1 /* Copyright 2002-2016 CS Systèmes d'Information
2 * Licensed to CS Systèmes d'Information (CS) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * CS licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.orekit.utils;
18
19 import java.util.Collection;
20
21 import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
22 import org.apache.commons.math3.analysis.interpolation.HermiteInterpolator;
23 import org.apache.commons.math3.geometry.euclidean.threed.FieldRotation;
24 import org.apache.commons.math3.geometry.euclidean.threed.Rotation;
25 import org.apache.commons.math3.geometry.euclidean.threed.RotationConvention;
26 import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
27 import org.apache.commons.math3.util.FastMath;
28 import org.apache.commons.math3.util.MathArrays;
29 import org.orekit.errors.OrekitException;
30 import org.orekit.errors.OrekitInternalError;
31 import org.orekit.errors.OrekitMessages;
32 import org.orekit.time.AbsoluteDate;
33 import org.orekit.time.TimeStamped;
34
35 /** {@link TimeStamped time-stamped} version of {@link AngularCoordinates}.
36 * <p>Instances of this class are guaranteed to be immutable.</p>
37 * @author Luc Maisonobe
38 * @since 7.0
39 */
40 public class TimeStampedAngularCoordinates extends AngularCoordinates implements TimeStamped {
41
42 /** Serializable UID. */
43 private static final long serialVersionUID = 20140723L;
44
45 /** The date. */
46 private final AbsoluteDate date;
47
48 /** Builds a rotation/rotation rate pair.
49 * @param date coordinates date
50 * @param rotation rotation
51 * @param rotationRate rotation rate Ω (rad/s)
52 * @param rotationAcceleration rotation acceleration dΩ/dt (rad²/s²)
53 */
54 public TimeStampedAngularCoordinates(final AbsoluteDate date,
55 final Rotation rotation,
56 final Vector3D rotationRate,
57 final Vector3D rotationAcceleration) {
58 super(rotation, rotationRate, rotationAcceleration);
59 this.date = date;
60 }
61
62 /** Build the rotation that transforms a pair of pv coordinates into another pair.
63
64 * <p><em>WARNING</em>! This method requires much more stringent assumptions on
65 * its parameters than the similar {@link Rotation#Rotation(Vector3D, Vector3D,
66 * Vector3D, Vector3D) constructor} from the {@link Rotation Rotation} class.
67 * As far as the Rotation constructor is concerned, the {@code v₂} vector from
68 * the second pair can be slightly misaligned. The Rotation constructor will
69 * compensate for this misalignment and create a rotation that ensure {@code
70 * v₁ = r(u₁)} and {@code v₂ ∈ plane (r(u₁), r(u₂))}. <em>THIS IS NOT
71 * TRUE ANYMORE IN THIS CLASS</em>! As derivatives are involved and must be
72 * preserved, this constructor works <em>only</em> if the two pairs are fully
73 * consistent, i.e. if a rotation exists that fulfill all the requirements: {@code
74 * v₁ = r(u₁)}, {@code v₂ = r(u₂)}, {@code dv₁/dt = dr(u₁)/dt}, {@code dv₂/dt
75 * = dr(u₂)/dt}, {@code d²v₁/dt² = d²r(u₁)/dt²}, {@code d²v₂/dt² = d²r(u₂)/dt²}.</p>
76
77 * @param date coordinates date
78 * @param u1 first vector of the origin pair
79 * @param u2 second vector of the origin pair
80 * @param v1 desired image of u1 by the rotation
81 * @param v2 desired image of u2 by the rotation
82 * @param tolerance relative tolerance factor used to check singularities
83 * @exception OrekitException if the vectors components cannot be converted to
84 * {@link DerivativeStructure} with proper order
85 */
86 public TimeStampedAngularCoordinates(final AbsoluteDate date,
87 final PVCoordinates u1, final PVCoordinates u2,
88 final PVCoordinates v1, final PVCoordinates v2,
89 final double tolerance)
90 throws OrekitException {
91 super(u1, u2, v1, v2, tolerance);
92 this.date = date;
93 }
94
95 /** Build one of the rotations that transform one pv coordinates into another one.
