jaewon lee
4180 final project
Dependencies: LSM9DS0 USBDevice mbed
Diff: Quaternion/Quaternion.cpp
- Revision:
- 0:ebbc3cd3a61e
diff -r 000000000000 -r ebbc3cd3a61e Quaternion/Quaternion.cpp
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Quaternion/Quaternion.cpp Sat Dec 05 18:39:33 2015 +0000
@@ -0,0 +1,302 @@
+
+#include "Quaternion.h"
+#include "mbed.h"
+#define M_PI 3.14159265
+
+Timer t;
+/**
+* Default constructor.
+**/
+Quaternion::Quaternion() {
+ q0 = 1.0f;
+ q1 = 0.0f;
+ q2 = 0.0f;
+ q3 = 0.0f;
+ twoKp = twoKpDef;
+ twoKi = twoKiDef;
+ sampleFreq = 0.0f;
+ lastUpdate = 0L;
+ now = 0L;
+ integralFBx = 0.0f;
+ integralFBy = 0.0f;
+ integralFBz = 0.0f;
+ t.start();
+}
+
+/**
+* Updates the sample frequency based on the elapsed time.
+**/
+void Quaternion::updateSampleFrequency() {
+ now = t.read();
+ sampleFreq = 1.0 / ((now - lastUpdate));
+ lastUpdate = now;
+}
+/**
+* Returns the quaternion representation of the orientation.
+**/
+void Quaternion::getQ(float * q) {
+ q[0] = q0;
+ q[1] = q1;
+ q[2] = q2;
+ q[3] = q3;
+}
+
+/**
+* Gets the linear acceleration by estimating gravity and then subtracting it. All accelerations
+* need to be scaled to 1 g. So if at 1 g your accelerometer reads 245, divide it by 245 before passing it
+* to this function.
+* @param *linearAccel, pointer to float array for linear accelerations,
+* @param ax, the scaled acceleration in the x direction.
+* @param ay, the scaled acceleration in the y direction.
+* @param az, the scaled acceleration in the z direction.
+**/
+void Quaternion::getLinearAcceleration(float * linearAccel, float ax, float ay, float az) {
+
+ float gravity[3];
+ getGravity(gravity);
+
+
+
+ float xwog = ax - gravity[0];
+ float ywog = ay - gravity[1];
+ float zwog = az - gravity[2];
+
+ linearAccel[0] = xwog * 9.8;
+ linearAccel[1] = ywog * 9.8;
+ linearAccel[2] = zwog * 9.8;
+}
+
+/**
+* Returns the euler angles psi, theta and phi.
+**/
+void Quaternion::getEulerAngles(float * angles) {
+ angles[0] = atan2(2 * q1 * q2- 2 * q0 * q3, 2 * q0*q0 + 2 * q1 * q1 - 1) * 180/M_PI; // psi
+ angles[1] = -asin(2 * q1 * q3 + 2 * q0 * q2) * 180/M_PI; // theta
+ angles[2] = atan2(2 * q2 * q3 - 2 * q0 * q1, 2 * q0 * q0 + 2 * q3 * q3 - 1) * 180/M_PI; // phi
+}
+
+/**
+* Returns the yaw pitch and roll of the device.
+**/
+void Quaternion::getYawPitchRoll(double * ypr) {
+
+ ypr[0] = atan2(double(2*q1*q2 + 2*q0*q3), double(q0*q0 + q1*q1 - q2*q2 - q3*q3)) * 180/M_PI; //yaw
+ ypr[1] = -asin(2*q0*q2 - 2*q1*q3) * 180/M_PI; // pitch
+ ypr[2] = -atan2(2*q2*q3 + 2*q0*q1, -q0*q0 + q1*q1 + q2*q2 - q3*q3) * 180/M_PI; //roll
+
+}
+/**
+* Gets an estimation of gravity based on quaternion orientation representation.
