【51单片机快速入门指南】4.4.3：Madgwick AHRS 九轴姿态融合获取四元数、欧拉角

STC15F2K60S2 22.1184MHz

Keil uVision V5.29.0.0

PK51 Prof.Developers Kit Version:9.60.0.0

上位机：Vofa+ 1.3.10

移植自AHRS —— LOXO，算法作者：SOH Madgwick

传感器的方向

源码

       所用MCU为STC15F2K60S2 使用内部RC时钟，22.1184MHz

       stdint.h见【51单片机快速入门指南】1：基础知识和工程创建

       软件I2C程序见【51单片机快速入门指南】4： 软件 I2C

       串口部分见【51单片机快速入门指南】3.3：USART 串口通信

       MPU6050驱动程序见【51单片机快速入门指南】4.3： I2C读取MPU6050陀螺仪的原始数据

       HMC5883L/QMC5883L驱动程序见【51单片机快速入门指南】4.4：I2C 读取HMC5883L / QMC5883L 磁力计

       磁力计的椭球拟合校准见【51单片机快速入门指南】4.4.1：python串口接收磁力计数据并进行最小二乘法椭球拟合

       beta要按需调整，我这里取1.0

Madgwick_9.c

//=====================================================================================================

//

// Implementation of Madgwick's IMU and AHRS algorithms.

// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms

//

// Date Author          Notes

// 29/09/2011 SOH Madgwick    Initial release

// 02/10/2011 SOH Madgwick Optimised for reduced CPU load

// 19/02/2012 SOH Madgwick Magnetometer measurement is normalised

//

//=====================================================================================================

//---------------------------------------------------------------------------------------------------

// Header files

#include

#include "MPU6050.h"

//---------------------------------------------------------------------------------------------------

// Definitions

#define beta 1.0f // 2 * proportional gain (Kp)

//---------------------------------------------------------------------------------------------------

// Variable definitions

float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame

float Pitch = 0.0f, Roll = 0.0f, Yaw = 0.0f;

//====================================================================================================

// Functions

float sampleFreq = 1;

float GYRO_K = 1;

void MPU6050_Madgwick_Init(float loop_ms)

{

sampleFreq = 1000. / loop_ms; //sample frequency in Hz

switch((MPU_Read_Byte(MPU_GYRO_CFG_REG) >> 3) & 3)

{

case 0:

GYRO_K = 1./131/57.3;

break;

case 1:

GYRO_K = 1./65.5/57.3;

break;

case 2:

GYRO_K = 1./32.8/57.3;

break;

case 3:

GYRO_K = 1./16.4/57.3;

break;

}

}

//---------------------------------------------------------------------------------------------------

// Fast inverse square-root

// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root

float invSqrt(float x) 

{

float halfx = 0.5f * x;

float y = x;

long i = *(long*)&y;

i = 0x5f3759df - (i>>1);

y = *(float*)&i;

y = y * (1.5f - (halfx * y * y));

return y;

}

//---------------------------------------------------------------------------------------------------

// AHRS algorithm update

//---------------------------------------------------------------------------------------------------

// IMU algorithm update

void MadgwickAHRSupdate_6(float gx, float gy, float gz, float ax, float ay, float az) 

{

float recipNorm;

float s0, s1, s2, s3;

float qDot1, qDot2, qDot3, qDot4;

float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;

//将陀螺仪AD值转换为 弧度/s

gx = gx * GYRO_K;

gy = gy * GYRO_K;

gz = gz * GYRO_K;

// Rate of change of quaternion from gyroscope

qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);

qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);

qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);

qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

// Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)

if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {

// Normalise accelerometer measurement

recipNorm = invSqrt(ax * ax + ay * ay + az * az);

ax *= recipNorm;

ay *= recipNorm;

az *= recipNorm;   

// Auxiliary variables to avoid repeated arithmetic

_2q0 = 2.0f * q0;

_2q1 = 2.0f * q1;

_2q2 = 2.0f * q2;

_2q3 = 2.0f * q3;

_4q0 = 4.0f * q0;

_4q1 = 4.0f * q1;

_4q2 = 4.0f * q2;

_8q1 = 8.0f * q1;

_8q2 = 8.0f * q2;

q0q0 = q0 * q0;

q1q1 = q1 * q1;

q2q2 = q2 * q2;

q3q3 = q3 * q3;

