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4674e7a Jul 22, 2013
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace AHRS
{
/// <summary>
/// MadgwickAHRS class. Implementation of Madgwick's IMU and AHRS algorithms.
/// </summary>
/// <remarks>
/// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
/// </remarks>
public class MadgwickAHRS
{
/// <summary>
/// Gets or sets the sample period.
/// </summary>
public float SamplePeriod { get; set; }
/// <summary>
/// Gets or sets the algorithm gain beta.
/// </summary>
public float Beta { get; set; }
/// <summary>
/// Gets or sets the Quaternion output.
/// </summary>
public float[] Quaternion { get; set; }
/// <summary>
/// Initializes a new instance of the <see cref="MadgwickAHRS"/> class.
/// </summary>
/// <param name="samplePeriod">
/// Sample period.
/// </param>
public MadgwickAHRS(float samplePeriod)
: this(samplePeriod, 1f)
{
}
/// <summary>
/// Initializes a new instance of the <see cref="MadgwickAHRS"/> class.
/// </summary>
/// <param name="samplePeriod">
/// Sample period.
/// </param>
/// <param name="beta">
/// Algorithm gain beta.
/// </param>
public MadgwickAHRS(float samplePeriod, float beta)
{
SamplePeriod = samplePeriod;
Beta = beta;
Quaternion = new float[] { 1f, 0f, 0f, 0f };
}
/// <summary>
/// Algorithm AHRS update method. Requires only gyroscope and accelerometer data.
/// </summary>
/// <param name="gx">
/// Gyroscope x axis measurement in radians/s.
/// </param>
/// <param name="gy">
/// Gyroscope y axis measurement in radians/s.
/// </param>
/// <param name="gz">
/// Gyroscope z axis measurement in radians/s.
/// </param>
/// <param name="ax">
/// Accelerometer x axis measurement in any calibrated units.
/// </param>
/// <param name="ay">
/// Accelerometer y axis measurement in any calibrated units.
/// </param>
/// <param name="az">
/// Accelerometer z axis measurement in any calibrated units.
/// </param>
/// <param name="mx">
/// Magnetometer x axis measurement in any calibrated units.
/// </param>
/// <param name="my">
/// Magnetometer y axis measurement in any calibrated units.
/// </param>
/// <param name="mz">
/// Magnetometer z axis measurement in any calibrated units.
/// </param>
/// <remarks>
/// Optimised for minimal arithmetic.
/// Total ±: 160
/// Total *: 172
/// Total /: 5
/// Total sqrt: 5
/// </remarks>
public void Update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz)
{
float q1 = Quaternion[0], q2 = Quaternion[1], q3 = Quaternion[2], q4 = Quaternion[3]; // short name local variable for readability
float norm;
float hx, hy, _2bx, _2bz;
float s1, s2, s3, s4;
float qDot1, qDot2, qDot3, qDot4;
// Auxiliary variables to avoid repeated arithmetic
float _2q1mx;
float _2q1my;
float _2q1mz;
float _2q2mx;
float _4bx;
float _4bz;
float _2q1 = 2f * q1;
float _2q2 = 2f * q2;
float _2q3 = 2f * q3;
float _2q4 = 2f * q4;
float _2q1q3 = 2f * q1 * q3;
float _2q3q4 = 2f * q3 * q4;
float q1q1 = q1 * q1;
float q1q2 = q1 * q2;
float q1q3 = q1 * q3;
float q1q4 = q1 * q4;
float q2q2 = q2 * q2;
float q2q3 = q2 * q3;
float q2q4 = q2 * q4;
float q3q3 = q3 * q3;
float q3q4 = q3 * q4;
float q4q4 = q4 * q4;
// Normalise accelerometer measurement
norm = (float)Math.Sqrt(ax * ax + ay * ay + az * az);
if (norm == 0f) return; // handle NaN
norm = 1 / norm; // use reciprocal for division
ax *= norm;
ay *= norm;
az *= norm;
// Normalise magnetometer measurement
norm = (float)Math.Sqrt(mx * mx + my * my + mz * mz);
if (norm == 0f) return; // handle NaN
norm = 1 / norm; // use reciprocal for division
mx *= norm;
my *= norm;
mz *= norm;
// Reference direction of Earth's magnetic field
_2q1mx = 2f * q1 * mx;
_2q1my = 2f * q1 * my;
_2q1mz = 2f * q1 * mz;
_2q2mx = 2f * 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 = (float)Math.Sqrt(hx * hx + hy * hy);
_2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
_4bx = 2f * _2bx;
_4bz = 2f * _2bz;
// Gradient decent algorithm corrective step
s1 = -_2q3 * (2f * q2q4 - _2q1q3 - ax) + _2q2 * (2f * q1q2 + _2q3q4 - ay) - _2bz * q3 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q4 + _2bz * q2) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q3 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
