Diff: mavlink_conversions.h

Revision:

0:bb2cacd02294

Child:

1:7e9af9a921f7

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/mavlink_conversions.h	Fri Jan 20 13:20:58 2017 +0000
@@ -0,0 +1,212 @@
+#ifndef  _MAVLINK_CONVERSIONS_H_
+#define  _MAVLINK_CONVERSIONS_H_
+
+/* enable math defines on Windows */
+#ifdef _MSC_VER
+#ifndef _USE_MATH_DEFINES
+#define _USE_MATH_DEFINES
+#endif
+#endif
+#include <math.h>
+
+#ifndef M_PI_2
+    #define M_PI_2 ((float)asin(1))
+#endif
+
+/**
+ * @file mavlink_conversions.h
+ *
+ * These conversion functions follow the NASA rotation standards definition file
+ * available online.
+ *
+ * Their intent is to lower the barrier for MAVLink adopters to use gimbal-lock free
+ * (both rotation matrices, sometimes called DCM, and quaternions are gimbal-lock free)
+ * rotation representations. Euler angles (roll, pitch, yaw) will be phased out of the
+ * protocol as widely as possible.
+ *
+ * @author James Goppert
+ * @author Thomas Gubler <thomasgubler@gmail.com>
+ */
+
+
+/**
+ * Converts a quaternion to a rotation matrix
+ *
+ * @param quaternion a [w, x, y, z] ordered quaternion (null-rotation being 1 0 0 0)
+ * @param dcm a 3x3 rotation matrix
+ */
+MAVLINK_HELPER void mavlink_quaternion_to_dcm(const float quaternion[4], float dcm[3][3])
+{
+    double a = quaternion[0];
+    double b = quaternion[1];
+    double c = quaternion[2];
+    double d = quaternion[3];
+    double aSq = a * a;
+    double bSq = b * b;
+    double cSq = c * c;
+    double dSq = d * d;
+    dcm[0][0] = aSq + bSq - cSq - dSq;
+    dcm[0][1] = 2 * (b * c - a * d);
+    dcm[0][2] = 2 * (a * c + b * d);
+    dcm[1][0] = 2 * (b * c + a * d);
+    dcm[1][1] = aSq - bSq + cSq - dSq;
+    dcm[1][2] = 2 * (c * d - a * b);
+    dcm[2][0] = 2 * (b * d - a * c);
+    dcm[2][1] = 2 * (a * b + c * d);
+    dcm[2][2] = aSq - bSq - cSq + dSq;
+}
+
+
+/**
+ * Converts a rotation matrix to euler angles
+ *
+ * @param dcm a 3x3 rotation matrix
+ * @param roll the roll angle in radians
+ * @param pitch the pitch angle in radians
+ * @param yaw the yaw angle in radians
+ */
+MAVLINK_HELPER void mavlink_dcm_to_euler(const float dcm[3][3], float* roll, float* pitch, float* yaw)
+{
+    float phi, theta, psi;
+    theta = asin(-dcm[2][0]);
+
+    if (fabsf(theta - (float)M_PI_2) < 1.0e-3f) {
+        phi = 0.0f;
+        psi = (atan2f(dcm[1][2] - dcm[0][1],
+                dcm[0][2] + dcm[1][1]) + phi);
+
+    } else if (fabsf(theta + (float)M_PI_2) < 1.0e-3f) {
+        phi = 0.0f;
+        psi = atan2f(dcm[1][2] - dcm[0][1],
+                  dcm[0][2] + dcm[1][1] - phi);
+
+    } else {
+        phi = atan2f(dcm[2][1], dcm[2][2]);
+        psi = atan2f(dcm[1][0], dcm[0][0]);
+    }
+
+    *roll = phi;
+    *pitch = theta;
+    *yaw = psi;
+}
+
+
+/**
+ * Converts a quaternion to euler angles
+ *
+ * @param quaternion a [w, x, y, z] ordered quaternion (null-rotation being 1 0 0 0)
+ * @param roll the roll angle in radians
+ * @param pitch the pitch angle in radians
+ * @param yaw the yaw angle in radians
+ */
+MAVLINK_HELPER void mavlink_quaternion_to_euler(const float quaternion[4], float* roll, float* pitch, float* yaw)
+{
+    float dcm[3][3];
+    mavlink_quaternion_to_dcm(quaternion, dcm);
+    mavlink_dcm_to_euler((const float(*)[3])dcm, roll, pitch, yaw);
+}
+
+
+/**
+ * Converts euler angles to a quaternion
+ *
