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LibrePilot/flight/Libraries/CoordinateConversions.c

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/**
******************************************************************************
*
* @file CoordinateConversions.c
* @author The OpenPilot Team, http://www.openpilot.org Copyright (C) 2010.
* @brief General conversions with different coordinate systems.
* - all angles in deg
* - distances in meters
* - altitude above WGS-84 elipsoid
*
* @see The GNU Public License (GPL) Version 3
*
*****************************************************************************/
/*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include <math.h>
#include <stdint.h>
#include "CoordinateConversions.h"
#define RAD2DEG (180.0/M_PI)
#define DEG2RAD (M_PI/180.0)
// ****** convert Lat,Lon,Alt to ECEF ************
void LLA2ECEF(double LLA[3], double ECEF[3])
{
const double a = 6378137.0; // Equatorial Radius
const double e = 8.1819190842622e-2; // Eccentricity
double sinLat, sinLon, cosLat, cosLon;
double N;
sinLat = sin(DEG2RAD * LLA[0]);
sinLon = sin(DEG2RAD * LLA[1]);
cosLat = cos(DEG2RAD * LLA[0]);
cosLon = cos(DEG2RAD * LLA[1]);
N = a / sqrt(1.0 - e * e * sinLat * sinLat); //prime vertical radius of curvature
ECEF[0] = (N + LLA[2]) * cosLat * cosLon;
ECEF[1] = (N + LLA[2]) * cosLat * sinLon;
ECEF[2] = ((1 - e * e) * N + LLA[2]) * sinLat;
}
// ****** convert ECEF to Lat,Lon,Alt (ITERATIVE!) *********
uint16_t ECEF2LLA(double ECEF[3], double LLA[3])
{
/**
* LLA parameter is used to prime the iteration.
* A position within 1 meter of the specified LLA
* will be calculated within at most 3 iterations.
* If unknown: Call with any valid LLA coordinate
* will compute within at most 5 iterations.
* Suggestion: [0,0,0]
**/
const double a = 6378137.0; // Equatorial Radius
const double e = 8.1819190842622e-2; // Eccentricity
double x = ECEF[0], y = ECEF[1], z = ECEF[2];
double Lat, N, NplusH, delta, esLat;
uint16_t iter;
#define MAX_ITER 10 // should not take more than 5 for valid coordinates
#define ACCURACY 1.0e-11 // used to be e-14, but we don't need sub micrometer exact calculations
LLA[1] = RAD2DEG * atan2(y, x);
Lat = DEG2RAD * LLA[0];
esLat = e * sin(Lat);
N = a / sqrt(1 - esLat * esLat);
NplusH = N + LLA[2];
delta = 1;
iter = 0;
while (((delta > ACCURACY) || (delta < -ACCURACY))
&& (iter < MAX_ITER)) {
delta = Lat - atan(z / (sqrt(x * x + y * y) * (1 - (N * e * e / NplusH))));
Lat = Lat - delta;
esLat = e * sin(Lat);
N = a / sqrt(1 - esLat * esLat);
NplusH = sqrt(x * x + y * y) / cos(Lat);
iter += 1;
}
LLA[0] = RAD2DEG * Lat;
LLA[2] = NplusH - N;
return (iter < MAX_ITER);
}
// ****** find ECEF to NED rotation matrix ********
void RneFromLLA(double LLA[3], float Rne[3][3])
