quadcopter cufe / Mbed 2 deprecated 2006_Theta_Control_yaw

Quadcopter Attitude Control(Yaw-Pitch-Roll)

Dependencies:   mbed

helper_3dmath.h@0:e63996fd7d3e, 2015-07-03 (annotated)

Committer:
khaledelmadawi
Date:
Fri Jul 03 11:16:02 2015 +0000
Revision:
0:e63996fd7d3e
Quadcopter Attitude Control(Yaw-Pitch-Roll)

Who changed what in which revision?

UserRevisionLine numberNew contents of line
khaledelmadawi 0:e63996fd7d3e 1 // I2C device class (I2Cdev) demonstration Arduino sketch for MPU6050 class, 3D math helper
khaledelmadawi 0:e63996fd7d3e 2 // 6/5/2012 by Jeff Rowberg <jeff@rowberg.net>
khaledelmadawi 0:e63996fd7d3e 3 // Updates should (hopefully) always be available at https://github.com/jrowberg/i2cdevlib
khaledelmadawi 0:e63996fd7d3e 4 //
khaledelmadawi 0:e63996fd7d3e 5 // Changelog:
khaledelmadawi 0:e63996fd7d3e 6 // 2012-06-05 - add 3D math helper file to DMP6 example sketch
khaledelmadawi 0:e63996fd7d3e 7
khaledelmadawi 0:e63996fd7d3e 8 /* ============================================
khaledelmadawi 0:e63996fd7d3e 9 I2Cdev device library code is placed under the MIT license
khaledelmadawi 0:e63996fd7d3e 10 Copyright (c) 2012 Jeff Rowberg
khaledelmadawi 0:e63996fd7d3e 11
khaledelmadawi 0:e63996fd7d3e 12 Permission is hereby granted, free of charge, to any person obtaining a copy
khaledelmadawi 0:e63996fd7d3e 13 of this software and associated documentation files (the "Software"), to deal
khaledelmadawi 0:e63996fd7d3e 14 in the Software without restriction, including without limitation the rights
khaledelmadawi 0:e63996fd7d3e 15 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
khaledelmadawi 0:e63996fd7d3e 16 copies of the Software, and to permit persons to whom the Software is
khaledelmadawi 0:e63996fd7d3e 17 furnished to do so, subject to the following conditions:
khaledelmadawi 0:e63996fd7d3e 18
khaledelmadawi 0:e63996fd7d3e 19 The above copyright notice and this permission notice shall be included in
khaledelmadawi 0:e63996fd7d3e 20 all copies or substantial portions of the Software.
khaledelmadawi 0:e63996fd7d3e 21
khaledelmadawi 0:e63996fd7d3e 22 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
khaledelmadawi 0:e63996fd7d3e 23 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
khaledelmadawi 0:e63996fd7d3e 24 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
khaledelmadawi 0:e63996fd7d3e 25 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
khaledelmadawi 0:e63996fd7d3e 26 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
khaledelmadawi 0:e63996fd7d3e 27 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
khaledelmadawi 0:e63996fd7d3e 28 THE SOFTWARE.
khaledelmadawi 0:e63996fd7d3e 29 ===============================================
khaledelmadawi 0:e63996fd7d3e 30 */
khaledelmadawi 0:e63996fd7d3e 31
khaledelmadawi 0:e63996fd7d3e 32 #ifndef _HELPER_3DMATH_H_
khaledelmadawi 0:e63996fd7d3e 33 #define _HELPER_3DMATH_H_
khaledelmadawi 0:e63996fd7d3e 34
khaledelmadawi 0:e63996fd7d3e 35 class Quaternion {
khaledelmadawi 0:e63996fd7d3e 36 public:
