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ardupilot/libraries/AP_Math/quaternion.cpp

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/*
* 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/>.
*/
#pragma GCC optimize("O2")
#include "AP_Math.h"
#include <AP_InternalError/AP_InternalError.h>
// return the rotation matrix equivalent for this quaternion
void Quaternion::rotation_matrix(Matrix3f &m) const
{
const float q3q3 = q3 * q3;
const float q3q4 = q3 * q4;
const float q2q2 = q2 * q2;
const float q2q3 = q2 * q3;
const float q2q4 = q2 * q4;
const float q1q2 = q1 * q2;
const float q1q3 = q1 * q3;
const float q1q4 = q1 * q4;
const 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 after normalization
void Quaternion::rotation_matrix_norm(Matrix3f &m) const
{
const float q1q1 = q1 * q1;
const float q1q2 = q1 * q2;
const float q1q3 = q1 * q3;
const float q1q4 = q1 * q4;
const float q2q2 = q2 * q2;
const float q2q3 = q2 * q3;
const float q2q4 = q2 * q4;
const float q3q3 = q3 * q3;
const float q3q4 = q3 * q4;
const float q4q4 = q4 * q4;
const float invs = 1.0f / (q1q1 + q2q2 + q3q3 + q4q4);
m.a.x = ( q2q2 - q3q3 - q4q4 + q1q1)*invs;
m.a.y = 2.0f*(q2q3 - q1q4)*invs;
m.a.z = 2.0f*(q2q4 + q1q3)*invs;
m.b.x = 2.0f*(q2q3 + q1q4)*invs;
m.b.y = (-q2q2 + q3q3 - q4q4 + q1q1)*invs;
m.b.z = 2.0f*(q3q4 - q1q2)*invs;
m.c.x = 2.0f*(q2q4 - q1q3)*invs;
m.c.y = 2.0f*(q3q4 + q1q2)*invs;
m.c.z = (-q2q2 - q3q3 + q4q4 + q1q1)*invs;
}
// 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;
const float tr = m00 + m11 + m22;
if (tr > 0) {
const 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)) {
const float S = sqrtf(1.0f + m00 - m11 - m22) * 2.0f;
qw = (m21 - m12) / S;
qx = 0.25f * S;
qy = (m01 + m10) / S;
qz = (m02 + m20) / S;
} else if (m11 > m22) {
const float S = sqrtf(1.0f + m11 - m00 - m22) * 2.0f;
qw = (m02 - m20) / S;
qx = (m01 + m10) / S;
qy = 0.25f * S;
qz = (m12 + m21) / S;
} else {
const float S = sqrtf(1.0f + m22 - m00 - m11) * 2.0f;
qw = (m10 - m01) / S;
qx = (m02 + m20) / S;
qy = (m12 + m21) / S;
qz = 0.25f * S;
}
}
// create a quaternion from a given rotation
void Quaternion::from_rotation(enum Rotation rotation)
{
// the constants below can be calculated using the following formula:
// Matrix3f m_from_rot;
// m_from_rot.from_rotation(rotation);
// Quaternion q_from_m;
// from_rotation_matrix(m_from_rot);
switch (rotation) {
case ROTATION_NONE:
q1 = 1;
q2 = q3 = q4 = 0;
return;
case ROTATION_YAW_45:
q1 = 0.92387956f;
q2 = q3 = 0;
q4 = 0.38268343f;
return;
case ROTATION_YAW_90:
q1 = HALF_SQRT_2;
q2 = q3 = 0;
q4 = HALF_SQRT_2;
return;
case ROTATION_YAW_135:
q1 = 0.38268343f;
q2 = q3 = 0;
q4 = 0.92387956f;
return;
case ROTATION_YAW_180:
q1 = q2 = q3 = 0;
q4=1;
return;
case ROTATION_YAW_225:
q1 = -0.38268343f;
q2 = q3 = 0;
q4 = 0.92387956f;
return;
case ROTATION_YAW_270:
q1 = HALF_SQRT_2;
q2 = q3 = 0;
q4 = -HALF_SQRT_2;
return;
