/Modules/AHRS/MadgwickAHRS.c

https://gitlab.com/krucios/Astraeus_FW · C · 278 lines · 190 code · 36 blank · 52 comment · 18 complexity · 77cc8abe24951cdbc422a8594eeb7602 MD5 · raw file 

    

  1. //=====================================================================================================
    2. 

  2. // MadgwickAHRS.c
    3. 

  3. //=====================================================================================================
    4. 

  4. //
    5. 

  5. // Implementation of Madgwick's IMU and AHRS algorithms.
    6. 

  6. // See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
    7. 

  7. //
    8. 

  8. // Date			Author          Notes
    9. 

  9. // 29/09/2011	SOH Madgwick    Initial release
    10. 

  10. // 02/10/2011	SOH Madgwick	Optimised for reduced CPU load
    11. 

  11. // 19/02/2012	SOH Madgwick	Magnetometer measurement is normalised
    12. 

  12. //
    13. 

  13. //=====================================================================================================
    14. 

  14. 

  15. //---------------------------------------------------------------------------------------------------
    16. 

  16. // Header files
    17. 

  17. 

  18. #include "MadgwickAHRS.h"
    19. 

  19. #include <math.h>
    20. 

  20. 

  21. #include <Modules/Time/timer.h>
    22. 

  22. 

  23. //---------------------------------------------------------------------------------------------------
    24. 

  24. // Definitions
    25. 

  25. 

  26. #define sampleFreq  (MSS_TIM1_FREQ * 1.0f)                       // sample frequency in Hz
    27. 

  27. #define betaDef     (M_PI * (5.0f / 180.0f) * 0.86602540378f)    // 2 * proportional gain (sqrt(3)/2)
    28. 

  28. 

  29. //---------------------------------------------------------------------------------------------------
    30. 

  30. // Variable definitions
    31. 

  31. 

  32. volatile float beta = betaDef;         // 2 * proportional gain (Kp)
    33. 

  33. float q[4] = {1.0f, 0.0f, 0.0f, 0.0f}; // quaternion of sensor frame relative to auxiliary frame
    34. 

  34. 

  35. //---------------------------------------------------------------------------------------------------
    36. 

  36. // Function declarations
    37. 

  37. 

  38. float invSqrt(float x);
    39. 

  39. 

  40. //====================================================================================================
    41. 

  41. // Functions
    42. 

  42. 

  43. //---------------------------------------------------------------------------------------------------
    44. 

  44. // AHRS algorithm update
    45. 

  45. 

  46. void MadgwickAHRSupdate(float gx, float gy, float gz,
    47. 

  47.                         float ax, float ay, float az,
    48. 

  48.                         float mx, float my, float mz) {
    49. 

  49.     float recipNorm;
    50. 

  50.     float s0, s1, s2, s3;
    51. 

  51.     float qDot1, qDot2, qDot3, qDot4;
    52. 

  52.     float hx, hy;
    53. 

  53.     float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1,
    54. 

  54.             _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2,
    55. 

  55.             q1q3, q2q2, q2q3, q3q3;
    56. 

  56. 

  57.     // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
    58. 

  58.     if ((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
    59. 

  59.         MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az);
    60. 

  60.         return;
    61. 

  61.     }
    62. 

  62. 

  63.     // Rate of change of quaternion from gyroscope
    64. 

  64.     qDot1 = 0.5f * (-q[1] * gx - q[2] * gy - q[3] * gz);
    65. 

  65.     qDot2 = 0.5f * (q[0] * gx + q[2] * gz - q[3] * gy);
    66. 

  66.     qDot3 = 0.5f * (q[0] * gy - q[1] * gz + q[3] * gx);
    67. 

  67.     qDot4 = 0.5f * (q[0] * gz + q[1] * gy - q[2] * gx);
    68. 

  68. 

  69.     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
    70. 

  70.     if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
    71. 

  71. 

  72.         // Normalise accelerometer measurement
    73. 

