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//=====================================================================================================
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// MahonyAHRS.c
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//=====================================================================================================
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//
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// Madgwick's implementation of Mayhony's AHRS algorithm.
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// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
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//
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// Date Author Notes
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// 29/09/2011 SOH Madgwick Initial release
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// 02/10/2011 SOH Madgwick Optimised for reduced CPU load
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//
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//=====================================================================================================
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//---------------------------------------------------------------------------------------------------
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// Header files
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#include "MahonyAHRS.h"
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#include <math.h>
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//---------------------------------------------------------------------------------------------------
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// Definitions
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#define sampleFreq 10.0f // sample frequency in Hz
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#define twoKpDef (2.0f * 1.0f) // 2 * proportional gain
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#define twoKiDef (2.0f * 0.0f) // 2 * integral gain
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//---------------------------------------------------------------------------------------------------
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// Variable definitions
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volatile float twoKp = twoKpDef; // 2 * proportional gain (Kp)
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volatile float twoKi = twoKiDef; // 2 * integral gain (Ki)
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volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame
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volatile float integralFBx = 0.0f, integralFBy = 0.0f, integralFBz = 0.0f; // integral error terms scaled by Ki
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//---------------------------------------------------------------------------------------------------
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// Function declarations
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//====================================================================================================
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// Functions
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//---------------------------------------------------------------------------------------------------
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// AHRS algorithm update
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void MahonyAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
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float recipNorm;
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float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
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float hx, hy, bx, bz;
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float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
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float halfex, halfey, halfez;
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float qa, qb, qc;
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// Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
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// 在磁力计数据无效时使用六轴融合算法
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if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
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MahonyAHRSupdateIMU(gx, gy, gz, ax, ay, az);
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return;
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}
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// Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
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// 只在加速度计数据有效时才进行运算
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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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// 将加速度计得到的实际重力加速度向量v单位化
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recipNorm = invSqrt(ax * ax + ay * ay + az * az);
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ax *= recipNorm;
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ay *= recipNorm;
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az *= recipNorm;
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// Normalise magnetometer measurement
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// 将磁力计得到的实际磁场向量m单位化
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recipNorm = invSqrt(mx * mx + my * my + mz * mz);
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mx *= recipNorm;
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my *= recipNorm;
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mz *= recipNorm;
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// Auxiliary variables to avoid repeated arithmetic
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// 辅助变量，以避免重复运算
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q0q0 = q0 * q0;
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q0q1 = q0 * q1;
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q0q2 = q0 * q2;
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q0q3 = q0 * q3;
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q1q1 = q1 * q1;
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q1q2 = q1 * q2;
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q1q3 = q1 * q3;
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q2q2 = q2 * q2;
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q2q3 = q2 * q3;
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q3q3 = q3 * q3;
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// Reference direction of Earth's magnetic field
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// 通过磁力计测量值与坐标转换矩阵得到大地坐标系下的理论地磁向量
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hx = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
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hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1));
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bx = sqrt(hx * hx + hy * hy);
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bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2));
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// Estimated direction of gravity and magnetic field
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// 将理论重力加速度向量与理论地磁向量变换至机体坐标系
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halfvx = q1q3 - q0q2;
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halfvy = q0q1 + q2q3;
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halfvz = q0q0 - 0.5f + q3q3;
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halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2);
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halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
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halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2);
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// Error is sum of cross product between estimated direction and measured direction of field vectors
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// 通过向量外积得到重力加速度向量和地磁向量的实际值与测量值之间误差
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halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy);
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halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz);
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halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx);
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// Compute and apply integral feedback if enabled
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// 在PI补偿器中积分项使能情况下计算并应用积分项
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if(twoKi > 0.0f) {
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integralFBx += twoKi * halfex * (1.0f / sampleFreq); // integral error scaled by Ki
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integralFBy += twoKi * halfey * (1.0f / sampleFreq);
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integralFBz += twoKi * halfez * (1.0f / sampleFreq);
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gx += integralFBx; // apply integral feedback // 应用误差补偿中的积分项
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gy += integralFBy;
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gz += integralFBz;
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}
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else {
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integralFBx = 0.0f; // prevent integral windup // 避免为负值的Ki时积分异常饱和
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integralFBy = 0.0f;
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integralFBz = 0.0f;
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}
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// Apply proportional feedback
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// 应用误差补偿中的比例项
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gx += twoKp * halfex;
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gy += twoKp * halfey;
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gz += twoKp * halfez;
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}
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// Integrate rate of change of quaternion
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// 微分方程迭代求解
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gx *= (0.5f * (1.0f / sampleFreq)); // pre-multiply common factors
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gy *= (0.5f * (1.0f / sampleFreq));
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gz *= (0.5f * (1.0f / sampleFreq));