khaledelmadawi 0:e63996fd7d3e 37 float w;
khaledelmadawi 0:e63996fd7d3e 38 float x;
khaledelmadawi 0:e63996fd7d3e 39 float y;
khaledelmadawi 0:e63996fd7d3e 40 float z;
khaledelmadawi 0:e63996fd7d3e 41
khaledelmadawi 0:e63996fd7d3e 42 Quaternion() {
khaledelmadawi 0:e63996fd7d3e 43 w = 1.0f;
khaledelmadawi 0:e63996fd7d3e 44 x = 0.0f;
khaledelmadawi 0:e63996fd7d3e 45 y = 0.0f;
khaledelmadawi 0:e63996fd7d3e 46 z = 0.0f;
khaledelmadawi 0:e63996fd7d3e 47 }
khaledelmadawi 0:e63996fd7d3e 48
khaledelmadawi 0:e63996fd7d3e 49 Quaternion(float nw, float nx, float ny, float nz) {
khaledelmadawi 0:e63996fd7d3e 50 w = nw;
khaledelmadawi 0:e63996fd7d3e 51 x = nx;
khaledelmadawi 0:e63996fd7d3e 52 y = ny;
khaledelmadawi 0:e63996fd7d3e 53 z = nz;
khaledelmadawi 0:e63996fd7d3e 54 }
khaledelmadawi 0:e63996fd7d3e 55
khaledelmadawi 0:e63996fd7d3e 56 Quaternion getProduct(Quaternion q) {
khaledelmadawi 0:e63996fd7d3e 57 // Quaternion multiplication is defined by:
khaledelmadawi 0:e63996fd7d3e 58 // (Q1 * Q2).w = (w1w2 - x1x2 - y1y2 - z1z2)
khaledelmadawi 0:e63996fd7d3e 59 // (Q1 * Q2).x = (w1x2 + x1w2 + y1z2 - z1y2)
khaledelmadawi 0:e63996fd7d3e 60 // (Q1 * Q2).y = (w1y2 - x1z2 + y1w2 + z1x2)
khaledelmadawi 0:e63996fd7d3e 61 // (Q1 * Q2).z = (w1z2 + x1y2 - y1x2 + z1w2
khaledelmadawi 0:e63996fd7d3e 62 return Quaternion(
khaledelmadawi 0:e63996fd7d3e 63 w*q.w - x*q.x - y*q.y - z*q.z, // new w
khaledelmadawi 0:e63996fd7d3e 64 w*q.x + x*q.w + y*q.z - z*q.y, // new x
khaledelmadawi 0:e63996fd7d3e 65 w*q.y - x*q.z + y*q.w + z*q.x, // new y
khaledelmadawi 0:e63996fd7d3e 66 w*q.z + x*q.y - y*q.x + z*q.w); // new z
khaledelmadawi 0:e63996fd7d3e 67 }
khaledelmadawi 0:e63996fd7d3e 68
khaledelmadawi 0:e63996fd7d3e 69 Quaternion getConjugate() {
khaledelmadawi 0:e63996fd7d3e 70 return Quaternion(w, -x, -y, -z);
khaledelmadawi 0:e63996fd7d3e 71 }
khaledelmadawi 0:e63996fd7d3e 72
khaledelmadawi 0:e63996fd7d3e 73 float getMagnitude() {
khaledelmadawi 0:e63996fd7d3e 74 return sqrt(w*w + x*x + y*y + z*z);
khaledelmadawi 0:e63996fd7d3e 75 }
khaledelmadawi 0:e63996fd7d3e 76
khaledelmadawi 0:e63996fd7d3e 77 void normalize() {
khaledelmadawi 0:e63996fd7d3e 78 float m = getMagnitude();
khaledelmadawi 0:e63996fd7d3e 79 w /= m;
khaledelmadawi 0:e63996fd7d3e 80 x /= m;
khaledelmadawi 0:e63996fd7d3e 81 y /= m;
khaledelmadawi 0:e63996fd7d3e 82 z /= m;
khaledelmadawi 0:e63996fd7d3e 83 }
khaledelmadawi 0:e63996fd7d3e 84
khaledelmadawi 0:e63996fd7d3e 85 Quaternion getNormalized() {
khaledelmadawi 0:e63996fd7d3e 86 Quaternion r(w, x, y, z);
khaledelmadawi 0:e63996fd7d3e 87 r.normalize();
khaledelmadawi 0:e63996fd7d3e 88 return r;
khaledelmadawi 0:e63996fd7d3e 89 }
khaledelmadawi 0:e63996fd7d3e 90 };
khaledelmadawi 0:e63996fd7d3e 91
khaledelmadawi 0:e63996fd7d3e 92 class VectorInt16 {
khaledelmadawi 0:e63996fd7d3e 93 public:
khaledelmadawi 0:e63996fd7d3e 94 int16_t x;
khaledelmadawi 0:e63996fd7d3e 95 int16_t y;
khaledelmadawi 0:e63996fd7d3e 96 int16_t z;
khaledelmadawi 0:e63996fd7d3e 97
khaledelmadawi 0:e63996fd7d3e 98 VectorInt16() {
khaledelmadawi 0:e63996fd7d3e 99 x = 0;
