Diff: ahrs.cpp

Revision:

0:efb1550773f1

Child:

1:8459e28d77a1

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ahrs.cpp	Fri Mar 19 21:59:25 2021 +0000
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+// Implementation of Sebastian Madgwick's "...efficient orientation filter
+// for... inertial/magnetic sensor arrays"
+// (see http://www.x-io.co.uk/category/open-source/ for examples & more details)
+// which fuses acceleration, rotation rate, and magnetic moments to produce a
+// quaternion-based estimate of absolute device orientation -- which can be
+// converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc.
+// The performance of the orientation filter is at least as good as conventional
+// Kalman-based filtering algorithms but is much less computationally
+// intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz!
+
+#include "AHRSAlgorithms.h"
+
+// These are the free parameters in the Mahony filter and fusion scheme, Kp
+// for proportional feedback, Ki for integral
+#define Kp 2.0f * 5.0f
+#define Ki 0.0f
+
+static float GyroMeasError = PI * (40.0f / 180.0f);
+// gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
+static float GyroMeasDrift = PI * (0.0f  / 180.0f);
+// There is a tradeoff in the beta parameter between accuracy and response
+// speed. In the original Madgwick study, beta of 0.041 (corresponding to
+// GyroMeasError of 2.7 degrees/s) was found to give optimal accuracy.
+// However, with this value, the LSM9SD0 response time is about 10 seconds
+// to a stable initial quaternion. Subsequent changes also require a
+// longish lag time to a stable output, not fast enough for a quadcopter or
+// robot car! By increasing beta (GyroMeasError) by about a factor of
+// fifteen, the response time constant is reduced to ~2 sec. I haven't
+// noticed any reduction in solution accuracy. This is essentially the I
+// coefficient in a PID control sense; the bigger the feedback coefficient,
+// the faster the solution converges, usually at the expense of accuracy.
+// In any case, this is the free parameter in the Madgwick filtering and
+// fusion scheme.
+static float beta = sqrt(3.0f / 4.0f) * GyroMeasError;   // Compute beta
+// Compute zeta, the other free parameter in the Madgwick scheme usually
+// set to a small or zero value
+static float zeta = sqrt(3.0f / 4.0f) * GyroMeasDrift;
+
+// Vector to hold integral error for Mahony method
+static float eInt[3] = {0.0f, 0.0f, 0.0f};
+// Vector to hold quaternion
+static float q[4] = {1.0f, 0.0f, 0.0f, 0.0f};
+
+void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz, float deltat)
+{
+  // short name local variable for readability
+  float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];
+  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 = 2.0f * q1;
+  float _2q2 = 2.0f * q2;
+  float _2q3 = 2.0f * q3;
+  float _2q4 = 2.0f * q4;
+  float _2q1q3 = 2.0f * q1 * q3;
+  float _2q3q4 = 2.0f * 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 = sqrt(ax * ax + ay * ay + az * az);
+  if (norm == 0.0f) return; // handle NaN
+  norm = 1.0f/norm;
+  ax *= norm;
+  ay *= norm;
+  az *= norm;
+
+  // Normalise magnetometer measurement
+  norm = sqrt(mx * mx + my * my + mz * mz);
+  if (norm == 0.0f) return; // handle NaN
+  norm = 1.0f/norm;
+  mx *= norm;
+  my *= norm;
+  mz *= norm;
+
+  // Reference direction of Earth's magnetic field
+  _2q1mx = 2.0f * q1 * mx;
+  _2q1my = 2.0f * q1 * my;
+  _2q1mz = 2.0f * q1 * mz;
+  _2q2mx = 2.0f * 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 = sqrt(hx * hx + hy * hy);
+  _2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
+  _4bx = 2.0f * _2bx;
+  _4bz = 2.0f * _2bz;
+
+  // Gradient decent algorithm corrective step
+  s1 = -_2q3 * (2.0f * q2q4 - _2q1q3 - ax) + _2q2 * (2.0f * 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 * (2.0f * q2q4 - _2q1q3 - ax) + _2q1 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q2 * (1.0f - 2.0f * q2q2 - 2.0f * 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 * (2.0f * q2q4 - _2q1q3 - ax) + _2q4 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q3 * (1.0f - 2.0f * q2q2 - 2.0f * 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 * (2.0f * q2q4 - _2q1q3 - ax) + _2q3 * (2.0f * 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 = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4);    // normalise step magnitude
+  norm = 1.0f/norm;
+  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 * deltat;
+  q2 += qDot2 * deltat;
+  q3 += qDot3 * deltat;
+  q4 += qDot4 * deltat;
+  norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);    // normalise quaternion
+  norm = 1.0f/norm;
+  q[0] = q1 * norm;
+  q[1] = q2 * norm;
+  q[2] = q3 * norm;
+  q[3] = q4 * norm;
+}
+
+
+
+// Similar to Madgwick scheme but uses proportional and integral filtering on
+// the error between estimated reference vectors and measured ones.
+void MahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz, float deltat)
+{
+  // short name local variable for readability
+  float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];
+  float norm;
+  float hx, hy, bx, bz;
+  float vx, vy, vz, wx, wy, wz;
+  float ex, ey, ez;
+  float pa, pb, pc;
+
+  // Auxiliary variables to avoid repeated arithmetic
+  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 = sqrt(ax * ax + ay * ay + az * az);
+  if (norm == 0.0f) return; // Handle NaN
+  norm = 1.0f / norm;       // Use reciprocal for division
+  ax *= norm;
+  ay *= norm;
+  az *= norm;
+
+  // Normalise magnetometer measurement
+  norm = sqrt(mx * mx + my * my + mz * mz);
+  if (norm == 0.0f) return; // Handle NaN
+  norm = 1.0f / norm;       // Use reciprocal for division
+  mx *= norm;
+  my *= norm;
+  mz *= norm;
+
+  // Reference direction of Earth's magnetic field
+  hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3);
+  hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2);
+  bx = sqrt((hx * hx) + (hy * hy));
+  bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3);
+
+  // Estimated direction of gravity and magnetic field
+  vx = 2.0f * (q2q4 - q1q3);
+  vy = 2.0f * (q1q2 + q3q4);
+  vz = q1q1 - q2q2 - q3q3 + q4q4;
+  wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3);
+  wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4);
+  wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3);
+
+  // Error is cross product between estimated direction and measured direction of gravity
+  ex = (ay * vz - az * vy) + (my * wz - mz * wy);
+  ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
+  ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
+  if (Ki > 0.0f)
+  {
+    eInt[0] += ex;      // accumulate integral error
+    eInt[1] += ey;
+    eInt[2] += ez;
+  }
+  else
+  {
+    eInt[0] = 0.0f;     // prevent integral wind up
+    eInt[1] = 0.0f;
+    eInt[2] = 0.0f;
+  }
+
+  // Apply feedback terms
+  gx = gx + Kp * ex + Ki * eInt[0];
+  gy = gy + Kp * ey + Ki * eInt[1];
+  gz = gz + Kp * ez + Ki * eInt[2];
+ 
+  // Integrate rate of change of quaternion
+  pa = q2;
+  pb = q3;
+  pc = q4;
+  q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * deltat);
+  q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * deltat);
+  q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * deltat);
+  q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * deltat);
+
+  // Normalise quaternion
+  norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
+  norm = 1.0f / norm;
+  q[0] = q1 * norm;
+  q[1] = q2 * norm;
+  q[2] = q3 * norm;
+  q[3] = q4 * norm;
+}
+
+const float * getQ () { return q; }
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