加速度计和陀螺仪求欧拉角程序

以下是一个使用加速度计和陀螺仪求欧拉角的示例程序：

import math
import time

# Calibration constants for the gyroscope
# These values are obtained by measuring the output of the gyroscope when it is at rest in all axes
GYRO_X_OFFSET = 0.0
GYRO_Y_OFFSET = 0.0
GYRO_Z_OFFSET = 0.0

# Calibration constants for the accelerometer
# These values are obtained by measuring the output of the accelerometer when it is at rest with the correct orientation
ACCEL_X_REF = 0.0
ACCEL_Y_REF = 0.0
ACCEL_Z_REF = 1.0

# Conversion factors for the gyroscope and accelerometer
GYRO_SCALE = 0.0010653  # degrees/second
ACCEL_SCALE = 0.000244  # g

# Time constants for the complementary filter
T_COMPLEMENTARY_FILTER = 0.1

# Initialize the angles to zero
roll = 0.0
pitch = 0.0
yaw = 0.0

# Initialize the gyroscope readings
gyro_x_prev = 0.0
gyro_y_prev = 0.0
gyro_z_prev = 0.0

# Main loop
while True:
    # Read the gyroscope and accelerometer data
    gyro_x = read_gyro_x() - GYRO_X_OFFSET
    gyro_y = read_gyro_y() - GYRO_Y_OFFSET
    gyro_z = read_gyro_z() - GYRO_Z_OFFSET
    accel_x = read_accel_x()
    accel_y = read_accel_y()
    accel_z = read_accel_z()

    # Convert the gyroscope readings to degrees/second
    gyro_x = gyro_x * GYRO_SCALE
    gyro_y = gyro_y * GYRO_SCALE
    gyro_z = gyro_z * GYRO_SCALE

    # Calculate the angle change from the gyroscope readings
    alpha_x = gyro_x * (time.time() - t_prev)
    alpha_y = gyro_y * (time.time() - t_prev)
    alpha_z = gyro_z * (time.time() - t_prev)

    # Calculate the angle change from the accelerometer readings
    accel_norm = math.sqrt(accel_x ** 2 + accel_y ** 2 + accel_z ** 2)
    if accel_norm > 0.0:
        roll_acc = math.atan2(accel_y, accel_z) * 180.0 / math.pi
        pitch_acc = math.atan2(-accel_x, math.sqrt(accel_y ** 2 + accel_z ** 2)) * 180.0 / math.pi
    else:
        roll_acc = roll
        pitch_acc = pitch

    # Apply a complementary filter to combine the gyroscope and accelerometer readings
    roll = T_COMPLEMENTARY_FILTER * (roll + alpha_x) + (1.0 - T_COMPLEMENTARY_FILTER) * roll_acc
    pitch = T_COMPLEMENTARY_FILTER * (pitch + alpha_y) + (1.0 - T_COMPLEMENTARY_FILTER) * pitch_acc
    yaw = yaw + alpha_z

    # Normalize the yaw angle to the range -180 to 180 degrees
    if yaw > 180.0:
        yaw -= 360.0
    elif yaw < -180.0:
        yaw += 360.0

    # Update the previous gyroscope readings and time
    gyro_x_prev = gyro_x
    gyro_y_prev = gyro_y
    gyro_z_prev = gyro_z
    t_prev = time.time()

    # Print the current angles
    print("Roll:", roll)
    print("Pitch:", pitch)
    print("Yaw:", yaw)

这个程序使用了一个基于加速度计和陀螺仪的姿态估计方法，称为互补滤波器。该滤波器基于以下思想：加速度计可以测量设备的倾斜角度，但由于加速度计受到重力的影响，无法测量设备的旋转；陀螺仪可以测量设备的旋转角速度，但由于陀螺仪存在漂移，无法准确测量设备的角度。因此，通过将加速度计测量的角度和陀螺仪测量的角速度结合起来，可以得到更准确的角度估计。

滤波器的基本原理如下：设当前姿态角为$\theta$，通过陀螺仪得到的角速度为$\omega_1$，通过加速计得到的角度为$\theta_{acc}$，则：

$$\theta = K \cdot (\theta + \omega_1 \cdot \Delta t) + (1-K) \cdot \theta_{acc}$$

其中$K$为滤波器参数，用于控制加速计和陀螺仪的权重。在本示例中，$K$取值为$0.1$。

此外，还需要进行一些微调，例如校准陀螺仪的偏移量和加速计的参考方向。校准方法可以参考传感器的数据手册。