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ardupilot/libraries/AP_Math/quaternion.cpp

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/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*-
/*
* quaternion.cpp
* Copyright (C) Andrew Tridgell 2012
*
* This file 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 file 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, see <http://www.gnu.org/licenses/>.
*/
#include "AP_Math.h"
// return the rotation matrix equivalent for this quaternion
void Quaternion::rotation_matrix(Matrix3f &m) const
{
float q3q3 = q3 * q3;
float q3q4 = q3 * q4;
float q2q2 = q2 * q2;
float q2q3 = q2 * q3;
float q2q4 = q2 * q4;
float q1q2 = q1 * q2;
float q1q3 = q1 * q3;
float q1q4 = q1 * q4;
float q4q4 = q4 * q4;
m.a.x = 1.0f-2.0f*(q3q3 + q4q4);
m.a.y = 2.0f*(q2q3 - q1q4);
m.a.z = 2.0f*(q2q4 + q1q3);
m.b.x = 2.0f*(q2q3 + q1q4);
m.b.y = 1.0f-2.0f*(q2q2 + q4q4);
m.b.z = 2.0f*(q3q4 - q1q2);
m.c.x = 2.0f*(q2q4 - q1q3);
m.c.y = 2.0f*(q3q4 + q1q2);
m.c.z = 1.0f-2.0f*(q2q2 + q3q3);
}
// return the rotation matrix equivalent for this quaternion
// Thanks to Martin John Baker
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
void Quaternion::from_rotation_matrix(const Matrix3f &m)
{
const float &m00 = m.a.x;
const float &m11 = m.b.y;
const float &m22 = m.c.z;
const float &m10 = m.b.x;
const float &m01 = m.a.y;
const float &m20 = m.c.x;
const float &m02 = m.a.z;
const float &m21 = m.c.y;
const float &m12 = m.b.z;
float &qw = q1;
float &qx = q2;
float &qy = q3;
float &qz = q4;
float tr = m00 + m11 + m22;
if (tr > 0) {
float S = sqrtf(tr+1) * 2;
qw = 0.25f * S;
qx = (m21 - m12) / S;
qy = (m02 - m20) / S;
qz = (m10 - m01) / S;
} else if ((m00 > m11) && (m00 > m22)) {
float S = sqrtf(1.0f + m00 - m11 - m22) * 2;
qw = (m21 - m12) / S;
qx = 0.25f * S;
qy = (m01 + m10) / S;
qz = (m02 + m20) / S;
} else if (m11 > m22) {
float S = sqrtf(1.0f + m11 - m00 - m22) * 2;
qw = (m02 - m20) / S;
qx = (m01 + m10) / S;
qy = 0.25f * S;
qz = (m12 + m21) / S;
} else {
float S = sqrtf(1.0f + m22 - m00 - m11) * 2;
qw = (m10 - m01) / S;
qx = (m02 + m20) / S;
qy = (m12 + m21) / S;
qz = 0.25f * S;
}
}
// convert a vector from earth to body frame
void Quaternion::earth_to_body(Vector3f &v) const
{
Matrix3f m;
rotation_matrix(m);
v = m * v;
}
// create a quaternion from Euler angles
void Quaternion::from_euler(float roll, float pitch, float yaw)
{
float cr2 = cosf(roll*0.5f);
float cp2 = cosf(pitch*0.5f);
float cy2 = cosf(yaw*0.5f);
float sr2 = sinf(roll*0.5f);
float sp2 = sinf(pitch*0.5f);
float sy2 = sinf(yaw*0.5f);
q1 = cr2*cp2*cy2 + sr2*sp2*sy2;
q2 = sr2*cp2*cy2 - cr2*sp2*sy2;
q3 = cr2*sp2*cy2 + sr2*cp2*sy2;
q4 = cr2*cp2*sy2 - sr2*sp2*cy2;
}
// create a quaternion from Euler angles
void Quaternion::from_vector312(float roll ,float pitch, float yaw)
{
float c3 = cosf(pitch);
float s3 = sinf(pitch);
float s2 = sinf(roll);
float c2 = cosf(roll);
float s1 = sinf(yaw);
float c1 = cosf(yaw);
Matrix3f m;
m.a.x = c1 * c3 - s1 * s2 * s3;
m.b.y = c1 * c2;
m.c.z = c3 * c2;
m.a.y = -c2*s1;
m.a.z = s3*c1 + c3*s2*s1;
m.b.x = c3*s1 + s3*s2*c1;
m.b.z = s1*s3 - s2*c1*c3;
m.c.x = -s3*c2;
m.c.y = s2;
from_rotation_matrix(m);
}
void Quaternion::from_axis_angle(Vector3f v) {
float theta = v.length();
if(theta < 1.0e-12f) {
q1 = 1.0f;
q2=q3=q4=0.0f;
return;
}
v /= theta;
from_axis_angle(v,theta);
}
void Quaternion::from_axis_angle(const Vector3f &axis, float theta) {
if(theta < 1.0e-12f) {
q1 = 1.0f;
q2=q3=q4=0.0f;
}
float st2 = sinf(theta/2.0f);
q1 = cos(theta/2.0f);
q2 = axis.x * st2;
q3 = axis.y * st2;
q4 = axis.z * st2;
}
void Quaternion::rotate(const Vector3f &v) {
Quaternion r;
r.from_axis_angle(v);
(*this) *= r;
}
void Quaternion::to_axis_angle(Vector3f &v) {
