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Mahony.js
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Mahony.js
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//= ====================================================================================================
// Based on MahonyAHRS.c
//= ====================================================================================================
//
// Madgwick's implementation of Mayhony's AHRS algorithm.
// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
//
//= ====================================================================================================
/* eslint-disable one-var-declaration-per-line */
'use strict';
/**
* The Mahony algorithm. See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/.
*
* @param {number} sampleInterval - The sample interval in milliseconds.
* @param {Object} options - The options.
*/
module.exports = function Mahony(sampleInterval, options) {
//---------------------------------------------------------------------------------------------------
// Definitions
options = options || {};
const kp = options.kp || 1.0;
const ki = options.ki || 0.0;
const sampleFreq = 1000 / sampleInterval; // sample frequency in Hz
let recipSampleFreq = 1 / sampleFreq;
let initalised = options.doInitialisation === true ? false : true;
//---------------------------------------------------------------------------------------------------
// Variable definitions
let twoKp = 2.0 * kp; // 2 * proportional gain (Kp)
const twoKi = 2.0 * ki; // 2 * integral gain (Ki)
let q0 = 1.0,
q1 = 0.0,
q2 = 0.0,
q3 = 0.0; // quaternion of sensor frame relative to auxiliary frame
let integralFBx = 0.0,
integralFBy = 0.0,
integralFBz = 0.0; // integral error terms scaled by Ki
//= ===================================================================================================
// Functions
//---------------------------------------------------------------------------------------------------
// IMU algorithm update
//
function mahonyAHRSUpdateIMU(gx, gy, gz, ax, ay, az) {
let recipNorm;
let halfvx, halfvy, halfvz;
let halfex, halfey, halfez;
// Compute feedback only if accelerometer measurement valid (NaN in accelerometer normalisation)
if (ax !== 0 && ay !== 0 && az !== 0) {
// Normalise accelerometer measurement
recipNorm = (ax * ax + ay * ay + az * az) ** -0.5;
ax *= recipNorm;
ay *= recipNorm;
az *= recipNorm;
// Estimated direction of gravity and vector perpendicular to magnetic flux
halfvx = q1 * q3 - q0 * q2;
halfvy = q0 * q1 + q2 * q3;
halfvz = q0 * q0 - 0.5 + q3 * q3;
// Error is sum of cross product between estimated and measured direction of gravity
halfex = ay * halfvz - az * halfvy;
halfey = az * halfvx - ax * halfvz;
halfez = ax * halfvy - ay * halfvx;
// Compute and apply integral feedback if enabled
if (twoKi > 0.0) {
integralFBx += twoKi * halfex * recipSampleFreq; // integral error scaled by Ki
integralFBy += twoKi * halfey * recipSampleFreq;
integralFBz += twoKi * halfez * recipSampleFreq;
gx += integralFBx; // apply integral feedback
gy += integralFBy;
gz += integralFBz;
} else {
integralFBx = 0.0; // prevent integral windup
integralFBy = 0.0;
integralFBz = 0.0;
}
// Apply proportional feedback
gx += twoKp * halfex;
gy += twoKp * halfey;
gz += twoKp * halfez;
}
// Integrate rate of change of quaternion
gx *= 0.5 * recipSampleFreq; // pre-multiply common factors
gy *= 0.5 * recipSampleFreq;
gz *= 0.5 * recipSampleFreq;
const qa = q0;
const qb = q1;
const qc = q2;
q0 += -qb * gx - qc * gy - q3 * gz;
q1 += qa * gx + qc * gz - q3 * gy;
q2 += qa * gy - qb * gz + q3 * gx;
q3 += qa * gz + qb * gy - qc * gx;
// Normalise quaternion
recipNorm = (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3) ** -0.5;
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
}
function cross_product(ax, ay, az, bx, by, bz) {
return {
x: ay * bz - az * by,
y: az * bx - ax * bz,
z: ax * by - ay * bx,
};
}
/**
* @param {number} ax - accel x
* @param {number} ay - accel y
* @param {number} az - accel z
* @param {number} mx - mag x
* @param {number} my - mag y
* @param {number} mz - mag z
* @returns {EulerAngles} - The Euler angles, in radians.
*/
function eulerAnglesFromImuRad(ax, ay, az, mx, my, mz) {
const pitch = -Math.atan2(ax, Math.sqrt(ay * ay + az * az));
const tmp1 = cross_product(ax, ay, az, 1.0, 0.0, 0.0);
const tmp2 = cross_product(1.0, 0.0, 0.0, tmp1.x, tmp1.y, tmp1.z);
const roll = Math.atan2(tmp2.y, tmp2.z);
const cr = Math.cos(roll);
const sp = Math.sin(pitch);
const sr = Math.sin(roll);
const yh = my * cr - mz * sr;
const xh = mx * Math.cos(pitch) + my * sr * sp + mz * cr * sp;
const heading = -Math.atan2(yh, xh);
return {
heading,
pitch,
roll,
};
}
// Pinched from here: https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
function toQuaternion(eulerAngles) {
const cy = Math.cos(eulerAngles.heading * 0.5);
const sy = Math.sin(eulerAngles.heading * 0.5);
const cp = Math.cos(eulerAngles.pitch * 0.5);
const sp = Math.sin(eulerAngles.pitch * 0.5);
const cr = Math.cos(eulerAngles.roll * 0.5);
const sr = Math.sin(eulerAngles.roll * 0.5);
return {
w: cr * cp * cy + sr * sp * sy,
x: sr * cp * cy - cr * sp * sy,
y: cr * sp * cy + sr * cp * sy,
z: cr * cp * sy - sr * sp * cy,
};
}
/**
* Initalise the internal quaternion values. This function only needs to be
* called once at the beginning. The attitude will be set by the accelometer
* and the heading by the magnetometer.