{
float sinLat, sinLon, cosLat, cosLon;
sinLat = (float)sin(DEG2RAD * LLA[0]);
sinLon = (float)sin(DEG2RAD * LLA[1]);
cosLat = (float)cos(DEG2RAD * LLA[0]);
cosLon = (float)cos(DEG2RAD * LLA[1]);
Rne[0][0] = -sinLat * cosLon;
Rne[0][1] = -sinLat * sinLon;
Rne[0][2] = cosLat;
Rne[1][0] = -sinLon;
Rne[1][1] = cosLon;
Rne[1][2] = 0;
Rne[2][0] = -cosLat * cosLon;
Rne[2][1] = -cosLat * sinLon;
Rne[2][2] = -sinLat;
}
// ****** find roll, pitch, yaw from quaternion ********
void Quaternion2RPY(const float q[4], float rpy[3])
{
float R13, R11, R12, R23, R33;
float q0s = q[0] * q[0];
float q1s = q[1] * q[1];
float q2s = q[2] * q[2];
float q3s = q[3] * q[3];
R13 = 2 * (q[1] * q[3] - q[0] * q[2]);
R11 = q0s + q1s - q2s - q3s;
R12 = 2 * (q[1] * q[2] + q[0] * q[3]);
R23 = 2 * (q[2] * q[3] + q[0] * q[1]);
R33 = q0s - q1s - q2s + q3s;
rpy[1] = RAD2DEG * asinf(-R13); // pitch always between -pi/2 to pi/2
rpy[2] = RAD2DEG * atan2f(R12, R11);
rpy[0] = RAD2DEG * atan2f(R23, R33);
//TODO: consider the cases where |R13| ~= 1, |pitch| ~= pi/2
}
// ****** find quaternion from roll, pitch, yaw ********
void RPY2Quaternion(const float rpy[3], float q[4])
{
float phi, theta, psi;
float cphi, sphi, ctheta, stheta, cpsi, spsi;
phi = DEG2RAD * rpy[0] / 2;
theta = DEG2RAD * rpy[1] / 2;
psi = DEG2RAD * rpy[2] / 2;
cphi = cosf(phi);
sphi = sinf(phi);
ctheta = cosf(theta);
stheta = sinf(theta);
cpsi = cosf(psi);
spsi = sinf(psi);
q[0] = cphi * ctheta * cpsi + sphi * stheta * spsi;
q[1] = sphi * ctheta * cpsi - cphi * stheta * spsi;
q[2] = cphi * stheta * cpsi + sphi * ctheta * spsi;
q[3] = cphi * ctheta * spsi - sphi * stheta * cpsi;
if (q[0] < 0) { // q0 always positive for uniqueness
q[0] = -q[0];
q[1] = -q[1];
q[2] = -q[2];
q[3] = -q[3];
}
}
//** Find Rbe, that rotates a vector from earth fixed to body frame, from quaternion **
void Quaternion2R(float q[4], float Rbe[3][3])
{
float q0s = q[0] * q[0], q1s = q[1] * q[1], q2s = q[2] * q[2], q3s = q[3] * q[3];
Rbe[0][0] = q0s + q1s - q2s - q3s;
Rbe[0][1] = 2 * (q[1] * q[2] + q[0] * q[3]);
Rbe[0][2] = 2 * (q[1] * q[3] - q[0] * q[2]);
Rbe[1][0] = 2 * (q[1] * q[2] - q[0] * q[3]);
Rbe[1][1] = q0s - q1s + q2s - q3s;
Rbe[1][2] = 2 * (q[2] * q[3] + q[0] * q[1]);
Rbe[2][0] = 2 * (q[1] * q[3] + q[0] * q[2]);
Rbe[2][1] = 2 * (q[2] * q[3] - q[0] * q[1]);
Rbe[2][2] = q0s - q1s - q2s + q3s;
}
// ****** Express LLA in a local NED Base Frame ********
void LLA2Base(double LLA[3], double BaseECEF[3], float Rne[3][3], float NED[3])
{
double ECEF[3];
float diff[3];
LLA2ECEF(LLA, ECEF);
diff[0] = (float)(ECEF[0] - BaseECEF[0]);
diff[1] = (float)(ECEF[1] - BaseECEF[1]);
diff[2] = (float)(ECEF[2] - BaseECEF[2]);
NED[0] = Rne[0][0] * diff[0] + Rne[0][1] * diff[1] + Rne[0][2] * diff[2];
