||
|
s0 *= recip_norm;
|
||
|
s1 *= recip_norm;
|
||
|
s2 *= recip_norm;
|
||
|
s3 *= recip_norm;
|
||
|
|
||
|
/* Apply feedback step */
|
||
|
q_dot1 -= beta * s0;
|
||
|
q_dot2 -= beta * s1;
|
||
|
q_dot3 -= beta * s2;
|
||
|
q_dot4 -= beta * s3;
|
||
|
}
|
||
|
|
||
|
/* Integrate rate of change of quaternion to yield quaternion */
|
||
|
ahrs->quat.q0 += q_dot1 * ahrs->inv_sample_freq;
|
||
|
ahrs->quat.q1 += q_dot2 * ahrs->inv_sample_freq;
|
||
|
ahrs->quat.q2 += q_dot3 * ahrs->inv_sample_freq;
|
||
|
ahrs->quat.q3 += q_dot4 * ahrs->inv_sample_freq;
|
||
|
|
||
|
/* Normalise quaternion */
|
||
|
recip_norm = InvSqrt(ahrs->quat.q0 * ahrs->quat.q0 +
|
||
|
ahrs->quat.q1 * ahrs->quat.q1 +
|
||
|
ahrs->quat.q2 * ahrs->quat.q2 +
|
||
|
ahrs->quat.q3 * ahrs->quat.q3);
|
||
|
ahrs->quat.q0 *= recip_norm;
|
||
|
ahrs->quat.q1 *= recip_norm;
|
||
|
ahrs->quat.q2 *= recip_norm;
|
||
|
ahrs->quat.q3 *= recip_norm;
|
||
|
|
||
|
return 0;
|
||
|
}
|
||
|
|
||
|
/**
|
||
|
* @brief 通过姿态解算主结构体中的四元数计算欧拉角
|
||
|
*
|
||
|
* @param eulr 欧拉角
|
||
|
* @param ahrs 姿态解算主结构体
|
||
|
* @return int8_t 0对应没有错误
|
||
|
*/
|
||
|
int8_t AHRS_GetEulr(AHRS_Eulr_t *eulr, const AHRS_t *ahrs) {
|
||
|
if (eulr == NULL) return -1;
|
||
|
if (ahrs == NULL) return -1;
|
||
|
|
||
|
const float sinr_cosp = 2.0f * (ahrs->quat.q0 * ahrs->quat.q1 +
|
||
|
ahrs->quat.q2 * ahrs->quat.q3);
|
||
|
const float cosr_cosp =
|
||
|
1.0f - 2.0f * (ahrs->quat.q1 * ahrs->quat.q1 +
|
||
|
ahrs->quat.q2 * ahrs->quat.q2);
|
||
|
eulr->pit = atan2f(sinr_cosp, cosr_cosp);
|
||
|
|
||
|
const float sinp = 2.0f * (ahrs->quat.q0 * ahrs->quat.q2 -
|
||
|
ahrs->quat.q3 * ahrs->quat.q1);
|
||
|
|
||
|
if (fabsf(sinp) >= 1.0f)
|
||
|
eulr->rol = copysignf(M_PI / 2.0f, sinp);
|
||
|
else
|
||
|
eulr->rol = asinf(sinp);
|
||
|
|
||
|
const float siny_cosp = 2.0f * (ahrs->quat.q0 * ahrs->quat.q3 +
|
||
|
ahrs->quat.q1 * ahrs->quat.q2);
|
||
|
const float cosy_cosp =
|
||
|
1.0f - 2.0f * (ahrs->quat.q2 * ahrs->quat.q2 +
|
||
|
ahrs->quat.q3 * ahrs->quat.q3);
|
||
|
eulr->yaw = atan2f(siny_cosp, cosy_cosp);
|
||
|
|
||
|
#if 0
|
||
|
eulr->yaw *= M_RAD2DEG_MULT;
|
||
|
eulr->rol *= M_RAD2DEG_MULT;
|
||
|
eulr->pit *= M_RAD2DEG_MULT;
|
||
|
#endif
|
||
|
|
||
|
return 0;
|
||
|
}
|
||
|
|
||
|
/**
|
||
|
* \brief 将对应数据置零
|
||
|
*
|
||
|
* \param eulr 被操作的数据
|
||
|
*/
|
||
|
void AHRS_ResetEulr(AHRS_Eulr_t *eulr) { memset(eulr, 0, sizeof(*eulr)); }
|