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3afdc7e41c
config plugin updates. Has not been tested in flight yet although seems sensible so please be careful when using this code. git-svn-id: svn://svn.openpilot.org/OpenPilot/trunk@3166 ebee16cc-31ac-478f-84a7-5cbb03baadba
429 lines
12 KiB
C
429 lines
12 KiB
C
/**
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******************************************************************************
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*
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* @file CoordinateConversions.c
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* @author The OpenPilot Team, http://www.openpilot.org Copyright (C) 2010.
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* @brief General conversions with different coordinate systems.
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* - all angles in deg
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* - distances in meters
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* - altitude above WGS-84 elipsoid
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*
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* @see The GNU Public License (GPL) Version 3
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*
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*****************************************************************************/
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/*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*/
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#include <math.h>
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#include <stdint.h>
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#include "CoordinateConversions.h"
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#define RAD2DEG (180.0/M_PI)
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#define DEG2RAD (M_PI/180.0)
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// ****** convert Lat,Lon,Alt to ECEF ************
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void LLA2ECEF(double LLA[3], double ECEF[3])
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{
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const double a = 6378137.0; // Equatorial Radius
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const double e = 8.1819190842622e-2; // Eccentricity
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double sinLat, sinLon, cosLat, cosLon;
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double N;
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sinLat = sin(DEG2RAD * LLA[0]);
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sinLon = sin(DEG2RAD * LLA[1]);
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cosLat = cos(DEG2RAD * LLA[0]);
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cosLon = cos(DEG2RAD * LLA[1]);
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N = a / sqrt(1.0 - e * e * sinLat * sinLat); //prime vertical radius of curvature
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ECEF[0] = (N + LLA[2]) * cosLat * cosLon;
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ECEF[1] = (N + LLA[2]) * cosLat * sinLon;
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ECEF[2] = ((1 - e * e) * N + LLA[2]) * sinLat;
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}
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// ****** convert ECEF to Lat,Lon,Alt (ITERATIVE!) *********
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uint16_t ECEF2LLA(double ECEF[3], double LLA[3])
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{
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/**
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* LLA parameter is used to prime the iteration.
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* A position within 1 meter of the specified LLA
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* will be calculated within at most 3 iterations.
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* If unknown: Call with any valid LLA coordinate
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* will compute within at most 5 iterations.
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* Suggestion: [0,0,0]
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**/
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const double a = 6378137.0; // Equatorial Radius
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const double e = 8.1819190842622e-2; // Eccentricity
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double x = ECEF[0], y = ECEF[1], z = ECEF[2];
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double Lat, N, NplusH, delta, esLat;
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uint16_t iter;
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#define MAX_ITER 10 // should not take more than 5 for valid coordinates
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#define ACCURACY 1.0e-11 // used to be e-14, but we don't need sub micrometer exact calculations
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LLA[1] = RAD2DEG * atan2(y, x);
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Lat = DEG2RAD * LLA[0];
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esLat = e * sin(Lat);
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N = a / sqrt(1 - esLat * esLat);
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NplusH = N + LLA[2];
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delta = 1;
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iter = 0;
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while (((delta > ACCURACY) || (delta < -ACCURACY))
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&& (iter < MAX_ITER)) {
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delta = Lat - atan(z / (sqrt(x * x + y * y) * (1 - (N * e * e / NplusH))));
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Lat = Lat - delta;
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esLat = e * sin(Lat);
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N = a / sqrt(1 - esLat * esLat);
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NplusH = sqrt(x * x + y * y) / cos(Lat);
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iter += 1;
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}
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LLA[0] = RAD2DEG * Lat;
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LLA[2] = NplusH - N;
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return (iter < MAX_ITER);
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}
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// ****** find ECEF to NED rotation matrix ********
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void RneFromLLA(double LLA[3], float Rne[3][3])
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{
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float sinLat, sinLon, cosLat, cosLon;
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sinLat = (float)sin(DEG2RAD * LLA[0]);
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sinLon = (float)sin(DEG2RAD * LLA[1]);
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cosLat = (float)cos(DEG2RAD * LLA[0]);
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cosLon = (float)cos(DEG2RAD * LLA[1]);
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Rne[0][0] = -sinLat * cosLon;
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Rne[0][1] = -sinLat * sinLon;
