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fusion_async.py
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# fusion_async.py Asynchronous sensor fusion for micropython targets.
# Ported to MicroPython by Peter Hinch, May 2017.
# Released under the MIT License (MIT) See LICENSE
# Copyright (c) 2017-2020 Peter Hinch
# Requires:
# uasyncio V3 (Included in daily builds and release builds later than V1.12).
# Uses the uasyncio library to enable updating to run as a background coroutine.
# Supports 6 and 9 degrees of freedom sensors. Tested with InvenSense MPU-9150 9DOF sensor.
# Source https://github.com/xioTechnologies/Open-Source-AHRS-With-x-IMU.git
# also https://github.com/kriswiner/MPU-9250.git
# Ported to Python. Integrator timing adapted for pyboard.
# See README.md for documentation.
# V0.9 Time calculations devolved to deltat.py
try:
import uasyncio as asyncio
except ImportError:
import asyncio
from math import sqrt, atan2, asin, degrees, radians
from deltat import DeltaT
class Fusion(object):
'''
Class provides sensor fusion allowing heading, pitch and roll to be extracted. This uses the Madgwick algorithm.
The update method runs as a coroutine. Its calculations take 1.6mS on the Pyboard.
'''
declination = 0 # Optional offset for true north. A +ve value adds to heading
def __init__(self, read_coro, timediff=None):
self.read_coro = read_coro
self.magbias = (0, 0, 0) # local magnetic bias factors: set from calibration
self.expect_ts = timediff is not None
self.deltat = DeltaT(timediff) # Time between updates
self.q = [1.0, 0.0, 0.0, 0.0] # vector to hold quaternion
GyroMeasError = radians(40) # Original code indicates this leads to a 2 sec response time
self.beta = sqrt(3.0 / 4.0) * GyroMeasError # compute beta (see README)
self.pitch = 0
self.heading = 0
self.roll = 0
async def calibrate(self, stopfunc):
res = await self.read_coro()
mag = res[2]
magmax = list(mag) # Initialise max and min lists with current values
magmin = magmax[:]
while not stopfunc():
res = await self.read_coro()
magxyz = res[2]
for x in range(3):
magmax[x] = max(magmax[x], magxyz[x])
magmin[x] = min(magmin[x], magxyz[x])
self.magbias = tuple(map(lambda a, b: (a +b)/2, magmin, magmax))
async def start(self, slow_platform=False):
data = await self.read_coro()
if len(data) == 2 or (self.expect_ts and len(data) == 3):
asyncio.create_task(self._update_nomag(slow_platform))
else:
asyncio.create_task(self._update_mag(slow_platform))
async def _update_nomag(self, slow_platform):
while True:
if self.expect_ts:
accel, gyro, ts = await self.read_coro()
else:
accel, gyro = await self.read_coro()
ts = None
ax, ay, az = accel # Units G (but later normalised)
gx, gy, gz = (radians(x) for x in gyro) # Units deg/s
q1, q2, q3, q4 = (self.q[x] for x in range(4)) # short name local variable for readability
# Auxiliary variables to avoid repeated arithmetic
_2q1 = 2 * q1
_2q2 = 2 * q2
_2q3 = 2 * q3
_2q4 = 2 * q4
_4q1 = 4 * q1
_4q2 = 4 * q2
_4q3 = 4 * q3
_8q2 = 8 * q2
_8q3 = 8 * q3
q1q1 = q1 * q1
q2q2 = q2 * q2
q3q3 = q3 * q3
q4q4 = q4 * q4
# Normalise accelerometer measurement
norm = sqrt(ax * ax + ay * ay + az * az)
if (norm == 0):
return # handle NaN
norm = 1 / norm # use reciprocal for division
ax *= norm
ay *= norm
az *= norm
# Gradient decent algorithm corrective step
s1 = _4q1 * q3q3 + _2q3 * ax + _4q1 * q2q2 - _2q2 * ay
s2 = _4q2 * q4q4 - _2q4 * ax + 4 * q1q1 * q2 - _2q1 * ay - _4q2 + _8q2 * q2q2 + _8q2 * q3q3 + _4q2 * az
s3 = 4 * q1q1 * q3 + _2q1 * ax + _4q3 * q4q4 - _2q4 * ay - _4q3 + _8q3 * q2q2 + _8q3 * q3q3 + _4q3 * az
s4 = 4 * q2q2 * q4 - _2q2 * ax + 4 * q3q3 * q4 - _2q3 * ay
norm = 1 / sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4) # normalise step magnitude
s1 *= norm
s2 *= norm
s3 *= norm
s4 *= norm
# Compute rate of change of quaternion
qDot1 = 0.5 * (-q2 * gx - q3 * gy - q4 * gz) - self.beta * s1
qDot2 = 0.5 * (q1 * gx + q3 * gz - q4 * gy) - self.beta * s2
qDot3 = 0.5 * (q1 * gy - q2 * gz + q4 * gx) - self.beta * s3
qDot4 = 0.5 * (q1 * gz + q2 * gy - q3 * gx) - self.beta * s4
if slow_platform:
await asyncio.sleep_ms(0)
# Integrate to yield quaternion
deltat = self.deltat(ts)
q1 += qDot1 * deltat
q2 += qDot2 * deltat
q3 += qDot3 * deltat
q4 += qDot4 * deltat
norm = 1 / sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4) # normalise quaternion
self.q = q1 * norm, q2 * norm, q3 * norm, q4 * norm
self.heading = 0 # Meaningless without a magnetometer