case ROTATION_YAW_315:
q1 = 0.92387956f;
q2 = q3 = 0;
q4 = -0.38268343f;
return;
case ROTATION_ROLL_180:
q1 = q3 = q4 = 0;
q2 = 1;
return;
case ROTATION_ROLL_180_YAW_45:
q1 = q4 = 0;
q2 = 0.92387956f;
q3 = 0.38268343f;
return;
case ROTATION_ROLL_180_YAW_90:
q1 = q4 = 0;
q2 = q3 = HALF_SQRT_2;
return;
case ROTATION_ROLL_180_YAW_135:
q1 = q4 = 0;
q2 = 0.38268343f;
q3 = 0.92387956f;
return;
case ROTATION_PITCH_180:
q1 = q2 = q4 = 0;
q3 = 1;
return;
case ROTATION_ROLL_180_YAW_225:
q1 = q4 = 0;
q2 = -0.38268343f;
q3 = 0.92387956f;
return;
case ROTATION_ROLL_180_YAW_270:
q1 = q4 = 0;
q2 = -HALF_SQRT_2;
q3 = HALF_SQRT_2;
return;
case ROTATION_ROLL_180_YAW_315:
q1 = q4 = 0;
q2 = 0.92387956f;
q3 = -0.38268343f;
return;
case ROTATION_ROLL_90:
q1 = q2 = HALF_SQRT_2;
q3 = q4 = 0;
return;
case ROTATION_ROLL_90_YAW_45:
q1 = 0.65328151f;
q2 = 0.65328145f;
q3 = q4 = 0.27059802f;
return;
case ROTATION_ROLL_90_YAW_90:
q1 = q2 = q3 = q4 = 0.5f;
return;
case ROTATION_ROLL_90_YAW_135:
q1 = q2 = 0.27059802f;
q3 = 0.65328145f;
q4 = 0.65328151f;
return;
case ROTATION_ROLL_270:
q1 = HALF_SQRT_2;
q2 = -HALF_SQRT_2;
q3 = q4 = 0;
return;
case ROTATION_ROLL_270_YAW_45:
q1 = 0.65328151f;
q2 = -0.65328145f;
q3 = -0.27059802f;
q4 = 0.27059802f;
return;
case ROTATION_ROLL_270_YAW_90:
q1 = q4 = 0.5f;
q2 = q3 = -0.5f;
return;
case ROTATION_ROLL_270_YAW_135:
q1 = 0.27059802f;
q2 = -0.27059802f;
q3 = -0.65328145f;
q4 = 0.65328151f;
return;
case ROTATION_PITCH_90:
q1 = q3 = HALF_SQRT_2;
q2 = q4 = 0;
return;
case ROTATION_PITCH_270:
q1 = HALF_SQRT_2;
q2 = q4 = 0;
q3 = -HALF_SQRT_2;
return;
case ROTATION_PITCH_180_YAW_90:
q1 = q4 = 0;
q2 = -HALF_SQRT_2;
q3 = HALF_SQRT_2;
return;
case ROTATION_PITCH_180_YAW_270:
q1 = q4 = 0;
q2 = q3 = HALF_SQRT_2;
return;
case ROTATION_ROLL_90_PITCH_90:
q1 = q2 = q3 = -0.5f;
q4 = 0.5f;
return;
case ROTATION_ROLL_180_PITCH_90:
q1 = q3 = 0;
q2 = -HALF_SQRT_2;
q4 = HALF_SQRT_2;
return;
case ROTATION_ROLL_270_PITCH_90:
q1 = q3 = q4 = 0.5f;
q2 = -0.5f;
return;
case ROTATION_ROLL_90_PITCH_180:
q1 = q2 = 0;
q3 = -HALF_SQRT_2;
q4 = HALF_SQRT_2;
return;
case ROTATION_ROLL_270_PITCH_180:
q1 = q2 = 0;
q3 = q4 = HALF_SQRT_2;
return;
case ROTATION_ROLL_90_PITCH_270:
q1 = q2 = q4 = 0.5f;
q3 = -0.5;
return;
case ROTATION_ROLL_180_PITCH_270:
q1 = q3 = 0;
q2 = q4 = HALF_SQRT_2;
return;
case ROTATION_ROLL_270_PITCH_270:
q1 = -0.5f;
q2 = q3 = q4 = 0.5f;
return;
case ROTATION_ROLL_90_PITCH_180_YAW_90:
q1 = q3 = -0.5f;
q2 = q4 = 0.5f;
return;
case ROTATION_ROLL_90_YAW_270:
q1 = q2 = -0.5f;
q3 = q4 = 0.5f;
return;
case ROTATION_ROLL_90_PITCH_68_YAW_293:
q1 = 0.26774535f;
q2 = 0.70698798f;
q3 = 0.01295743f;
q4 = -0.65445596f;
return;
case ROTATION_PITCH_315:
q1 = 0.92387956f;
q2 = q4 = 0;
q3 = -0.38268343f;
return;
case ROTATION_ROLL_90_PITCH_315:
q1 = 0.65328151f;
q2 = 0.65328145f;
q3 = -0.27059802f;
q4 = 0.27059802f;
return;
case ROTATION_PITCH_7:
q1 = 0.99813479f;