float l = sqrt(sq(q2)+sq(q3)+sq(q4));
v = Vector3f(q2,q3,q4);
if(l >= 1.0e-12f) {
v /= l;
v *= wrap_PI(2.0f * atan2(l,q1));
}
}
void Quaternion::from_axis_angle_fast(Vector3f v) {
float theta = v.length();
if(theta < 1.0e-12f) {
q1 = 1.0f;
q2=q3=q4=0.0f;
}
v /= theta;
from_axis_angle_fast(v,theta);
}
void Quaternion::from_axis_angle_fast(const Vector3f &axis, float theta) {
float t2 = theta/2.0f;
float sqt2 = sq(t2);
float st2 = t2-sqt2*t2/6.0f;
q1 = 1.0f-(sqt2/2.0f)+sq(sqt2)/24.0f;
q2 = axis.x * st2;
q3 = axis.y * st2;
q4 = axis.z * st2;
}
void Quaternion::rotate_fast(const Vector3f &v) {
float theta = v.length();
if(theta < 1.0e-12f) return;
float t2 = theta/2.0f;
float sqt2 = sq(t2);
float st2 = t2-sqt2*t2/6.0f;
st2 /= theta;
//"rotation quaternion"
float w2 = 1.0f-(sqt2/2.0f)+sq(sqt2)/24.0f;
float x2 = v.x * st2;
float y2 = v.y * st2;
float z2 = v.z * st2;
//copy our quaternion
float w1 = q1;
float x1 = q2;
float y1 = q3;
float z1 = q4;
//do the multiply into our quaternion
q1 = w1*w2 - x1*x2 - y1*y2 - z1*z2;
q2 = w1*x2 + x1*w2 + y1*z2 - z1*y2;
q3 = w1*y2 - x1*z2 + y1*w2 + z1*x2;
q4 = w1*z2 + x1*y2 - y1*x2 + z1*w2;
}
// get euler roll angle
float Quaternion::get_euler_roll() const
{
return (atan2f(2.0f*(q1*q2 + q3*q4), 1 - 2.0f*(q2*q2 + q3*q3)));
}
// get euler pitch angle
float Quaternion::get_euler_pitch() const
{
return safe_asin(2.0f*(q1*q3 - q4*q2));
}
// get euler yaw angle
float Quaternion::get_euler_yaw() const
{
return atan2f(2.0f*(q1*q4 + q2*q3), 1 - 2.0f*(q3*q3 + q4*q4));
}
// create eulers from a quaternion
void Quaternion::to_euler(float &roll, float &pitch, float &yaw) const
{
roll = get_euler_roll();
pitch = get_euler_pitch();
yaw = get_euler_yaw();
}
// create eulers from a quaternion
void Quaternion::to_vector312(float &roll, float &pitch, float &yaw) const
{
Matrix3f m;
rotation_matrix(m);
float T21 = m.a.y;
float T22 = m.b.y;
float T23 = m.c.y;
float T13 = m.c.x;
float T33 = m.c.z;
yaw = atan2f(-T21, T22);
roll = safe_asin(T23);
pitch = atan2f(-T13, T33);
}
float Quaternion::length(void) const
{
return sqrtf(sq(q1) + sq(q2) + sq(q3) + sq(q4));
}
Quaternion Quaternion::inverse(void) const
{
return Quaternion(q1, -q2, -q3, -q4);
}
void Quaternion::normalize(void)
{
float quatMag = length();
if (quatMag > 1e-16f)
{
float quatMagInv = 1.0f/quatMag;
q1 *= quatMagInv;
q2 *= quatMagInv;
q3 *= quatMagInv;
q4 *= quatMagInv;
}
}
Quaternion Quaternion::operator*(const Quaternion &v) const {
Quaternion ret;
const float &w1 = q1;
const float &x1 = q2;
const float &y1 = q3;
const float &z1 = q4;
float w2 = v.q1;
float x2 = v.q2;
float y2 = v.q3;
float z2 = v.q4;
ret.q1 = w1*w2 - x1*x2 - y1*y2 - z1*z2;
ret.q2 = w1*x2 + x1*w2 + y1*z2 - z1*y2;
ret.q3 = w1*y2 - x1*z2 + y1*w2 + z1*x2;
ret.q4 = w1*z2 + x1*y2 - y1*x2 + z1*w2;
return ret;
}
Quaternion &Quaternion::operator*=(const Quaternion &v) {
float &w1 = q1;
float &x1 = q2;
float &y1 = q3;
float &z1 = q4;
float w2 = v.q1;
float x2 = v.q2;
float y2 = v.q3;
float z2 = v.q4;
q1 = w1*w2 - x1*x2 - y1*y2 - z1*z2;
q2 = w1*x2 + x1*w2 + y1*z2 - z1*y2;
q3 = w1*y2 - x1*z2 + y1*w2 + z1*x2;
q4 = w1*z2 + x1*y2 - y1*x2 + z1*w2;
return *this;
}
Quaternion Quaternion::operator/(const Quaternion &v) const {
Quaternion ret;
const float &quat0 = q1;
const float &quat1 = q2;
const float &quat2 = q3;
const float &quat3 = q4;
float rquat0 = v.q1;
float rquat1 = v.q2;
float rquat2 = v.q3;
float rquat3 = v.q4;
ret.q1 = (rquat0*quat0 + rquat1*quat1 + rquat2*quat2 + rquat3*quat3);
ret.q2 = (rquat0*quat1 - rquat1*quat0 - rquat2*quat3 + rquat3*quat2);
ret.q3 = (rquat0*quat2 + rquat1*quat3 - rquat2*quat0 - rquat3*quat1);
ret.q4 = (rquat0*quat3 - rquat1*quat2 + rquat2*quat1 - rquat3*quat0);
return ret;
}
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