// Gradient decent algorithm corrective step

s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;

s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;

s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;

s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;

recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude

s0 *= recipNorm;

s1 *= recipNorm;

s2 *= recipNorm;

s3 *= recipNorm;

// Apply feedback step

qDot1 -= beta * s0;

qDot2 -= beta * s1;

qDot3 -= beta * s2;

qDot4 -= beta * s3;

}

// Integrate rate of change of quaternion to yield quaternion

q0 += qDot1 * (1.0f / sampleFreq);

q1 += qDot2 * (1.0f / sampleFreq);

q2 += qDot3 * (1.0f / sampleFreq);

q3 += qDot4 * (1.0f / sampleFreq);

// Normalise quaternion

recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);

q0 *= recipNorm;

q1 *= recipNorm;

q2 *= recipNorm;

q3 *= recipNorm;

Pitch = asin(-2.0f * (q1*q3 - q0*q2))* 57.3f;

Roll = atan2(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2) * 57.3f;

Yaw = atan2(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3)* 57.3f;

}

void MadgwickAHRSupdate_9(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) 

{

float recipNorm;

float s0, s1, s2, s3;

float qDot1, qDot2, qDot3, qDot4;

float hx, hy;

float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;

// Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)

if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) 

{

MadgwickAHRSupdate_6(gx, gy, gz, ax, ay, az);

return;

}

//将陀螺仪AD值转换为 弧度/s

gx = gx * GYRO_K;

gy = gy * GYRO_K;

gz = gz * GYRO_K;

// Rate of change of quaternion from gyroscope

qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);

qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);

qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);

qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

// Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)

if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) 

{

// Normalise accelerometer measurement

recipNorm = invSqrt(ax * ax + ay * ay + az * az);

ax *= recipNorm;

ay *= recipNorm;

az *= recipNorm;   

// Normalise magnetometer measurement

recipNorm = invSqrt(mx * mx + my * my + mz * mz);

mx *= recipNorm;

my *= recipNorm;

mz *= recipNorm;

// Auxiliary variables to avoid repeated arithmetic

_2q0mx = 2.0f * q0 * mx;

_2q0my = 2.0f * q0 * my;

_2q0mz = 2.0f * q0 * mz;

_2q1mx = 2.0f * q1 * mx;

_2q0 = 2.0f * q0;

_2q1 = 2.0f * q1;

_2q2 = 2.0f * q2;

_2q3 = 2.0f * q3;

_2q0q2 = 2.0f * q0 * q2;

_2q2q3 = 2.0f * q2 * q3;

q0q0 = q0 * q0;

q0q1 = q0 * q1;

q0q2 = q0 * q2;

q0q3 = q0 * q3;

q1q1 = q1 * q1;

q1q2 = q1 * q2;

q1q3 = q1 * q3;

q2q2 = q2 * q2;

q2q3 = q2 * q3;

q3q3 = q3 * q3;

// Reference direction of Earth's magnetic field

hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;

hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;

_2bx = sqrt(hx * hx + hy * hy);

_2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;

_4bx = 2.0f * _2bx;

_4bz = 2.0f * _2bz;

// Gradient decent algorithm corrective step

s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);

s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);

s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);

s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);

recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude

s0 *= recipNorm;

s1 *= recipNorm;

s2 *= recipNorm;

s3 *= recipNorm;

// Apply feedback step

qDot1 -= beta * s0;

qDot2 -= beta * s1;

qDot3 -= beta * s2;

qDot4 -= beta * s3;

}

// Integrate rate of change of quaternion to yield quaternion

q0 += qDot1 * (1.0f / sampleFreq);

q1 += qDot2 * (1.0f / sampleFreq);

q2 += qDot3 * (1.0f / sampleFreq);

q3 += qDot4 * (1.0f / sampleFreq);

// Normalise quaternion

recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);

q0 *= recipNorm;

q1 *= recipNorm;

q2 *= recipNorm;

q3 *= recipNorm;

Pitch = asin(-2.0f * (q1*q3 - q0*q2))* 57.3f;

Roll = atan2(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2) * 57.3f;

Yaw = atan2(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3)* 57.3f;

}

//====================================================================================================

// END OF CODE

//====================================================================================================