NED[1] = Rne[1][0] * diff[0] + Rne[1][1] * diff[1] + Rne[1][2] * diff[2];
NED[2] = Rne[2][0] * diff[0] + Rne[2][1] * diff[1] + Rne[2][2] * diff[2];
}
// ****** Express ECEF in a local NED Base Frame ********
void ECEF2Base(double ECEF[3], double BaseECEF[3], float Rne[3][3], float NED[3])
{
float diff[3];
diff[0] = (float)(ECEF[0] - BaseECEF[0]);
diff[1] = (float)(ECEF[1] - BaseECEF[1]);
diff[2] = (float)(ECEF[2] - BaseECEF[2]);
NED[0] = Rne[0][0] * diff[0] + Rne[0][1] * diff[1] + Rne[0][2] * diff[2];
NED[1] = Rne[1][0] * diff[0] + Rne[1][1] * diff[1] + Rne[1][2] * diff[2];
NED[2] = Rne[2][0] * diff[0] + Rne[2][1] * diff[1] + Rne[2][2] * diff[2];
}
// ****** convert Rotation Matrix to Quaternion ********
// ****** if R converts from e to b, q is rotation from e to b ****
void R2Quaternion(float R[3][3], float q[4])
{
float m[4], mag;
uint8_t index,i;
m[0] = 1 + R[0][0] + R[1][1] + R[2][2];
m[1] = 1 + R[0][0] - R[1][1] - R[2][2];
m[2] = 1 - R[0][0] + R[1][1] - R[2][2];
m[3] = 1 - R[0][0] - R[1][1] + R[2][2];
// find maximum divisor
index = 0;
mag = m[0];
for (i=1;i<4;i++){
if (m[i] > mag){
mag = m[i];
index = i;
}
}
mag = 2*sqrt(mag);
if (index == 0) {
q[0] = mag/4;
q[1] = (R[1][2]-R[2][1])/mag;
q[2] = (R[2][0]-R[0][2])/mag;
q[3] = (R[0][1]-R[1][0])/mag;
}
else if (index == 1) {
q[1] = mag/4;
q[0] = (R[1][2]-R[2][1])/mag;
q[2] = (R[0][1]+R[1][0])/mag;
q[3] = (R[0][2]+R[2][0])/mag;
}
else if (index == 2) {
q[2] = mag/4;
q[0] = (R[2][0]-R[0][2])/mag;
q[1] = (R[0][1]+R[1][0])/mag;
q[3] = (R[1][2]+R[2][1])/mag;
}
else {
q[3] = mag/4;
q[0] = (R[0][1]-R[1][0])/mag;
q[1] = (R[0][2]+R[2][0])/mag;
q[2] = (R[1][2]+R[2][1])/mag;
}
// q0 positive, i.e. angle between pi and -pi
if (q[0] < 0){
q[0] = -q[0];
q[1] = -q[1];
q[2] = -q[2];
q[3] = -q[3];
}
}
// ****** Rotation Matrix from Two Vector Directions ********
// ****** given two vector directions (v1 and v2) known in two frames (b and e) find Rbe ***
// ****** solution is approximate if can't be exact ***
uint8_t RotFrom2Vectors(const float v1b[3], const float v1e[3], const float v2b[3], const float v2e[3], float Rbe[3][3])
{
float Rib[3][3], Rie[3][3];
float mag;
uint8_t i,j,k;
// identity rotation in case of error
for (i=0;i<3;i++){
for (j=0;j<3;j++)
Rbe[i][j]=0;
Rbe[i][i]=1;
}
// The first rows of rot matrices chosen in direction of v1
mag = VectorMagnitude(v1b);
if (fabs(mag) < 1e-30)
return (-1);
for (i=0;i<3;i++)
Rib[0][i]=v1b[i]/mag;
mag = VectorMagnitude(v1e);
if (fabs(mag) < 1e-30)
return (-1);
for (i=0;i<3;i++)
Rie[0][i]=v1e[i]/mag;
// The second rows of rot matrices chosen in direction of v1xv2
CrossProduct(v1b,v2b,&Rib[1][0]);
mag = VectorMagnitude(&Rib[1][0]);
if (fabs(mag) < 1e-30)
return (-1);
for (i=0;i<3;i++)
Rib[1][i]=Rib[1][i]/mag;
CrossProduct(v1e,v2e,&Rie[1][0]);