  73.         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
    74. 

  74.         ax *= recipNorm;
    75. 

  75.         ay *= recipNorm;
    76. 

  76.         az *= recipNorm;
    77. 

  77. 

  78.         // Normalise magnetometer measurement
    79. 

  79.         recipNorm = invSqrt(mx * mx + my * my + mz * mz);
    80. 

  80.         mx *= recipNorm;
    81. 

  81.         my *= recipNorm;
    82. 

  82.         mz *= recipNorm;
    83. 

  83. 

  84.         // Auxiliary variables to avoid repeated arithmetic
    85. 

  85.         _2q0mx = 2.0f * q[0] * mx;
    86. 

  86.         _2q0my = 2.0f * q[0] * my;
    87. 

  87.         _2q0mz = 2.0f * q[0] * mz;
    88. 

  88.         _2q1mx = 2.0f * q[1] * mx;
    89. 

  89.         _2q0 = 2.0f * q[0];
    90. 

  90.         _2q1 = 2.0f * q[1];
    91. 

  91.         _2q2 = 2.0f * q[2];
    92. 

  92.         _2q3 = 2.0f * q[3];
    93. 

  93.         _2q0q2 = 2.0f * q[0] * q[2];
    94. 

  94.         _2q2q3 = 2.0f * q[2] * q[3];
    95. 

  95.         q0q0 = q[0] * q[0];
    96. 

  96.         q0q1 = q[0] * q[1];
    97. 

  97.         q0q2 = q[0] * q[2];
    98. 

  98.         q0q3 = q[0] * q[3];
    99. 

  99.         q1q1 = q[1] * q[1];
    100. 

  100.         q1q2 = q[1] * q[2];
    101. 

  101.         q1q3 = q[1] * q[3];
    102. 

  102.         q2q2 = q[2] * q[2];
    103. 

  103.         q2q3 = q[2] * q[3];
    104. 

  104.         q3q3 = q[3] * q[3];
    105. 

  105. 

  106.         // Reference direction of Earth's magnetic field
    107. 

  107.         hx = mx * q0q0 - _2q0my * q[3] + _2q0mz * q[2] + mx * q1q1 + _2q1 * my * q[2]
    108. 

  108.                 + _2q1 * mz * q[3] - mx * q2q2 - mx * q3q3;
    109. 

  109.         hy = _2q0mx * q[3] + my * q0q0 - _2q0mz * q[1] + _2q1mx * q[2] - my * q1q1
    110. 

  110.                 + my * q2q2 + _2q2 * mz * q[3] - my * q3q3;
    111. 

  111.         _2bx = sqrt(hx * hx + hy * hy);
    112. 

  112.         _2bz = -_2q0mx * q[2] + _2q0my * q[1] + mz * q0q0 + _2q1mx * q[3] - mz * q1q1
    113. 

  113.                 + _2q2 * my * q[3] - mz * q2q2 + mz * q3q3;
    114. 

  114.         _4bx = 2.0f * _2bx;
    115. 

  115.         _4bz = 2.0f * _2bz;
    116. 

  116. 

  117.         // Gradient decent algorithm corrective step
    118. 

  118.         s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax)
    119. 

  119.                 + _2q1 * (2.0f * q0q1 + _2q2q3 - ay)
    120. 

  120.                 - _2bz * q[2]
    121. 

  121.                         * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2)
    122. 

  122.                                 - mx)
    123. 

  123.                 + (-_2bx * q[3] + _2bz * q[1])
    124. 

  124.                         * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my)
    125. 

  125.                 + _2bx * q[2]
    126. 

  126.                         * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2)
    127. 

  127.                                 - mz);
    128. 

  128.         s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax)
    129. 

  129.                 + _2q0 * (2.0f * q0q1 + _2q2q3 - ay)
    130. 

  130.                 - 4.0f * q[1] * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az)
    131. 

  131.                 + _2bz * q[3]
    132. 

  132.                         * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2)
    133. 