+ * @param roll the roll angle in radians
+ * @param pitch the pitch angle in radians
+ * @param yaw the yaw angle in radians
+ * @param quaternion a [w, x, y, z] ordered quaternion (null-rotation being 1 0 0 0)
+ */
+MAVLINK_HELPER void mavlink_euler_to_quaternion(float roll, float pitch, float yaw, float quaternion[4])
+{
+    float cosPhi_2 = cosf(roll / 2);
+    float sinPhi_2 = sinf(roll / 2);
+    float cosTheta_2 = cosf(pitch / 2);
+    float sinTheta_2 = sinf(pitch / 2);
+    float cosPsi_2 = cosf(yaw / 2);
+    float sinPsi_2 = sinf(yaw / 2);
+    quaternion[0] = (cosPhi_2 * cosTheta_2 * cosPsi_2 +
+            sinPhi_2 * sinTheta_2 * sinPsi_2);
+    quaternion[1] = (sinPhi_2 * cosTheta_2 * cosPsi_2 -
+            cosPhi_2 * sinTheta_2 * sinPsi_2);
+    quaternion[2] = (cosPhi_2 * sinTheta_2 * cosPsi_2 +
+            sinPhi_2 * cosTheta_2 * sinPsi_2);
+    quaternion[3] = (cosPhi_2 * cosTheta_2 * sinPsi_2 -
+            sinPhi_2 * sinTheta_2 * cosPsi_2);
+}
+
+
+/**
+ * Converts a rotation matrix to a quaternion
+ * Reference:
+ *  - Shoemake, Quaternions,
+ *  http://www.cs.ucr.edu/~vbz/resources/quatut.pdf
+ *
+ * @param dcm a 3x3 rotation matrix
+ * @param quaternion a [w, x, y, z] ordered quaternion (null-rotation being 1 0 0 0)
+ */
+MAVLINK_HELPER void mavlink_dcm_to_quaternion(const float dcm[3][3], float quaternion[4])
+{
+    float tr = dcm[0][0] + dcm[1][1] + dcm[2][2];
+    if (tr > 0.0f) {
+        float s = sqrtf(tr + 1.0f);
+        quaternion[0] = s * 0.5f;
+        s = 0.5f / s;
+        quaternion[1] = (dcm[2][1] - dcm[1][2]) * s;
+        quaternion[2] = (dcm[0][2] - dcm[2][0]) * s;
+        quaternion[3] = (dcm[1][0] - dcm[0][1]) * s;
+    } else {
+        /* Find maximum diagonal element in dcm
+         * store index in dcm_i */
+        int dcm_i = 0;
+        int i;
+        for (i = 1; i < 3; i++) {
+            if (dcm[i][i] > dcm[dcm_i][dcm_i]) {
+                dcm_i = i;
+            }
+        }
+
+        int dcm_j = (dcm_i + 1) % 3;
+        int dcm_k = (dcm_i + 2) % 3;
+
+        float s = sqrtf((dcm[dcm_i][dcm_i] - dcm[dcm_j][dcm_j] -
+                    dcm[dcm_k][dcm_k]) + 1.0f);
+        quaternion[dcm_i + 1] = s * 0.5f;
+        s = 0.5f / s;
+        quaternion[dcm_j + 1] = (dcm[dcm_i][dcm_j] + dcm[dcm_j][dcm_i]) * s;
+        quaternion[dcm_k + 1] = (dcm[dcm_k][dcm_i] + dcm[dcm_i][dcm_k]) * s;
+        quaternion[0] = (dcm[dcm_k][dcm_j] - dcm[dcm_j][dcm_k]) * s;
+    }
+}
+
+
+/**
+ * Converts euler angles to a rotation matrix
+ *
+ * @param roll the roll angle in radians
+ * @param pitch the pitch angle in radians
+ * @param yaw the yaw angle in radians
+ * @param dcm a 3x3 rotation matrix
+ */
+MAVLINK_HELPER void mavlink_euler_to_dcm(float roll, float pitch, float yaw, float dcm[3][3])
+{
+    float cosPhi = cosf(roll);
+    float sinPhi = sinf(roll);
+    float cosThe = cosf(pitch);
+    float sinThe = sinf(pitch);
+    float cosPsi = cosf(yaw);
+    float sinPsi = sinf(yaw);
+
+    dcm[0][0] = cosThe * cosPsi;
+    dcm[0][1] = -cosPhi * sinPsi + sinPhi * sinThe * cosPsi;
+    dcm[0][2] = sinPhi * sinPsi + cosPhi * sinThe * cosPsi;
+
+    dcm[1][0] = cosThe * sinPsi;
+    dcm[1][1] = cosPhi * cosPsi + sinPhi * sinThe * sinPsi;
+    dcm[1][2] = -sinPhi * cosPsi + cosPhi * sinThe * sinPsi;
+
+    dcm[2][0] = -sinThe;
+    dcm[2][1] = sinPhi * cosThe;
+    dcm[2][2] = cosPhi * cosThe;
+}
+
+#endif
+