【51单片机快速入门指南】4.3.4： MPU6050使用Madgwick AHRS算法实现六轴姿态融合获取四元数、欧拉角

STC89C516 32MHz
Keil uVision V5.29.0.0
PK51 Prof.Developers Kit Version:9.60.0.0
上位机：Vofa+ 1.3.10

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移植自AHRS —— LOXO，算法作者：SOH Madgwick

源码

       为了避免所用RAM超标，部分变量设为idata类型，移植时需注意。
       所用MCU为STC89C516 晶振16MHz 6T模式

       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.c、MPU6050.h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

        beta要按需调整，我这里取0.1

Madgwick_6.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	0.1f										// 2 * proportional gain (Kp)

//---------------------------------------------------------------------------------------------------
// Variable definitions

idata volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f;	// quaternion of sensor frame relative to auxiliary frame
idata volatile float Pitch = 0.0f, Roll = 0.0f, Yaw = 0.0f;

//====================================================================================================
// Functions

idata float sampleFreq = 1;
idata 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;
}

//====================================================================================================
// END OF CODE
//====================================================================================================

Madgwick_6.h

#ifndef Madgwick_6_H_
#define Madgwick_6_H_

extern idata float Pitch, Roll, Yaw;
extern idata float q0, q1, q2, q3;

void MPU6050_Madgwick_Init(float loop_ms);
void MadgwickAHRSupdate_6(float gx, float gy, float gz, float ax, float ay, float az);

#endif

使用方法

先调用MPU6050_Madgwick_Init(dt)，参数为一次循环的时间，单位为ms
再使用MadgwickAHRSupdate_6姿态融合函数。

测试程序

main.c

#include 
#include "intrins.h"
#include "stdint.h"
#include "USART.h"
#include "./MPU6050/MPU6050.h"
#include "./MPU6050/Madgwick_6.h"

void Delay1ms()		//@32MHz
{
	unsigned char i, j;

	i = 6;
	j = 44;
	do
	{
		while (--j);
	} while (--i);
}


void Delay_ms(int i)
{
	while(i--)
		Delay1ms();
}

void main(void)
{
	idata int16_t aacx,aacy,aacz;		//加速度传感器原始数据
	idata int16_t gyrox,gyroy,gyroz;	//陀螺仪原始数据

	USART_Init(USART_MODE_1, Rx_ENABLE, STC_USART_Priority_Lowest, 32000000, 4800, DOUBLE_BAUD_DISABLE, USART_TIMER_2);
	MPU_Init(); 
	MPU6050_Madgwick_Init(95);
	while(1)
	{	
		MPU_Get_Accelerometer(&aacx, &aacy, &aacz);	//得到加速度传感器数据
		MPU_Get_Gyroscope(&gyrox, &gyroy, &gyroz);	//得到陀螺仪数据
		MadgwickAHRSupdate_6(gyrox, gyroy, gyroz, aacx, aacy, aacz);
		printf("%f, ", Pitch);
		printf("%f, ", Roll);
		printf("%f\r\n", Yaw);
	}
}

效果