  133.                                 - mx)
    134. 

  134.                 + (_2bx * q[2] + _2bz * q[0])
    135. 

  135.                         * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my)
    136. 

  136.                 + (_2bx * q[3] - _4bz * q[1])
    137. 

  137.                         * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2)
    138. 

  138.                                 - mz);
    139. 

  139.         s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax)
    140. 

  140.                 + _2q3 * (2.0f * q0q1 + _2q2q3 - ay)
    141. 

  141.                 - 4.0f * q[2] * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az)
    142. 

  142.                 + (-_4bx * q[2] - _2bz * q[0])
    143. 

  143.                         * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2)
    144. 

  144.                                 - mx)
    145. 

  145.                 + (_2bx * q[1] + _2bz * q[3])
    146. 

  146.                         * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my)
    147. 

  147.                 + (_2bx * q[0] - _4bz * q[2])
    148. 

  148.                         * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2)
    149. 

  149.                                 - mz);
    150. 

  150.         s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax)
    151. 

  151.                 + _2q2 * (2.0f * q0q1 + _2q2q3 - ay)
    152. 

  152.                 + (-_4bx * q[3] + _2bz * q[1])
    153. 

  153.                         * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2)
    154. 

  154.                                 - mx)
    155. 

  155.                 + (-_2bx * q[0] + _2bz * q[2])
    156. 

  156.                         * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my)
    157. 

  157.                 + _2bx * q[1]
    158. 

  158.                         * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2)
    159. 

  159.                                 - mz);
    160. 

  160.         recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
    161. 

  161.         s0 *= recipNorm;
    162. 

  162.         s1 *= recipNorm;
    163. 

  163.         s2 *= recipNorm;
    164. 

  164.         s3 *= recipNorm;
    165. 

  165. 

  166.         // Apply feedback step
    167. 

  167.         qDot1 -= beta * s0;
    168. 

  168.         qDot2 -= beta * s1;
    169. 

  169.         qDot3 -= beta * s2;
    170. 

  170.         qDot4 -= beta * s3;
    171. 

  171.     }
    172. 

  172. 

  173.     // Integrate rate of change of quaternion to yield quaternion
    174. 

  174.     q[0] += qDot1 * (1.0f / sampleFreq);
    175. 

  175.     q[1] += qDot2 * (1.0f / sampleFreq);
    176. 

  176.     q[2] += qDot3 * (1.0f / sampleFreq);
    177. 

  177.     q[3] += qDot4 * (1.0f / sampleFreq);
    178. 

  178. 

  179.     // Normalise quaternion
    180. 

  180.     recipNorm = invSqrt(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);
    181. 

  181.     q[0] *= recipNorm;
    182. 

  182.     q[1] *= recipNorm;
    183. 

  183.     q[2] *= recipNorm;
    184. 

  184.     q[3] *= recipNorm;
    185. 

  185. }
    186. 

  186. 

  187. //---------------------------------------------------------------------------------------------------
    188. 

  188. // IMU algorithm update
    189. 

  189. 

  190. void MadgwickAHRSupdateIMU(float gx, float gy, float gz,
    191. 

  191.                            float ax, float ay, float az) {
    192. 

  192.     float recipNorm;
    193. 

  193.     float s0, s1, s2, s3;
    194. 

  194.     float qDot1, qDot2, qDot3, qDot4;
    195. 

  195.     float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2, _8q1, _8q2, q0q0, q1q1,
    196. 

  196.             q2q2, q3q3;
    197. 

  197. 

  198.     // Rate of change of quaternion from gyroscope
    199. 

  199.     qDot1 = 0.5f * (-q[1] * gx - q[2] * gy - q[3] * gz);
    200. 

  200.     qDot2 = 0.5f * (q[0] * gx + q[2] * gz - q[3] * gy);
    201. 

  201.     qDot3 = 0.5f * (q[0] * gy - q[1] * gz + q[3] * gx);
    202. 