*
* @param {number} ax - accel x
* @param {number} ay - accel y
* @param {number} az - accel z
* @param {number} mx - mag x
* @param {number} my - mag y
* @param {number} mz - mag z
*/
function init(ax, ay, az, mx, my, mz) {
const ea = eulerAnglesFromImuRad(ax, ay, az, mx, my, mz);
const iq = toQuaternion(ea);
// Normalise quaternion
const recipNorm = (iq.w * iq.w + iq.x * iq.x + iq.y * iq.y + iq.z * iq.z) ** -0.5;
q0 = iq.w * recipNorm;
q1 = iq.x * recipNorm;
q2 = iq.y * recipNorm;
q3 = iq.z * recipNorm;
initalised = true;
}
//
//---------------------------------------------------------------------------------------------------
// AHRS algorithm update
//
function mahonyAHRSUpdate(gx, gy, gz, ax, ay, az, mx, my, mz, deltaTimeSec) {
recipSampleFreq = deltaTimeSec || recipSampleFreq;
if (!initalised) {
init(ax, ay, az, mx, my, mz);
}
let recipNorm;
let q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
let hx, hy, bx, bz;
let halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
let halfex, halfey, halfez;
// Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
if (mx === undefined || my === undefined || mz === undefined || (mx === 0 && my === 0 && mz === 0)) {
mahonyAHRSUpdateIMU(gx, gy, gz, ax, ay, az);
return;
}
// Compute feedback only if accelerometer measurement valid (NaN in accelerometer normalisation)
if (ax !== 0 && ay !== 0 && az !== 0) {
// Normalise accelerometer measurement
recipNorm = (ax * ax + ay * ay + az * az) ** -0.5;
ax *= recipNorm;
ay *= recipNorm;
az *= recipNorm;
// Normalise magnetometer measurement
recipNorm = (mx * mx + my * my + mz * mz) ** -0.5;
mx *= recipNorm;
my *= recipNorm;
mz *= recipNorm;
// Auxiliary variables to repeated arithmetic
q0q0 = q0 * q0;
q0q1 = q0 * q1;
q0q2 = q0 * q2;
q0q3 = q0 * q3;
q1q1 = q1 * q1;
q1q2 = q1 * q2;
q1q3 = q1 * q3;
q2q2 = q2 * q2;
q2q3 = q2 * q3;
q3q3 = q3 * q3;
// Reference direction of Earth's magnetic field
hx = 2.0 * (mx * (0.5 - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
hy = 2.0 * (mx * (q1q2 + q0q3) + my * (0.5 - q1q1 - q3q3) + mz * (q2q3 - q0q1));
bx = Math.sqrt(hx * hx + hy * hy);
bz = 2.0 * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5 - q1q1 - q2q2));
// Estimated direction of gravity and magnetic field
halfvx = q1q3 - q0q2;
halfvy = q0q1 + q2q3;
halfvz = q0q0 - 0.5 + q3q3;
halfwx = bx * (0.5 - q2q2 - q3q3) + bz * (q1q3 - q0q2);
halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
halfwz = bx * (q0q2 + q1q3) + bz * (0.5 - q1q1 - q2q2);
// Error is sum of cross product between estimated direction and measured direction of field vectors
halfex = ay * halfvz - az * halfvy + (my * halfwz - mz * halfwy);
halfey = az * halfvx - ax * halfvz + (mz * halfwx - mx * halfwz);
halfez = ax * halfvy - ay * halfvx + (mx * halfwy - my * halfwx);
// Compute and apply integral feedback if enabled
if (twoKi > 0.0) {
integralFBx += twoKi * halfex * recipSampleFreq; // integral error scaled by Ki
integralFBy += twoKi * halfey * recipSampleFreq;
integralFBz += twoKi * halfez * recipSampleFreq;
gx += integralFBx; // apply integral feedback
gy += integralFBy;
gz += integralFBz;
} else {
integralFBx = 0.0; // prevent integral windup
integralFBy = 0.0;
integralFBz = 0.0;
}
// Apply proportional feedback
gx += twoKp * halfex;
gy += twoKp * halfey;
gz += twoKp * halfez;
}
// Integrate rate of change of quaternion
gx *= 0.5 * recipSampleFreq; // pre-multiply common factors
gy *= 0.5 * recipSampleFreq;
gz *= 0.5 * recipSampleFreq;
const qa = q0;
const qb = q1;
const qc = q2;
q0 += -qb * gx - qc * gy - q3 * gz;
q1 += qa * gx + qc * gz - q3 * gy;
q2 += qa * gy - qb * gz + q3 * gx;
q3 += qa * gz + qb * gy - qc * gx;
// Normalise quaternion
recipNorm = (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3) ** -0.5;
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
}
return {
update: mahonyAHRSUpdate,
init,
getQuaternion() {
return {
w: q0,
x: q1,
y: q2,
z: q3,
};
},
};
//= ===================================================================================================
// END OF CODE
//= ===================================================================================================
};