+**/
+void Quaternion::getGravity(float * gravity) {
+ float q[4];
+ getQ(q);
+ gravity[0] = 2 * (q[1] * q[3] - q[0] *q[2]);
+ gravity[1] = 2 * (q[0] * q[1] + q[2] * q[3]);
+ gravity[2] = q[0] * q[0] - q[1] * q[1] - q[2] * q[2] + q[3] * q[3];
+}
+
+/**
+* Calculates the quaternion representation based on a 6DOF sensor.
+* @param gx, the rotation about the x axis in rad/sec
+* @param gy, the rotation about the y axis in rad/sec
+* @param gz, the rotation about the z axis in rad/sec
+* @param ax, the raw acceleration in the x direction.
+* @param ay, the raw acceleration in the y direction.
+* @param az, the raw acceleration in the z direction.
+**/
+void Quaternion::update6DOF(float gx, float gy, float gz, float ax, float ay, float az) {
+ updateSampleFrequency();
+ float recipNorm;
+ float halfvx, halfvy, halfvz;
+ float halfex, halfey, halfez;
+ float qa, qb, qc;
+
+ // 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 = invSqrt(ax * ax + ay * ay + az * az);
+ 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 - 0.5f + 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) {
+ integralFBx += twoKi * halfex * (1.0f / sampleFreq); // integral error scaled by Ki
+ integralFBy += twoKi * halfey * (1.0f / sampleFreq);
+ integralFBz += twoKi * halfez * (1.0f / sampleFreq);
+ 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 * (1.0f / sampleFreq)); // pre-multiply common factors
+ gy *= (0.5f * (1.0f / sampleFreq));
+ gz *= (0.5f * (1.0f / sampleFreq));
+ 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 = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+ q0 *= recipNorm;
+ q1 *= recipNorm;
+ q2 *= recipNorm;
+ q3 *= recipNorm;
+
+}
+
+/**
+* Calculates the quaternion representation based on a 9DOF sensor.
+* @param gx, the rotation about the x axis in rad/sec
+* @param gy, the rotation about the y axis in rad/sec
+* @param gz, the rotation about the z axis in rad/sec
+* @param ax, the raw acceleration in the x direction.
+* @param ay, the raw acceleration in the y direction.
+* @param az, the raw acceleration in the z direction.
+* @param mx, the raw magnometer heading in the x direction.
+* @param my, the raw magnometer heading in the y direction.
+* @param mz, the raw magnometer heading in the z direction.
+**/
+void Quaternion::update9DOF(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
+ //update the frequency first.
+ updateSampleFrequency();
+ float recipNorm;
+ float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
+ float hx, hy, bx, bz;
+ float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
+ float halfex, halfey, halfez;
+ 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)) {
+ update6DOF(gx, gy, gz, ax, ay, az);
+ return;
+ }
+
+ // 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 = invSqrt(ax * ax + ay * ay + az * az);
+ ax *= recipNorm;
+ ay *= recipNorm;
+ az *= recipNorm;
+
+ // Normalise magnetometer measurement
+ recipNorm = invSqrt(mx * mx + my * my + mz * mz);
+ mx *= recipNorm;
+ my *= recipNorm;
+ mz *= recipNorm;
+
+ // 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;
+
+ // 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 = sqrt(hx * hx + hy * hy);
+ bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2));
+
+ // 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) {
+ integralFBx += twoKi * halfex * (1.0f / sampleFreq); // integral error scaled by Ki
+ integralFBy += twoKi * halfey * (1.0f / sampleFreq);
+ integralFBz += twoKi * halfez * (1.0f / sampleFreq);
+ 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 * (1.0f / sampleFreq)); // pre-multiply common factors
+ gy *= (0.5f * (1.0f / sampleFreq));
+ gz *= (0.5f * (1.0f / sampleFreq));
+ 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 = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+ q0 *= recipNorm;
+ q1 *= recipNorm;
+ q2 *= recipNorm;
+ q3 *= recipNorm;
+}
+
+/**
+* Super fast inverted square root.
+**/
+float Quaternion::invSqrt(float x) {
+ float halfx = 0.5f * x;
+ float y = x;
+ long i = *(long*)&y;
+ i = 0x5f3759df - (i>>1);
+ y = *(float*)&i;
+ y = y * (1.5f - (halfx * y * y));
+ return y;
+}