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qa = q0;
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qb = q1;
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qc = q2;
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q0 += (-qb * gx - qc * gy - q3 * gz);
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q1 += (qa * gx + qc * gz - q3 * gy);
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q2 += (qa * gy - qb * gz + q3 * gx);
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q3 += (qa * gz + qb * gy - qc * gx);
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// Normalise quaternion
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// 单位化四元数 保证四元数在迭代过程中保持单位性质
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recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
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q0 *= recipNorm;
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q1 *= recipNorm;
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q2 *= recipNorm;
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q3 *= recipNorm;
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//Mahony官方程序到此结束，使用时只需在函数外进行四元数反解欧拉角即可完成全部姿态解算过程
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}
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//---------------------------------------------------------------------------------------------------
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// IMU algorithm update
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void MahonyAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
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float recipNorm;
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float halfvx, halfvy, halfvz;//1/2 重力分量
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float halfex, halfey, halfez;//1/2 重力误差
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float qa, qb, qc;
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// Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
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// 在磁力计数据无效时使用六轴融合算法
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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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recipNorm = invSqrt(ax * ax + ay * ay + az * az);
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ax *= recipNorm;
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ay *= recipNorm;
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az *= recipNorm;
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// Estimated direction of gravity and vector perpendicular to magnetic flux
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halfvx = q1 * q3 - q0 * q2;
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halfvy = q0 * q1 + q2 * q3;
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halfvz = q0 * q0 - 0.5f + q3 * q3;
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// Error is sum of cross product between estimated and measured direction of gravity
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halfex = (ay * halfvz - az * halfvy);
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halfey = (az * halfvx - ax * halfvz);
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halfez = (ax * halfvy - ay * halfvx);
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// Compute and apply integral feedback if enabled
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if(twoKi > 0.0f) {
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integralFBx += twoKi * halfex * (1.0f / sampleFreq); // integral error scaled by Ki
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integralFBy += twoKi * halfey * (1.0f / sampleFreq);
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integralFBz += twoKi * halfez * (1.0f / sampleFreq);
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gx += integralFBx; // apply integral feedback
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gy += integralFBy;
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gz += integralFBz;
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}
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else {
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integralFBx = 0.0f; // prevent integral windup
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integralFBy = 0.0f;
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integralFBz = 0.0f;
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}
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// Apply proportional feedback
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gx += twoKp * halfex;
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gy += twoKp * halfey;
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gz += twoKp * halfez;
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}
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// Integrate rate of change of quaternion
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gx *= (0.5f * (1.0f / sampleFreq)); // pre-multiply common factors
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gy *= (0.5f * (1.0f / sampleFreq));
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gz *= (0.5f * (1.0f / sampleFreq));
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qa = q0;
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qb = q1;
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qc = q2;
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q0 += (-qb * gx - qc * gy - q3 * gz);
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q1 += (qa * gx + qc * gz - q3 * gy);
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q2 += (qa * gy - qb * gz + q3 * gx);
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q3 += (qa * gz + qb * gy - qc * gx);
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// Normalise quaternion
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recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
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q0 *= recipNorm;
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q1 *= recipNorm;
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q2 *= recipNorm;
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q3 *= recipNorm;
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}
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//---------------------------------------------------------------------------------------------------
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// Fast inverse square-root
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// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
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float invSqrt(float x) {
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float halfx = 0.5f * x;
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float y = x;
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long i = *(long*)&y;
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i = 0x5f3759df - (i>>1);
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y = *(float*)&i;
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y = y * (1.5f - (halfx * y * y));
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return y;
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}
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//====================================================================================================
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// END OF CODE
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//====================================================================================================
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@@ -0,0 +1,32 @@
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//=====================================================================================================
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// MahonyAHRS.h
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//=====================================================================================================
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//
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// Madgwick's implementation of Mayhony's AHRS algorithm.
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// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
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//
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// Date Author Notes
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// 29/09/2011 SOH Madgwick Initial release
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// 02/10/2011 SOH Madgwick Optimised for reduced CPU load
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//
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//=====================================================================================================
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#ifndef MahonyAHRS_h
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#define MahonyAHRS_h
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//----------------------------------------------------------------------------------------------------
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// Variable declaration
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extern volatile float twoKp; // 2 * proportional gain (Kp)
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extern volatile float twoKi; // 2 * integral gain (Ki)
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extern volatile float q0, q1, q2, q3; // quaternion of sensor frame relative to auxiliary frame
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//---------------------------------------------------------------------------------------------------
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// Function declarations
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float invSqrt(float x);
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void MahonyAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz);
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void MahonyAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az);
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#endif
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//=====================================================================================================
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// End of file
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//=====================================================================================================
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