khaledelmadawi 0:e63996fd7d3e 100 y = 0;
khaledelmadawi 0:e63996fd7d3e 101 z = 0;
khaledelmadawi 0:e63996fd7d3e 102 }
khaledelmadawi 0:e63996fd7d3e 103
khaledelmadawi 0:e63996fd7d3e 104 VectorInt16(int16_t nx, int16_t ny, int16_t nz) {
khaledelmadawi 0:e63996fd7d3e 105 x = nx;
khaledelmadawi 0:e63996fd7d3e 106 y = ny;
khaledelmadawi 0:e63996fd7d3e 107 z = nz;
khaledelmadawi 0:e63996fd7d3e 108 }
khaledelmadawi 0:e63996fd7d3e 109
khaledelmadawi 0:e63996fd7d3e 110 float getMagnitude() {
khaledelmadawi 0:e63996fd7d3e 111 return sqrt((float)(x*x + y*y + z*z));
khaledelmadawi 0:e63996fd7d3e 112 }
khaledelmadawi 0:e63996fd7d3e 113
khaledelmadawi 0:e63996fd7d3e 114 void normalize() {
khaledelmadawi 0:e63996fd7d3e 115 float m = getMagnitude();
khaledelmadawi 0:e63996fd7d3e 116 x /= m;
khaledelmadawi 0:e63996fd7d3e 117 y /= m;
khaledelmadawi 0:e63996fd7d3e 118 z /= m;
khaledelmadawi 0:e63996fd7d3e 119 }
khaledelmadawi 0:e63996fd7d3e 120
khaledelmadawi 0:e63996fd7d3e 121 VectorInt16 getNormalized() {
khaledelmadawi 0:e63996fd7d3e 122 VectorInt16 r(x, y, z);
khaledelmadawi 0:e63996fd7d3e 123 r.normalize();
khaledelmadawi 0:e63996fd7d3e 124 return r;
khaledelmadawi 0:e63996fd7d3e 125 }
khaledelmadawi 0:e63996fd7d3e 126
khaledelmadawi 0:e63996fd7d3e 127 void rotate(Quaternion *q) {
khaledelmadawi 0:e63996fd7d3e 128 // http://www.cprogramming.com/tutorial/3d/quaternions.html
khaledelmadawi 0:e63996fd7d3e 129 // http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/transforms/index.htm
khaledelmadawi 0:e63996fd7d3e 130 // http://content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation
khaledelmadawi 0:e63996fd7d3e 131 // ^ or: http://webcache.googleusercontent.com/search?q=cache:xgJAp3bDNhQJ:content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation&hl=en&gl=us&strip=1
khaledelmadawi 0:e63996fd7d3e 132
khaledelmadawi 0:e63996fd7d3e 133 // P_out = q * P_in * conj(q)
khaledelmadawi 0:e63996fd7d3e 134 // - P_out is the output vector
khaledelmadawi 0:e63996fd7d3e 135 // - q is the orientation quaternion
khaledelmadawi 0:e63996fd7d3e 136 // - P_in is the input vector (a*aReal)
khaledelmadawi 0:e63996fd7d3e 137 // - conj(q) is the conjugate of the orientation quaternion (q=[w,x,y,z], q*=[w,-x,-y,-z])
khaledelmadawi 0:e63996fd7d3e 138 Quaternion p(0, x, y, z);
khaledelmadawi 0:e63996fd7d3e 139
khaledelmadawi 0:e63996fd7d3e 140 // quaternion multiplication: q * p, stored back in p
khaledelmadawi 0:e63996fd7d3e 141 p = q -> getProduct(p);
khaledelmadawi 0:e63996fd7d3e 142
khaledelmadawi 0:e63996fd7d3e 143 // quaternion multiplication: p * conj(q), stored back in p
khaledelmadawi 0:e63996fd7d3e 144 p = p.getProduct(q -> getConjugate());
khaledelmadawi 0:e63996fd7d3e 145
khaledelmadawi 0:e63996fd7d3e 146 // p quaternion is now [0, x', y', z']
khaledelmadawi 0:e63996fd7d3e 147 x = p.x;
khaledelmadawi 0:e63996fd7d3e 148 y = p.y;
khaledelmadawi 0:e63996fd7d3e 149 z = p.z;
khaledelmadawi 0:e63996fd7d3e 150 }
khaledelmadawi 0:e63996fd7d3e 151
khaledelmadawi 0:e63996fd7d3e 152 VectorInt16 getRotated(Quaternion *q) {