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Rne[0][2] = cosLat;
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Rne[1][0] = -sinLon;
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Rne[1][1] = cosLon;
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Rne[1][2] = 0;
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Rne[2][0] = -cosLat * cosLon;
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Rne[2][1] = -cosLat * sinLon;
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Rne[2][2] = -sinLat;
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}
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// ****** find roll, pitch, yaw from quaternion ********
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void Quaternion2RPY(const float q[4], float rpy[3])
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{
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float R13, R11, R12, R23, R33;
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float q0s = q[0] * q[0];
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float q1s = q[1] * q[1];
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float q2s = q[2] * q[2];
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float q3s = q[3] * q[3];
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R13 = 2 * (q[1] * q[3] - q[0] * q[2]);
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R11 = q0s + q1s - q2s - q3s;
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R12 = 2 * (q[1] * q[2] + q[0] * q[3]);
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R23 = 2 * (q[2] * q[3] + q[0] * q[1]);
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R33 = q0s - q1s - q2s + q3s;
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rpy[1] = RAD2DEG * asinf(-R13); // pitch always between -pi/2 to pi/2
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rpy[2] = RAD2DEG * atan2f(R12, R11);
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rpy[0] = RAD2DEG * atan2f(R23, R33);
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//TODO: consider the cases where |R13| ~= 1, |pitch| ~= pi/2
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}
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// ****** find quaternion from roll, pitch, yaw ********
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void RPY2Quaternion(const float rpy[3], float q[4])
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{
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float phi, theta, psi;
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float cphi, sphi, ctheta, stheta, cpsi, spsi;
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phi = DEG2RAD * rpy[0] / 2;
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theta = DEG2RAD * rpy[1] / 2;
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psi = DEG2RAD * rpy[2] / 2;
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cphi = cosf(phi);
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sphi = sinf(phi);
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ctheta = cosf(theta);
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stheta = sinf(theta);
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cpsi = cosf(psi);
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spsi = sinf(psi);
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q[0] = cphi * ctheta * cpsi + sphi * stheta * spsi;
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q[1] = sphi * ctheta * cpsi - cphi * stheta * spsi;
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q[2] = cphi * stheta * cpsi + sphi * ctheta * spsi;
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q[3] = cphi * ctheta * spsi - sphi * stheta * cpsi;
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if (q[0] < 0) { // q0 always positive for uniqueness
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q[0] = -q[0];
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q[1] = -q[1];
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q[2] = -q[2];
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q[3] = -q[3];
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}
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}
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//** Find Rbe, that rotates a vector from earth fixed to body frame, from quaternion **
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void Quaternion2R(float q[4], float Rbe[3][3])
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{
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float q0s = q[0] * q[0], q1s = q[1] * q[1], q2s = q[2] * q[2], q3s = q[3] * q[3];
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Rbe[0][0] = q0s + q1s - q2s - q3s;
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Rbe[0][1] = 2 * (q[1] * q[2] + q[0] * q[3]);
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Rbe[0][2] = 2 * (q[1] * q[3] - q[0] * q[2]);
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Rbe[1][0] = 2 * (q[1] * q[2] - q[0] * q[3]);
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Rbe[1][1] = q0s - q1s + q2s - q3s;
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Rbe[1][2] = 2 * (q[2] * q[3] + q[0] * q[1]);
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Rbe[2][0] = 2 * (q[1] * q[3] + q[0] * q[2]);
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Rbe[2][1] = 2 * (q[2] * q[3] - q[0] * q[1]);
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Rbe[2][2] = q0s - q1s - q2s + q3s;
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}
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// ****** Express LLA in a local NED Base Frame ********
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void LLA2Base(double LLA[3], double BaseECEF[3], float Rne[3][3], float NED[3])
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{
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double ECEF[3];
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float diff[3];
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LLA2ECEF(LLA, ECEF);
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diff[0] = (float)(ECEF[0] - BaseECEF[0]);
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diff[1] = (float)(ECEF[1] - BaseECEF[1]);
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diff[2] = (float)(ECEF[2] - BaseECEF[2]);
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NED[0] = Rne[0][0] * diff[0] + Rne[0][1] * diff[1] + Rne[0][2] * diff[2];
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NED[1] = Rne[1][0] * diff[0] + Rne[1][1] * diff[1] + Rne[1][2] * diff[2];
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NED[2] = Rne[2][0] * diff[0] + Rne[2][1] * diff[1] + Rne[2][2] * diff[2];
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}
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// ****** Express ECEF in a local NED Base Frame ********
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void ECEF2Base(double ECEF[3], double BaseECEF[3], float Rne[3][3], float NED[3])
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{
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float diff[3];
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diff[0] = (float)(ECEF[0] - BaseECEF[0]);
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diff[1] = (float)(ECEF[1] - BaseECEF[1]);
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diff[2] = (float)(ECEF[2] - BaseECEF[2]);
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NED[0] = Rne[0][0] * diff[0] + Rne[0][1] * diff[1] + Rne[0][2] * diff[2];