mag = VectorMagnitude(&Rie[1][0]);
if (fabs(mag) < 1e-30)
return (-1);
for (i=0;i<3;i++)
Rie[1][i]=Rie[1][i]/mag;
// The third rows of rot matrices are XxY (Row1xRow2)
CrossProduct(&Rib[0][0],&Rib[1][0],&Rib[2][0]);
CrossProduct(&Rie[0][0],&Rie[1][0],&Rie[2][0]);
// Rbe = Rbi*Rie = Rib'*Rie
for (i=0;i<3;i++)
for(j=0;j<3;j++){
Rbe[i][j]=0;
for(k=0;k<3;k++)
Rbe[i][j] += Rib[k][i]*Rie[k][j];
}
return 1;
}
void Rv2Rot(float Rv[3], float R[3][3])
{
// Compute rotation matrix from a rotation vector
// To save .text space, uses Quaternion2R()
float q[4];
float angle = VectorMagnitude(Rv);
if (angle <= 0.00048828125f) {
// angle < sqrt(2*machine_epsilon(float)), so flush cos(x) to 1.0f
q[0] = 1.0f;
// and flush sin(x/2)/x to 0.5
q[1] = 0.5f*Rv[0];
q[2] = 0.5f*Rv[1];
q[3] = 0.5f*Rv[2];
// This prevents division by zero, while retaining full accuracy
}
else {
q[0] = cosf(angle*0.5f);
float scale = sinf(angle*0.5f) / angle;
q[1] = scale*Rv[0];
q[2] = scale*Rv[1];
q[3] = scale*Rv[2];
}
Quaternion2R(q, R);
}
// ****** Vector Cross Product ********
void CrossProduct(const float v1[3], const float v2[3], float result[3])
{
result[0] = v1[1]*v2[2] - v2[1]*v1[2];
result[1] = v2[0]*v1[2] - v1[0]*v2[2];
result[2] = v1[0]*v2[1] - v2[0]*v1[1];
}
// ****** Vector Magnitude ********
float VectorMagnitude(const float v[3])
{
return(sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]));
}
/**
* @brief Compute the inverse of a quaternion
* @param [in][out] q The matrix to invert
*/
void quat_inverse(float q[4])
{
q[1] = -q[1];
q[2] = -q[2];
q[3] = -q[3];
}
/**
* @brief Duplicate a quaternion
* @param[in] q quaternion in
* @param[out] qnew quaternion to copy to
*/
void quat_copy(const float q[4], float qnew[4])
{
qnew[0] = q[0];
qnew[1] = q[1];
qnew[2] = q[2];
qnew[3] = q[3];
}
/**
* @brief Multiply two quaternions into a third
* @param[in] q1 First quaternion
* @param[in] q2 Second quaternion
* @param[out] qout Output quaternion
*/
void quat_mult(const float q1[4], const float q2[4], float qout[4])
{
qout[0] = q1[0]*q2[0] - q1[1]*q2[1] - q1[2]*q2[2] - q1[3]*q2[3];
qout[1] = q1[0]*q2[1] + q1[1]*q2[0] + q1[2]*q2[3] - q1[3]*q2[2];
qout[2] = q1[0]*q2[2] - q1[1]*q2[3] + q1[2]*q2[0] + q1[3]*q2[1];
qout[3] = q1[0]*q2[3] + q1[1]*q2[2] - q1[2]*q2[1] + q1[3]*q2[0];
}
/**
* @brief Rotate a vector by a rotation matrix
* @param[in] R a three by three rotation matrix (first index is row)
* @param[in] vec the source vector
* @param[out] vec_out the output vector
*/
void rot_mult(float R[3][3], const float vec[3], float vec_out[3])
{
vec_out[0] = R[0][0] * vec[0] + R[0][1] * vec[1] + R[0][2] * vec[2];
vec_out[1] = R[1][0] * vec[0] + R[1][1] * vec[1] + R[1][2] * vec[2];
vec_out[2] = R[2][0] * vec[0] + R[2][1] * vec[1] + R[2][2] * vec[2];
}