khaledelmadawi 0:e63996fd7d3e 153 VectorInt16 r(x, y, z);
khaledelmadawi 0:e63996fd7d3e 154 r.rotate(q);
khaledelmadawi 0:e63996fd7d3e 155 return r;
khaledelmadawi 0:e63996fd7d3e 156 }
khaledelmadawi 0:e63996fd7d3e 157 };
khaledelmadawi 0:e63996fd7d3e 158
khaledelmadawi 0:e63996fd7d3e 159 class VectorFloat {
khaledelmadawi 0:e63996fd7d3e 160 public:
khaledelmadawi 0:e63996fd7d3e 161 float x;
khaledelmadawi 0:e63996fd7d3e 162 float y;
khaledelmadawi 0:e63996fd7d3e 163 float z;
khaledelmadawi 0:e63996fd7d3e 164
khaledelmadawi 0:e63996fd7d3e 165 VectorFloat() {
khaledelmadawi 0:e63996fd7d3e 166 x = 0;
khaledelmadawi 0:e63996fd7d3e 167 y = 0;
khaledelmadawi 0:e63996fd7d3e 168 z = 0;
khaledelmadawi 0:e63996fd7d3e 169 }
khaledelmadawi 0:e63996fd7d3e 170
khaledelmadawi 0:e63996fd7d3e 171 VectorFloat(float nx, float ny, float nz) {
khaledelmadawi 0:e63996fd7d3e 172 x = nx;
khaledelmadawi 0:e63996fd7d3e 173 y = ny;
khaledelmadawi 0:e63996fd7d3e 174 z = nz;
khaledelmadawi 0:e63996fd7d3e 175 }
khaledelmadawi 0:e63996fd7d3e 176
khaledelmadawi 0:e63996fd7d3e 177 float getMagnitude() {
khaledelmadawi 0:e63996fd7d3e 178 return sqrt(x*x + y*y + z*z);
khaledelmadawi 0:e63996fd7d3e 179 }
khaledelmadawi 0:e63996fd7d3e 180
khaledelmadawi 0:e63996fd7d3e 181 void normalize() {
khaledelmadawi 0:e63996fd7d3e 182 float m = getMagnitude();
khaledelmadawi 0:e63996fd7d3e 183 x /= m;
khaledelmadawi 0:e63996fd7d3e 184 y /= m;
khaledelmadawi 0:e63996fd7d3e 185 z /= m;
khaledelmadawi 0:e63996fd7d3e 186 }
khaledelmadawi 0:e63996fd7d3e 187
khaledelmadawi 0:e63996fd7d3e 188 VectorFloat getNormalized() {
khaledelmadawi 0:e63996fd7d3e 189 VectorFloat r(x, y, z);
khaledelmadawi 0:e63996fd7d3e 190 r.normalize();
khaledelmadawi 0:e63996fd7d3e 191 return r;
khaledelmadawi 0:e63996fd7d3e 192 }
khaledelmadawi 0:e63996fd7d3e 193
khaledelmadawi 0:e63996fd7d3e 194 void rotate(Quaternion *q) {
khaledelmadawi 0:e63996fd7d3e 195 Quaternion p(0, x, y, z);
khaledelmadawi 0:e63996fd7d3e 196
khaledelmadawi 0:e63996fd7d3e 197 // quaternion multiplication: q * p, stored back in p
khaledelmadawi 0:e63996fd7d3e 198 p = q -> getProduct(p);
khaledelmadawi 0:e63996fd7d3e 199
khaledelmadawi 0:e63996fd7d3e 200 // quaternion multiplication: p * conj(q), stored back in p
khaledelmadawi 0:e63996fd7d3e 201 p = p.getProduct(q -> getConjugate());
khaledelmadawi 0:e63996fd7d3e 202
khaledelmadawi 0:e63996fd7d3e 203 // p quaternion is now [0, x', y', z']
khaledelmadawi 0:e63996fd7d3e 204 x = p.x;
khaledelmadawi 0:e63996fd7d3e 205 y = p.y;
khaledelmadawi 0:e63996fd7d3e 206 z = p.z;
khaledelmadawi 0:e63996fd7d3e 207 }
khaledelmadawi 0:e63996fd7d3e 208
khaledelmadawi 0:e63996fd7d3e 209 VectorFloat getRotated(Quaternion *q) {
khaledelmadawi 0:e63996fd7d3e 210 VectorFloat r(x, y, z);
khaledelmadawi 0:e63996fd7d3e 211 r.rotate(q);
khaledelmadawi 0:e63996fd7d3e 212 return r;
khaledelmadawi 0:e63996fd7d3e 213 }
khaledelmadawi 0:e63996fd7d3e 214 };
khaledelmadawi 0:e63996fd7d3e 215
khaledelmadawi 0:e63996fd7d3e 216 #endif /* _HELPER_3DMATH_H_ */