.. _program_listing_file_src_tap_algorithms_MahonyAHRS.cpp:

Program Listing for File MahonyAHRS.cpp
=======================================

|exhale_lsh| :ref:`Return to documentation for file <file_src_tap_algorithms_MahonyAHRS.cpp>` (``src/tap/algorithms/MahonyAHRS.cpp``)

.. |exhale_lsh| unicode:: U+021B0 .. UPWARDS ARROW WITH TIP LEFTWARDS

.. code-block:: cpp

   //=============================================================================================
   // MahonyAHRS.c
   //=============================================================================================
   //
   // Madgwick's implementation of Mayhony's AHRS algorithm.
   // See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/
   //
   // From the x-io website "Open-source resources available on this website are
   // provided under the GNU General Public Licence unless an alternative licence
   // is provided in source."
   //
   // Date          Author          Notes
   // 29/09/2011    SOH Madgwick    Initial release
   // 02/10/2011    SOH Madgwick    Optimised for reduced CPU load
   // 09/06/2020    Matthew Arnold  Update style, use safer casting
   //
   // Algorithm paper:
   // http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4608934&url=http%3A%2F%2Fieeexplore.ieee.org%2Fstamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D4608934
   //
   //=============================================================================================
   
   //-------------------------------------------------------------------------------------------
   // Header files
   
   #include "MahonyAHRS.h"
   
   #include <cinttypes>
   #include <cmath>
   #include <cstring>
   
   //-------------------------------------------------------------------------------------------
   // Definitions
   
   #define DEFAULT_SAMPLE_FREQ 500.0f  // sample frequency in Hz
   #define twoKpDef (2.0f * 0.5f)      // 2 * proportional gain
   #define twoKiDef (2.0f * 0.0f)      // 2 * integral gain
   
   //============================================================================================
   // Functions
   
   static float fastInvSqrt(float x);
   
   //-------------------------------------------------------------------------------------------
   // AHRS algorithm update
   
   Mahony::Mahony()
   {
       twoKp = twoKpDef;  // 2 * proportional gain (Kp)
       twoKi = twoKiDef;  // 2 * integral gain (Ki)
       q0 = 1.0f;
       q1 = 0.0f;
       q2 = 0.0f;
       q3 = 0.0f;
       integralFBx = 0.0f;
       integralFBy = 0.0f;
       integralFBz = 0.0f;
       anglesComputed = 0;
       invSampleFreq = 1.0f / DEFAULT_SAMPLE_FREQ;
       roll = 0.0f;
       pitch = 0.0f;
       yaw = 0.0f;
   }
   
   void Mahony::update(
       float gx,
       float gy,
       float gz,
       float ax,
       float ay,
       float az,
       float mx,
       float my,
       float mz)
   {
       float recipNorm;
       float qa, qb, qc;
   
       // Use IMU algorithm if magnetometer measurement invalid
       // (avoids NaN in magnetometer normalisation)
       if ((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f))
       {
           updateIMU(gx, gy, gz, ax, ay, az);
           return;
       }
   
       // Convert gyroscope degrees/sec to radians/sec
       gx *= 0.0174533f;
       gy *= 0.0174533f;
       gz *= 0.0174533f;
   
       // Compute feedback only if accelerometer measurement valid
       // (avoids NaN in accelerometer normalisation)
       if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f)))
       {
           // Normalise accelerometer measurement
           recipNorm = fastInvSqrt(ax * ax + ay * ay + az * az);
           ax *= recipNorm;
           ay *= recipNorm;
           az *= recipNorm;
   
           // Normalise magnetometer measurement
           recipNorm = fastInvSqrt(mx * mx + my * my + mz * mz);
           mx *= recipNorm;
           my *= recipNorm;
           mz *= recipNorm;
   
           float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
   
           // Auxiliary variables to avoid 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;
   
           float hx, hy, bx, bz;
   
           // Reference direction of Earth's magnetic field
           hx = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
           hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1));
           bx = sqrtf(hx * hx + hy * hy);
           bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2));
   
           float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
           float halfex, halfey, halfez;
   