s2 = _2q4 * (2f * q2q4 - _2q1q3 - ax) + _2q1 * (2f * q1q2 + _2q3q4 - ay) - 4f * q2 * (1 - 2f * q2q2 - 2f * q3q3 - az) + _2bz * q4 * (_2bx * (0.5f - 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 * (0.5f - q2q2 - q3q3) - mz);
s3 = -_2q1 * (2f * q2q4 - _2q1q3 - ax) + _2q4 * (2f * q1q2 + _2q3q4 - ay) - 4f * q3 * (1 - 2f * q2q2 - 2f * q3q3 - az) + (-_4bx * q3 - _2bz * q1) * (_2bx * (0.5f - 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 * (0.5f - q2q2 - q3q3) - mz);
s4 = _2q2 * (2f * q2q4 - _2q1q3 - ax) + _2q3 * (2f * q1q2 + _2q3q4 - ay) + (-_4bx * q4 + _2bz * q2) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q1 + _2bz * q3) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q2 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
norm = 1f / (float)Math.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 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - Beta * s1;
qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - Beta * s2;
qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - Beta * s3;
qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - Beta * s4;
// Integrate to yield quaternion
q1 += qDot1 * SamplePeriod;
q2 += qDot2 * SamplePeriod;
q3 += qDot3 * SamplePeriod;
q4 += qDot4 * SamplePeriod;
norm = 1f / (float)Math.Sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4); // normalise quaternion
Quaternion[0] = q1 * norm;
Quaternion[1] = q2 * norm;
Quaternion[2] = q3 * norm;
Quaternion[3] = q4 * norm;
}
/// <summary>
/// Algorithm IMU update method. Requires only gyroscope and accelerometer data.
/// </summary>
/// <param name="gx">
/// Gyroscope x axis measurement in radians/s.
/// </param>
/// <param name="gy">
/// Gyroscope y axis measurement in radians/s.
/// </param>
/// <param name="gz">
/// Gyroscope z axis measurement in radians/s.
/// </param>
/// <param name="ax">
/// Accelerometer x axis measurement in any calibrated units.
/// </param>
/// <param name="ay">
/// Accelerometer y axis measurement in any calibrated units.
/// </param>
/// <param name="az">
/// Accelerometer z axis measurement in any calibrated units.
/// </param>
/// <remarks>
/// Optimised for minimal arithmetic.
/// Total ±: 45
/// Total *: 85
/// Total /: 3
/// Total sqrt: 3
/// </remarks>
public void Update(float gx, float gy, float gz, float ax, float ay, float az)
{
float q1 = Quaternion[0], q2 = Quaternion[1], q3 = Quaternion[2], q4 = Quaternion[3]; // short name local variable for readability
float norm;
float s1, s2, s3, s4;
float qDot1, qDot2, qDot3, qDot4;
// Auxiliary variables to avoid repeated arithmetic
float _2q1 = 2f * q1;
float _2q2 = 2f * q2;
float _2q3 = 2f * q3;
float _2q4 = 2f * q4;
float _4q1 = 4f * q1;
float _4q2 = 4f * q2;
float _4q3 = 4f * q3;
float _8q2 = 8f * q2;
float _8q3 = 8f * q3;
float q1q1 = q1 * q1;
float q2q2 = q2 * q2;
float q3q3 = q3 * q3;
float q4q4 = q4 * q4;
// Normalise accelerometer measurement
norm = (float)Math.Sqrt(ax * ax + ay * ay + az * az);
if (norm == 0f) 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 + 4f * q1q1 * q2 - _2q1 * ay - _4q2 + _8q2 * q2q2 + _8q2 * q3q3 + _4q2 * az;
s3 = 4f * q1q1 * q3 + _2q1 * ax + _4q3 * q4q4 - _2q4 * ay - _4q3 + _8q3 * q2q2 + _8q3 * q3q3 + _4q3 * az;
s4 = 4f * q2q2 * q4 - _2q2 * ax + 4f * q3q3 * q4 - _2q3 * ay;
norm = 1f / (float)Math.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 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - Beta * s1;
qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - Beta * s2;
qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - Beta * s3;
qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - Beta * s4;
// Integrate to yield quaternion
q1 += qDot1 * SamplePeriod;
q2 += qDot2 * SamplePeriod;
q3 += qDot3 * SamplePeriod;
q4 += qDot4 * SamplePeriod;
norm = 1f / (float)Math.Sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4); // normalise quaternion
Quaternion[0] = q1 * norm;
Quaternion[1] = q2 * norm;
Quaternion[2] = q3 * norm;
Quaternion[3] = q4 * norm;
}
}
}