self.pitch = degrees(-asin(2.0 * (self.q[1] * self.q[3] - self.q[0] * self.q[2])))
self.roll = degrees(atan2(2.0 * (self.q[0] * self.q[1] + self.q[2] * self.q[3]),
self.q[0] * self.q[0] - self.q[1] * self.q[1] - self.q[2] * self.q[2] + self.q[3] * self.q[3]))
async def _update_mag(self, slow_platform):
while True:
if self.expect_ts:
accel, gyro, mag, ts = await self.read_coro()
else:
accel, gyro, mag = await self.read_coro()
ts = None
mx, my, mz = (mag[x] - self.magbias[x] for x in range(3)) # Units irrelevant (normalised)
ax, ay, az = accel # Units irrelevant (normalised)
gx, gy, gz = (radians(x) for x in gyro) # Units deg/s
q1, q2, q3, q4 = (self.q[x] for x in range(4)) # short name local variable for readability
# Auxiliary variables to avoid repeated arithmetic
_2q1 = 2 * q1
_2q2 = 2 * q2
_2q3 = 2 * q3
_2q4 = 2 * q4
_2q1q3 = 2 * q1 * q3
_2q3q4 = 2 * q3 * q4
q1q1 = q1 * q1
q1q2 = q1 * q2
q1q3 = q1 * q3
q1q4 = q1 * q4
q2q2 = q2 * q2
q2q3 = q2 * q3
q2q4 = q2 * q4
q3q3 = q3 * q3
q3q4 = q3 * q4
q4q4 = q4 * q4
# Normalise accelerometer measurement
norm = sqrt(ax * ax + ay * ay + az * az)
if (norm == 0):
return # handle NaN
norm = 1 / norm # use reciprocal for division
ax *= norm
ay *= norm
az *= norm
# Normalise magnetometer measurement
norm = sqrt(mx * mx + my * my + mz * mz)
if (norm == 0):
return # handle NaN
norm = 1 / norm # use reciprocal for division
mx *= norm
my *= norm
mz *= norm
# Reference direction of Earth's magnetic field
_2q1mx = 2 * q1 * mx
_2q1my = 2 * q1 * my
_2q1mz = 2 * q1 * mz
_2q2mx = 2 * q2 * mx
hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4
hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4
_2bx = sqrt(hx * hx + hy * hy)
_2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4
_4bx = 2 * _2bx
_4bz = 2 * _2bz
# Gradient descent algorithm corrective step
s1 = (-_2q3 * (2 * q2q4 - _2q1q3 - ax) + _2q2 * (2 * q1q2 + _2q3q4 - ay) - _2bz * q3 * (_2bx * (0.5 - q3q3 - q4q4)
+ _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q4 + _2bz * q2) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my)
+ _2bx * q3 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5 - q2q2 - q3q3) - mz))
s2 = (_2q4 * (2 * q2q4 - _2q1q3 - ax) + _2q1 * (2 * q1q2 + _2q3q4 - ay) - 4 * q2 * (1 - 2 * q2q2 - 2 * q3q3 - az)
+ _2bz * q4 * (_2bx * (0.5 - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q3 + _2bz * q1) * (_2bx * (q2q3 - q1q4)
+ _2bz * (q1q2 + q3q4) - my) + (_2bx * q4 - _4bz * q2) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5 - q2q2 - q3q3) - mz))
if slow_platform:
await asyncio.sleep_ms(0)
s3 = (-_2q1 * (2 * q2q4 - _2q1q3 - ax) + _2q4 * (2 * q1q2 + _2q3q4 - ay) - 4 * q3 * (1 - 2 * q2q2 - 2 * q3q3 - az)
+ (-_4bx * q3 - _2bz * q1) * (_2bx * (0.5 - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx)
+ (_2bx * q2 + _2bz * q4) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my)
+ (_2bx * q1 - _4bz * q3) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5 - q2q2 - q3q3) - mz))
s4 = (_2q2 * (2 * q2q4 - _2q1q3 - ax) + _2q3 * (2 * q1q2 + _2q3q4 - ay) + (-_4bx * q4 + _2bz * q2) * (_2bx * (0.5 - q3q3 - q4q4)
+ _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q1 + _2bz * q3) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my)
+ _2bx * q2 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5 - q2q2 - q3q3) - mz))
norm = 1 / sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4) # normalise step magnitude
s1 *= norm
s2 *= norm
s3 *= norm
s4 *= norm
# Compute rate of change of quaternion
qDot1 = 0.5 * (-q2 * gx - q3 * gy - q4 * gz) - self.beta * s1
qDot2 = 0.5 * (q1 * gx + q3 * gz - q4 * gy) - self.beta * s2
qDot3 = 0.5 * (q1 * gy - q2 * gz + q4 * gx) - self.beta * s3
qDot4 = 0.5 * (q1 * gz + q2 * gy - q3 * gx) - self.beta * s4
# Integrate to yield quaternion
deltat = self.deltat(ts)
q1 += qDot1 * deltat
q2 += qDot2 * deltat
q3 += qDot3 * deltat
q4 += qDot4 * deltat
norm = 1 / sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4) # normalise quaternion
self.q = q1 * norm, q2 * norm, q3 * norm, q4 * norm
self.heading = self.declination + degrees(atan2(2.0 * (self.q[1] * self.q[2] + self.q[0] * self.q[3]),
self.q[0] * self.q[0] + self.q[1] * self.q[1] - self.q[2] * self.q[2] - self.q[3] * self.q[3]))
self.pitch = degrees(-asin(2.0 * (self.q[1] * self.q[3] - self.q[0] * self.q[2])))
self.roll = degrees(atan2(2.0 * (self.q[0] * self.q[1] + self.q[2] * self.q[3]),
self.q[0] * self.q[0] - self.q[1] * self.q[1] - self.q[2] * self.q[2] + self.q[3] * self.q[3]))