           // Estimated direction of gravity and magnetic field
           halfvx = q1q3 - q0q2;
           halfvy = q0q1 + q2q3;
           halfvz = q0q0 - 0.5f + q3q3;
           halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2);
           halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
           halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - 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 > 0.0f)
           {
               // integral error scaled by Ki
               integralFBx += twoKi * halfex * invSampleFreq;
               integralFBy += twoKi * halfey * invSampleFreq;
               integralFBz += twoKi * halfez * invSampleFreq;
               gx += integralFBx;  // apply integral feedback
               gy += integralFBy;
               gz += integralFBz;
           }
           else
           {
               integralFBx = 0.0f;  // prevent integral windup
               integralFBy = 0.0f;
               integralFBz = 0.0f;
           }
   
           // Apply proportional feedback
           gx += twoKp * halfex;
           gy += twoKp * halfey;
           gz += twoKp * halfez;
       }
   
       // Integrate rate of change of quaternion
       gx *= (0.5f * invSampleFreq);  // pre-multiply common factors
       gy *= (0.5f * invSampleFreq);
       gz *= (0.5f * invSampleFreq);
       qa = q0;
       qb = q1;
       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 = fastInvSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
       q0 *= recipNorm;
       q1 *= recipNorm;
       q2 *= recipNorm;
       q3 *= recipNorm;
       anglesComputed = 0;
   }
   
   //-------------------------------------------------------------------------------------------
   // IMU algorithm update
   
   void Mahony::updateIMU(float gx, float gy, float gz, float ax, float ay, float az)
   {
       float recipNorm;
       float qa, qb, qc;
   
       // Convert gyroscope degrees/sec to radians/sec
       gx *= 0.0174533f;
       gy *= 0.0174533f;
       gz *= 0.0174533f;
   
       // Compute feedback only if accelerometer measurement valid
       // (avoids NaN in accelerometer normalisation)
       if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f)))
       {
           // Normalise accelerometer measurement
           recipNorm = fastInvSqrt(ax * ax + ay * ay + az * az);
           ax *= recipNorm;
           ay *= recipNorm;
           az *= recipNorm;
   
           float halfvx, halfvy, halfvz;
           float halfex, halfey, halfez;
   
           // Estimated direction of gravity
           halfvx = q1 * q3 - q0 * q2;
           halfvy = q0 * q1 + q2 * q3;
           halfvz = q0 * q0 - 0.5f + 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 > 0.0f)
           {
               // integral error scaled by Ki
               integralFBx += twoKi * halfex * invSampleFreq;
               integralFBy += twoKi * halfey * invSampleFreq;
               integralFBz += twoKi * halfez * invSampleFreq;
               gx += integralFBx;  // apply integral feedback
               gy += integralFBy;
               gz += integralFBz;
           }
           else
           {
               integralFBx = 0.0f;  // prevent integral windup
               integralFBy = 0.0f;
               integralFBz = 0.0f;
           }
   
           // Apply proportional feedback
           gx += twoKp * halfex;
           gy += twoKp * halfey;
           gz += twoKp * halfez;
       }
   
       // Integrate rate of change of quaternion
       gx *= (0.5f * invSampleFreq);  // pre-multiply common factors
       gy *= (0.5f * invSampleFreq);
       gz *= (0.5f * invSampleFreq);
       qa = q0;
       qb = q1;
       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 = fastInvSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
       q0 *= recipNorm;
       q1 *= recipNorm;
       q2 *= recipNorm;
       q3 *= recipNorm;
       anglesComputed = 0;
   }
   
   //-------------------------------------------------------------------------------------------
   
   void Mahony::computeAngles()
   {
       roll = atan2f(q0 * q1 + q2 * q3, 0.5f - q1 * q1 - q2 * q2);
       pitch = asinf(-2.0f * (q1 * q3 - q0 * q2));
       yaw = atan2f(q1 * q2 + q0 * q3, 0.5f - q2 * q2 - q3 * q3);
       anglesComputed = 1;
   }
   
   template <typename From, typename To>
   To reinterpretCopy(From from)
   {
       static_assert(sizeof(From) == sizeof(To), "can only reinterpret-copy types of the same size");
       To result;
       memcpy(static_cast<void*>(&result), static_cast<void*>(&from), sizeof(To));
       return result;
   }
   
   float fastInvSqrt(float x)
   {
       static_assert(sizeof(float) == 4, "fast inverse sqrt requires 32-bit float");
       float halfx = 0.5f * x;
       float y = x;
       int32_t i = reinterpretCopy<float, int32_t>(y);
       i = 0x5f3759df - (i >> 1);
       y = reinterpretCopy<int32_t, float>(i);
       y = y * (1.5f - (halfx * y * y));
       return y;
   }
   
   //============================================================================================
   // END OF CODE
   //============================================================================================