  202.     qDot4 = 0.5f * (q[0] * gz + q[1] * gy - q[2] * gx);
    203. 

  203. 

  204.     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
    205. 

  205.     if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
    206. 

  206. 

  207.         // Normalise accelerometer measurement
    208. 

  208.         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
    209. 

  209.         ax *= recipNorm;
    210. 

  210.         ay *= recipNorm;
    211. 

  211.         az *= recipNorm;
    212. 

  212. 

  213.         // Auxiliary variables to avoid repeated arithmetic
    214. 

  214.         _2q0 = 2.0f * q[0];
    215. 

  215.         _2q1 = 2.0f * q[1];
    216. 

  216.         _2q2 = 2.0f * q[2];
    217. 

  217.         _2q3 = 2.0f * q[3];
    218. 

  218.         _4q0 = 4.0f * q[0];
    219. 

  219.         _4q1 = 4.0f * q[1];
    220. 

  220.         _4q2 = 4.0f * q[2];
    221. 

  221.         _8q1 = 8.0f * q[1];
    222. 

  222.         _8q2 = 8.0f * q[2];
    223. 

  223.         q0q0 = q[0] * q[0];
    224. 

  224.         q1q1 = q[1] * q[1];
    225. 

  225.         q2q2 = q[2] * q[2];
    226. 

  226.         q3q3 = q[3] * q[3];
    227. 

  227. 

  228.         // Gradient decent algorithm corrective step
    229. 

  229.         s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
    230. 

  230.         s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q[1] - _2q0 * ay - _4q1
    231. 

  231.                 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
    232. 

  232.         s2 = 4.0f * q0q0 * q[2] + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2
    233. 

  233.                 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
    234. 

  234.         s3 = 4.0f * q1q1 * q[3] - _2q1 * ax + 4.0f * q2q2 * q[3] - _2q2 * ay;
    235. 

  235.         recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
    236. 

  236.         s0 *= recipNorm;
    237. 

  237.         s1 *= recipNorm;
    238. 

  238.         s2 *= recipNorm;
    239. 

  239.         s3 *= recipNorm;
    240. 

  240. 

  241.         // Apply feedback step
    242. 

  242.         qDot1 -= beta * s0;
    243. 

  243.         qDot2 -= beta * s1;
    244. 

  244.         qDot3 -= beta * s2;
    245. 

  245.         qDot4 -= beta * s3;
    246. 

  246.     }
    247. 

  247. 

  248.     // Integrate rate of change of quaternion to yield quaternion
    249. 

  249.     q[0] += qDot1 * (1.0f / sampleFreq);
    250. 

  250.     q[1] += qDot2 * (1.0f / sampleFreq);
    251. 

  251.     q[2] += qDot3 * (1.0f / sampleFreq);
    252. 

  252.     q[3] += qDot4 * (1.0f / sampleFreq);
    253. 

  253. 

  254.     // Normalise quaternion
    255. 

  255.     recipNorm = invSqrt(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);
    256. 

  256.     q[0] *= recipNorm;
    257. 

  257.     q[1] *= recipNorm;
    258. 

  258.     q[2] *= recipNorm;
    259. 

  259.     q[3] *= recipNorm;
    260. 

  260. }
    261. 

  261. 

  262. //---------------------------------------------------------------------------------------------------
    263. 

  263. // Fast inverse square-root
    264. 

  264. // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
    265. 

  265. 

  266. float invSqrt(float x) {
    267. 

  267.     float halfx = 0.5f * x;
    268. 

  268.     float y = x;
    269. 

  269.     long i = *(long*) &y;
    270. 

  270.     i = 0x5f3759df - (i >> 1);
    271. 

  271.     y = *(float*) &i;
    272. 

  272.     y = y * (1.5f - (halfx * y * y));
    273. 

  273.     return y;
    274. 

  274. }
    275. 

  275. 

  276. //====================================================================================================
    277. 

  277. // END OF CODE
    278. 

  278. //====================================================================================================
    279.