q2 = q4 = 0;
q3 = 0.06104854f;
return;
case ROTATION_CUSTOM:
// Error; custom rotations not supported
INTERNAL_ERROR(AP_InternalError::error_t::flow_of_control);
return;
case ROTATION_MAX:
break;
}
// rotation invalid
INTERNAL_ERROR(AP_InternalError::error_t::bad_rotation);
}
// rotate this quaternion by the given rotation
void Quaternion::rotate(enum Rotation rotation)
{
// create quaternion from rotation matrix
Quaternion q_from_rot;
q_from_rot.from_rotation(rotation);
// rotate this quaternion
*this *= q_from_rot;
}
// 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)
{
const float cr2 = cosf(roll*0.5f);
const float cp2 = cosf(pitch*0.5f);
const float cy2 = cosf(yaw*0.5f);
const float sr2 = sinf(roll*0.5f);
const float sp2 = sinf(pitch*0.5f);
const 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 applied in yaw, roll, pitch order
// instead of the normal yaw, pitch, roll order
void Quaternion::from_vector312(float roll, float pitch, float yaw)
{
Matrix3f m;
m.from_euler312(roll, pitch, yaw);
from_rotation_matrix(m);
}
// create a quaternion from its axis-angle representation
void Quaternion::from_axis_angle(Vector3f v)
{
const float theta = v.length();
if (is_zero(theta)) {
q1 = 1.0f;
q2=q3=q4=0.0f;
return;
}
v /= theta;
from_axis_angle(v,theta);
}
// create a quaternion from its axis-angle representation
// the axis vector must be length 1, theta is in radians
void Quaternion::from_axis_angle(const Vector3f &axis, float theta)
{
// axis must be a unit vector as there is no check for length
if (is_zero(theta)) {
q1 = 1.0f;
q2=q3=q4=0.0f;
return;
}
const float st2 = sinf(theta/2.0f);
q1 = cosf(theta/2.0f);
q2 = axis.x * st2;
q3 = axis.y * st2;
q4 = axis.z * st2;
}
// rotate by the provided axis angle
void Quaternion::rotate(const Vector3f &v)
{
Quaternion r;
r.from_axis_angle(v);
(*this) *= r;
}
// convert this quaternion to a rotation vector where the direction of the vector represents
// the axis of rotation and the length of the vector represents the angle of rotation
void Quaternion::to_axis_angle(Vector3f &v) const
{
const float l = sqrtf(sq(q2)+sq(q3)+sq(q4));
v = Vector3f(q2,q3,q4);
if (!is_zero(l)) {
v /= l;
v *= wrap_PI(2.0f * atan2f(l,q1));
}
}
// create a quaternion from its axis-angle representation
// only use with small angles. I.e. length of v should less than 0.17 radians (i.e. 10 degrees)
void Quaternion::from_axis_angle_fast(Vector3f v)
{
const float theta = v.length();
if (is_zero(theta)) {
q1 = 1.0f;
q2=q3=q4=0.0f;
return;
}
v /= theta;
from_axis_angle_fast(v,theta);
}
// create a quaternion from its axis-angle representation
// theta should less than 0.17 radians (i.e. 10 degrees)
void Quaternion::from_axis_angle_fast(const Vector3f &axis, float theta)
{
const float t2 = theta/2.0f;
const float sqt2 = sq(t2);
const 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;
}
// rotate by the provided axis angle
