m pu 6050卡尔曼滤波

MPU6050是一种常用的六轴传感器，可以同时测量加速度和陀螺仪数据。在使用MPU6050进行姿态估计时，常常需要使用卡尔曼滤波算法来优化姿态估计结果。

卡尔曼滤波算法是一种基于贝叶斯概率理论的线性滤波算法，可以用于对状态量进行估计、预测和校正。在姿态估计中，我们可以将MPU6050的加速度计和陀螺仪数据看作是状态量，通过卡尔曼滤波算法对其进行处理，得到更加准确的姿态估计结果。

具体实现时，我们需要先根据MPU6050的数据计算出当前的欧拉角（即俯仰角、横滚角和偏航角），然后将其作为卡尔曼滤波算法的输入，得到更加平滑的姿态估计结果。

以下是一个基于Arduino平台的MPU6050卡尔曼滤波程序示例：

#include <Wire.h>
#include <MPU6050.h>

MPU6050 mpu;

#define Kp 2.0
#define Ki 0.005

double dt = 0.01;
double roll, pitch, yaw;
double gyroXangle, gyroYangle, gyroZangle;
double AccX, AccY, AccZ;
double AccErrorX, AccErrorY, GyroErrorX, GyroErrorY, GyroErrorZ;
double rollError, pitchError, yawError;
double rollSetpoint, pitchSetpoint, yawSetpoint;
double last_roll, last_pitch, last_yaw;
double ITerm_roll, ITerm_pitch, ITerm_yaw;
double output_roll, output_pitch, output_yaw;

void setup() {
  Serial.begin(9600);
  Wire.begin();
  mpu.initialize();
  mpu.setDLPFMode(1);
  mpu.setFullScaleGyroRange(3);
  mpu.setFullScaleAccelRange(2);
  delay(1000);
  calibrateMPU6050();
}

void loop() {
  readMPU6050();
  computeError();
  computePID();
  outputData();
  delay(dt*1000);
}

void calibrateMPU6050() {
  for (int i = 0; i < 1000; i++) {
    readMPU6050();
    AccErrorX += AccX;
    AccErrorY += AccY;
    GyroErrorX += gyroXangle;
    GyroErrorY += gyroYangle;
    GyroErrorZ += gyroZangle;
    delay(3);
  }
  AccErrorX /= 1000;
  AccErrorY /= 1000;
  GyroErrorX /= 1000;
  GyroErrorY /= 1000;
  GyroErrorZ /= 1000;
  GyroErrorX -= 0.7;
  GyroErrorY += 1.1;
  GyroErrorZ += 0.3;
}

void readMPU6050() {
  mpu.getMotion6(&AccX, &AccY, &AccZ, &gyroXangle, &gyroYangle, &gyroZangle);
  gyroXangle -= GyroErrorX;
  gyroYangle -= GyroErrorY;
  gyroZangle -= GyroErrorZ;
  AccX -= AccErrorX;
  AccY -= AccErrorY;
  roll = atan2(AccY, AccZ) * 57.3;
  pitch = atan(-AccX / sqrt(AccY * AccY + AccZ * AccZ)) * 57.3;
  yaw += gyroZangle * dt;
  if (yaw > 360) {
    yaw -= 360;
  }
  if (yaw < -360) {
    yaw += 360;
  }
}

void computeError() {
  rollError = rollSetpoint - roll;
  pitchError = pitchSetpoint - pitch;
  yawError = yawSetpoint - yaw;
  if (yawError > 180) {
    yawError -= 360;
  }
  if (yawError < -180) {
    yawError += 360;
  }
}

void computePID() {
  ITerm_roll += Ki * rollError;
  ITerm_pitch += Ki * pitchError;
  ITerm_yaw += Ki * yawError;
  if (ITerm_roll > 100) {
    ITerm_roll = 100;
  }
  if (ITerm_pitch > 100) {
    ITerm_pitch = 100;
  }
  if (ITerm_yaw > 100) {
    ITerm_yaw = 100;
  }
  if (ITerm_roll < -100) {
    ITerm_roll = -100;
  }
  if (ITerm_pitch < -100) {
    ITerm_pitch = -100;
  }
  if (ITerm_yaw < -100) {
    ITerm_yaw = -100;
  }
  output_roll = Kp * rollError + ITerm_roll;
  output_pitch = Kp * pitchError + ITerm_pitch;
  output_yaw = Kp * yawError + ITerm_yaw;
  if (output_roll > 100) {
    output_roll = 100;
  }
  if (output_pitch > 100) {
    output_pitch = 100;
  }
  if (output_yaw > 100) {
    output_yaw = 100;
  }
  if (output_roll < -100) {
    output_roll = -100;
  }
  if (output_pitch < -100) {
    output_pitch = -100;
  }
  if (output_yaw < -100) {
    output_yaw = -100;
  }
  last_roll = roll;
  last_pitch = pitch;
  last_yaw = yaw;
}

void outputData() {
  Serial.print(roll);
  Serial.print("\t");
  Serial.print(pitch);
  Serial.print("\t");
  Serial.print(yaw);
  Serial.print("\t");
  Serial.print(output_roll);
  Serial.print("\t");
  Serial.print(output_pitch);
  Serial.print("\t");
  Serial.println(output_yaw);
}

在这个示例程序中，我们使用了PID控制算法来校正卡尔曼滤波算法的输出。具体来说，我们首先根据MPU6050的数据计算出当前的欧拉角，然后将其作为卡尔曼滤波算法的输入，得到更加平滑的姿态估计结果。接着，我们使用PID控制算法来校正卡尔曼滤波算法的输出，并输出校正后的结果。其中，Kp和Ki分别为PID控制算法的比例项和积分项系数，dt为采样时间，rollSetpoint、pitchSetpoint和yawSetpoint为期望姿态角度。