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madgwickahrs.py
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madgwickahrs.py
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# -*- coding: utf-8 -*-
"""
Copyright (c) 2015 Jonas Böer, [email protected]
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
"""
import warnings
import numpy as np
from numpy.linalg import norm
from .quaternion import Quaternion
class MadgwickAHRS:
samplePeriod = 1/256
quaternion = Quaternion(1, 0, 0, 0)
beta = 1
zeta = 0
def __init__(self, sampleperiod=None, quaternion=None, beta=None, zeta=None):
"""
Initialize the class with the given parameters.
:param sampleperiod: The sample period
:param quaternion: Initial quaternion
:param beta: Algorithm gain beta
:param beta: Algorithm gain zeta
:return:
"""
if sampleperiod is not None:
self.samplePeriod = sampleperiod
if quaternion is not None:
self.quaternion = quaternion
if beta is not None:
self.beta = beta
if zeta is not None:
self.zeta = zeta
def update(self, gyroscope, accelerometer, magnetometer):
"""
Perform one update step with data from a AHRS sensor array
:param gyroscope: A three-element array containing the gyroscope data in radians per second.
:param accelerometer: A three-element array containing the accelerometer data. Can be any unit since a normalized value is used.
:param magnetometer: A three-element array containing the magnetometer data. Can be any unit since a normalized value is used.
:return:
"""
q = self.quaternion
gyroscope = np.array(gyroscope, dtype=float).flatten()
accelerometer = np.array(accelerometer, dtype=float).flatten()
magnetometer = np.array(magnetometer, dtype=float).flatten()
# Normalise accelerometer measurement
if norm(accelerometer) is 0:
warnings.warn("accelerometer is zero")
return
accelerometer /= norm(accelerometer)
# Normalise magnetometer measurement
if norm(magnetometer) is 0:
warnings.warn("magnetometer is zero")
return
magnetometer /= norm(magnetometer)
h = q * (Quaternion(0, magnetometer[0], magnetometer[1], magnetometer[2]) * q.conj())
b = np.array([0, norm(h[1:3]), 0, h[3]])
# Gradient descent algorithm corrective step
f = np.array([
2*(q[1]*q[3] - q[0]*q[2]) - accelerometer[0],
2*(q[0]*q[1] + q[2]*q[3]) - accelerometer[1],
2*(0.5 - q[1]**2 - q[2]**2) - accelerometer[2],
2*b[1]*(0.5 - q[2]**2 - q[3]**2) + 2*b[3]*(q[1]*q[3] - q[0]*q[2]) - magnetometer[0],
2*b[1]*(q[1]*q[2] - q[0]*q[3]) + 2*b[3]*(q[0]*q[1] + q[2]*q[3]) - magnetometer[1],
2*b[1]*(q[0]*q[2] + q[1]*q[3]) + 2*b[3]*(0.5 - q[1]**2 - q[2]**2) - magnetometer[2]
])
j = np.array([
[-2*q[2], 2*q[3], -2*q[0], 2*q[1]],
[2*q[1], 2*q[0], 2*q[3], 2*q[2]],
[0, -4*q[1], -4*q[2], 0],
[-2*b[3]*q[2], 2*b[3]*q[3], -4*b[1]*q[2]-2*b[3]*q[0], -4*b[1]*q[3]+2*b[3]*q[1]],
[-2*b[1]*q[3]+2*b[3]*q[1], 2*b[1]*q[2]+2*b[3]*q[0], 2*b[1]*q[1]+2*b[3]*q[3], -2*b[1]*q[0]+2*b[3]*q[2]],
[2*b[1]*q[2], 2*b[1]*q[3]-4*b[3]*q[1], 2*b[1]*q[0]-4*b[3]*q[2], 2*b[1]*q[1]]
])
step = j.T.dot(f)
step /= norm(step) # normalise step magnitude
# Gyroscope compensation drift
gyroscopeQuat = Quaternion(0, gyroscope[0], gyroscope[1], gyroscope[2])
stepQuat = Quaternion(step.T[0], step.T[1], step.T[2], step.T[3])
gyroscopeQuat = gyroscopeQuat + (q.conj() * stepQuat) * 2 * self.samplePeriod * self.zeta * -1
# Compute rate of change of quaternion
qdot = (q * gyroscopeQuat) * 0.5 - self.beta * step.T
# Integrate to yield quaternion
q += qdot * self.samplePeriod
self.quaternion = Quaternion(q / norm(q)) # normalise quaternion
def update_imu(self, gyroscope, accelerometer):
"""
Perform one update step with data from a IMU sensor array
:param gyroscope: A three-element array containing the gyroscope data in radians per second.
:param accelerometer: A three-element array containing the accelerometer data. Can be any unit since a normalized value is used.
"""
q = self.quaternion
gyroscope = np.array(gyroscope, dtype=float).flatten()
accelerometer = np.array(accelerometer, dtype=float).flatten()
# Normalise accelerometer measurement
if norm(accelerometer) is 0:
warnings.warn("accelerometer is zero")
return
accelerometer /= norm(accelerometer)
# Gradient descent algorithm corrective step
f = np.array([
2*(q[1]*q[3] - q[0]*q[2]) - accelerometer[0],
2*(q[0]*q[1] + q[2]*q[3]) - accelerometer[1],
2*(0.5 - q[1]**2 - q[2]**2) - accelerometer[2]
])
j = np.array([
[-2*q[2], 2*q[3], -2*q[0], 2*q[1]],
[2*q[1], 2*q[0], 2*q[3], 2*q[2]],
[0, -4*q[1], -4*q[2], 0]
])
step = j.T.dot(f)
step /= norm(step) # normalise step magnitude
# Compute rate of change of quaternion
qdot = (q * Quaternion(0, gyroscope[0], gyroscope[1], gyroscope[2])) * 0.5 - self.beta * step.T
# Integrate to yield quaternion
q += qdot * self.samplePeriod
self.quaternion = Quaternion(q / norm(q)) # normalise quaternion