// only use with small angles. I.e. length of v should less than 0.17 radians (i.e. 10 degrees)
void Quaternion::rotate_fast(const Vector3f &v)
{
const float theta = v.length();
if (is_zero(theta)) {
return;
}
const float t2 = theta/2.0f;
const float sqt2 = sq(t2);
float st2 = t2-sqt2*t2/6.0f;
st2 /= theta;
//"rotation quaternion"
const float w2 = 1.0f-(sqt2/2.0f)+sq(sqt2)/24.0f;
const float x2 = v.x * st2;
const float y2 = v.y * st2;
const float z2 = v.z * st2;
//copy our quaternion
const float w1 = q1;
const float x1 = q2;
const float y1 = q3;
const 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), 1.0f - 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), 1.0f - 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
Vector3f Quaternion::to_vector312(void) const
{
Matrix3f m;
rotation_matrix(m);
return m.to_euler312();
}
float Quaternion::length(void) const
{
return sqrtf(sq(q1) + sq(q2) + sq(q3) + sq(q4));
}
// return the reverse rotation of this quaternion
Quaternion Quaternion::inverse(void) const
{
return Quaternion(q1, -q2, -q3, -q4);
}
// reverse the rotation of this quaternion
void Quaternion::invert()
{
q2 = -q2;
q3 = -q3;
q4 = -q4;
}
void Quaternion::normalize(void)
{
const float quatMag = length();
if (!is_zero(quatMag)) {
const 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;
const float w2 = v.q1;
const float x2 = v.q2;
const float y2 = v.q3;
const 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;
}
// Optimized quaternion rotation operator, equivalent to converting
// (*this) to a rotation matrix then multiplying it to the argument `v`.
//
// 15 multiplies and 15 add / subtracts. Caches 3 floats
Vector3f Quaternion::operator*(const Vector3f &v) const
{
// This uses the formula
//
// v2 = v1 + 2 q1 * qv x v1 + 2 qv x qv x v1
//
// where "x" is the cross product (explicitly inlined for performance below),
// "q1" is the scalar part and "qv" is the vector part of this quaternion
Vector3f ret = v;
// Compute and cache "qv x v1"
float uv[] = {q3 * v.z - q4 * v.y, q4 * v.x - q2 * v.z, q2 * v.y - q3 * v.x};
uv[0] += uv[0];
uv[1] += uv[1];
uv[2] += uv[2];
ret.x += q1 * uv[0] + q3 * uv[2] - q4 * uv[1];
ret.y += q1 * uv[1] + q4 * uv[0] - q2 * uv[2];
ret.z += q1 * uv[2] + q2 * uv[1] - q3 * uv[0];
return ret;
}
Quaternion &Quaternion::operator*=(const Quaternion &v)
{
const float w1 = q1;
const float x1 = q2;
const float y1 = q3;
const float z1 = q4;
const float w2 = v.q1;
const float x2 = v.q2;
const float y2 = v.q3;
const 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;
const float rquat0 = v.q1;
const float rquat1 = v.q2;
const float rquat2 = v.q3;
const 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;
}
// angular difference in radians between quaternions
Quaternion Quaternion::angular_difference(const Quaternion &v) const
{
return v.inverse() * *this;
}
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