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NED[1] = Rne[1][0] * diff[0] + Rne[1][1] * diff[1] + Rne[1][2] * diff[2];
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NED[2] = Rne[2][0] * diff[0] + Rne[2][1] * diff[1] + Rne[2][2] * diff[2];
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}
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// ****** convert Rotation Matrix to Quaternion ********
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// ****** if R converts from e to b, q is rotation from e to b ****
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void R2Quaternion(float R[3][3], float q[4])
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{
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float m[4], mag;
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uint8_t index,i;
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m[0] = 1 + R[0][0] + R[1][1] + R[2][2];
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m[1] = 1 + R[0][0] - R[1][1] - R[2][2];
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m[2] = 1 - R[0][0] + R[1][1] - R[2][2];
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m[3] = 1 - R[0][0] - R[1][1] + R[2][2];
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// find maximum divisor
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index = 0;
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mag = m[0];
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for (i=1;i<4;i++){
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if (m[i] > mag){
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mag = m[i];
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index = i;
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}
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}
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mag = 2*sqrt(mag);
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if (index == 0) {
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q[0] = mag/4;
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q[1] = (R[1][2]-R[2][1])/mag;
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q[2] = (R[2][0]-R[0][2])/mag;
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q[3] = (R[0][1]-R[1][0])/mag;
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}
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else if (index == 1) {
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q[1] = mag/4;
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q[0] = (R[1][2]-R[2][1])/mag;
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q[2] = (R[0][1]+R[1][0])/mag;
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q[3] = (R[0][2]+R[2][0])/mag;
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}
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else if (index == 2) {
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q[2] = mag/4;
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q[0] = (R[2][0]-R[0][2])/mag;
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q[1] = (R[0][1]+R[1][0])/mag;
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q[3] = (R[1][2]+R[2][1])/mag;
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}
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else {
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q[3] = mag/4;
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q[0] = (R[0][1]-R[1][0])/mag;
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q[1] = (R[0][2]+R[2][0])/mag;
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q[2] = (R[1][2]+R[2][1])/mag;
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}
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// q0 positive, i.e. angle between pi and -pi
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if (q[0] < 0){
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q[0] = -q[0];
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q[1] = -q[1];
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q[2] = -q[2];
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q[3] = -q[3];
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}
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}
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// ****** Rotation Matrix from Two Vector Directions ********
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// ****** given two vector directions (v1 and v2) known in two frames (b and e) find Rbe ***
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// ****** solution is approximate if can't be exact ***
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uint8_t RotFrom2Vectors(const float v1b[3], const float v1e[3], const float v2b[3], const float v2e[3], float Rbe[3][3])
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{
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float Rib[3][3], Rie[3][3];
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float mag;
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uint8_t i,j,k;
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// identity rotation in case of error
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for (i=0;i<3;i++){
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for (j=0;j<3;j++)
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Rbe[i][j]=0;
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Rbe[i][i]=1;
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}
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// The first rows of rot matrices chosen in direction of v1
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mag = VectorMagnitude(v1b);
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if (fabs(mag) < 1e-30)
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return (-1);
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for (i=0;i<3;i++)
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Rib[0][i]=v1b[i]/mag;
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mag = VectorMagnitude(v1e);
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if (fabs(mag) < 1e-30)
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return (-1);
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for (i=0;i<3;i++)
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Rie[0][i]=v1e[i]/mag;
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// The second rows of rot matrices chosen in direction of v1xv2
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CrossProduct(v1b,v2b,&Rib[1][0]);
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mag = VectorMagnitude(&Rib[1][0]);
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if (fabs(mag) < 1e-30)
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return (-1);
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for (i=0;i<3;i++)
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Rib[1][i]=Rib[1][i]/mag;
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CrossProduct(v1e,v2e,&Rie[1][0]);
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mag = VectorMagnitude(&Rie[1][0]);
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if (fabs(mag) < 1e-30)
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return (-1);
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for (i=0;i<3;i++)
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Rie[1][i]=Rie[1][i]/mag;
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// The third rows of rot matrices are XxY (Row1xRow2)
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CrossProduct(&Rib[0][0],&Rib[1][0],&Rib[2][0]);
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CrossProduct(&Rie[0][0],&Rie[1][0],&Rie[2][0]);
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// Rbe = Rbi*Rie = Rib'*Rie
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for (i=0;i<3;i++)
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for(j=0;j<3;j++){
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Rbe[i][j]=0;
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for(k=0;k<3;k++)
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Rbe[i][j] += Rib[k][i]*Rie[k][j];
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}
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return 1;
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}
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void Rv2Rot(float Rv[3], float R[3][3])
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{
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// Compute rotation matrix from a rotation vector
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// To save .text space, uses Quaternion2R()
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float q[4];
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float angle = VectorMagnitude(Rv);
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if (angle <= 0.00048828125f) {
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// angle < sqrt(2*machine_epsilon(float)), so flush cos(x) to 1.0f
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q[0] = 1.0f;
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// and flush sin(x/2)/x to 0.5
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q[1] = 0.5f*Rv[0];
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q[2] = 0.5f*Rv[1];
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q[3] = 0.5f*Rv[2];
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// This prevents division by zero, while retaining full accuracy
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}
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else {
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q[0] = cosf(angle*0.5f);
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float scale = sinf(angle*0.5f) / angle;
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q[1] = scale*Rv[0];
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q[2] = scale*Rv[1];
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q[3] = scale*Rv[2];
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}
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Quaternion2R(q, R);
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}
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// ****** Vector Cross Product ********
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void CrossProduct(const float v1[3], const float v2[3], float result[3])
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{
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result[0] = v1[1]*v2[2] - v2[1]*v1[2];
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result[1] = v2[0]*v1[2] - v1[0]*v2[2];
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result[2] = v1[0]*v2[1] - v2[0]*v1[1];
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}
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// ****** Vector Magnitude ********
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float VectorMagnitude(const float v[3])
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{
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return(sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]));
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}
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/**
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* @brief Compute the inverse of a quaternion
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* @param [in][out] q The matrix to invert
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*/
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void quat_inverse(float q[4])
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{
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q[1] = -q[1];
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q[2] = -q[2];
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q[3] = -q[3];
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}
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/**
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* @brief Duplicate a quaternion
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* @param[in] q quaternion in
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* @param[out] qnew quaternion to copy to
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*/
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void quat_copy(const float q[4], float qnew[4])
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{
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qnew[0] = q[0];
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qnew[1] = q[1];
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qnew[2] = q[2];
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qnew[3] = q[3];
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}
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/**
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* @brief Multiply two quaternions into a third
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* @param[in] q1 First quaternion
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* @param[in] q2 Second quaternion
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* @param[out] qout Output quaternion
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*/
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void quat_mult(const float q1[4], const float q2[4], float qout[4])
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{
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qout[0] = q1[0]*q2[0] - q1[1]*q2[1] - q1[2]*q2[2] - q1[3]*q2[3];
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qout[1] = q1[0]*q2[1] + q1[1]*q2[0] + q1[2]*q2[3] - q1[3]*q2[2];
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qout[2] = q1[0]*q2[2] - q1[1]*q2[3] + q1[2]*q2[0] + q1[3]*q2[1];
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qout[3] = q1[0]*q2[3] + q1[1]*q2[2] - q1[2]*q2[1] + q1[3]*q2[0];
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}
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/**
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* @brief Rotate a vector by a rotation matrix
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* @param[in] R a three by three rotation matrix (first index is row)
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* @param[in] vec the source vector
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* @param[out] vec_out the output vector
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*/
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void rot_mult(float R[3][3], const float vec[3], float vec_out[3])
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{
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vec_out[0] = R[0][0] * vec[0] + R[0][1] * vec[1] + R[0][2] * vec[2];
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vec_out[1] = R[1][0] * vec[0] + R[1][1] * vec[1] + R[1][2] * vec[2];
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vec_out[2] = R[2][0] * vec[0] + R[2][1] * vec[1] + R[2][2] * vec[2];
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}
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