96
97 * <p>Except for a possible scale factor, if the instance were
98 * applied to the vector u it will produce the vector v. There is an
99 * infinite number of such rotations, this constructor choose the
100 * one with the smallest associated angle (i.e. the one whose axis
101 * is orthogonal to the (u, v) plane). If u and v are collinear, an
102 * arbitrary rotation axis is chosen.</p>
103
104 * @param date coordinates date
105 * @param u origin vector
106 * @param v desired image of u by the rotation
107 * @exception OrekitException if the vectors components cannot be converted to
108 * {@link DerivativeStructure} with proper order
109 */
110 public TimeStampedAngularCoordinates(final AbsoluteDate date,
111 final PVCoordinates u, final PVCoordinates v)
112 throws OrekitException {
113 super(u, v);
114 this.date = date;
115 }
116
117 /** Builds a TimeStampedAngularCoordinates from a {@link FieldRotation}<{@link DerivativeStructure}>.
118 * <p>
119 * The rotation components must have time as their only derivation parameter and
120 * have consistent derivation orders.
121 * </p>
122 * @param date coordinates date
123 * @param r rotation with time-derivatives embedded within the coordinates
124 */
125 public TimeStampedAngularCoordinates(final AbsoluteDate date,
126 final FieldRotation<DerivativeStructure> r) {
127 super(r);
128 this.date = date;
129 }
130
131 /** {@inheritDoc} */
132 public AbsoluteDate getDate() {
133 return date;
134 }
135
136 /** Revert a rotation/rotation rate pair.
137 * Build a pair which reverse the effect of another pair.
138 * @return a new pair whose effect is the reverse of the effect
139 * of the instance
140 */
141 public TimeStampedAngularCoordinates revert() {
142 return new TimeStampedAngularCoordinates(date,
143 getRotation().revert(),
144 getRotation().applyInverseTo(getRotationRate().negate()),
145 getRotation().applyInverseTo(getRotationAcceleration().negate()));
146 }
147
148 /** Get a time-shifted state.
149 * <p>
150 * The state can be slightly shifted to close dates. This shift is based on
151 * a simple linear model. It is <em>not</em> intended as a replacement for
152 * proper attitude propagation but should be sufficient for either small
153 * time shifts or coarse accuracy.
154 * </p>
155 * @param dt time shift in seconds
156 * @return a new state, shifted with respect to the instance (which is immutable)
157 */
158 public TimeStampedAngularCoordinates shiftedBy(final double dt) {
159 final AngularCoordinates sac = super.shiftedBy(dt);
160 return new TimeStampedAngularCoordinates(date.shiftedBy(dt),
161 sac.getRotation(), sac.getRotationRate(), sac.getRotationAcceleration());
162
163 }
164
165 /** Add an offset from the instance.
166 * <p>
167 * We consider here that the offset rotation is applied first and the
168 * instance is applied afterward. Note that angular coordinates do <em>not</em>
169 * commute under this operation, i.e. {@code a.addOffset(b)} and {@code
170 * b.addOffset(a)} lead to <em>different</em> results in most cases.
171 * </p>
172 * <p>
173 * The two methods {@link #addOffset(AngularCoordinates) addOffset} and
174 * {@link #subtractOffset(AngularCoordinates) subtractOffset} are designed
175 * so that round trip applications are possible. This means that both {@code
176 * ac1.subtractOffset(ac2).addOffset(ac2)} and {@code
177 * ac1.addOffset(ac2).subtractOffset(ac2)} return angular coordinates equal to ac1.
178 * </p>
179 * @param offset offset to subtract
180 * @return new instance, with offset subtracted
181 * @see #subtractOffset(AngularCoordinates)
182 */
183 @Override
184 public TimeStampedAngularCoordinates addOffset(final AngularCoordinates offset) {
185 final Vector3D rOmega = getRotation().applyTo(offset.getRotationRate());
186 final Vector3D rOmegaDot = getRotation().applyTo(offset.getRotationAcceleration());
187 return new TimeStampedAngularCoordinates(date,
188 getRotation().compose(offset.getRotation(), RotationConvention.VECTOR_OPERATOR),
189 getRotationRate().add(rOmega),
190 new Vector3D( 1.0, getRotationAcceleration(),
191 1.0, rOmegaDot,
192 -1.0, Vector3D.crossProduct(getRotationRate(), rOmega)));
193 }
194
195 /** Subtract an offset from the instance.
196 * <p>
197 * We consider here that the offset rotation is applied first and the
198 * instance is applied afterward. Note that angular coordinates do <em>not</em>
199 * commute under this operation, i.e. {@code a.subtractOffset(b)} and {@code
200 * b.subtractOffset(a)} lead to <em>different</em> results in most cases.
201 * </p>
202 * <p>
203 * The two methods {@link #addOffset(AngularCoordinates) addOffset} and
204 * {@link #subtractOffset(AngularCoordinates) subtractOffset} are designed
205 * so that round trip applications are possible. This means that both {@code
206 * ac1.subtractOffset(ac2).addOffset(ac2)} and {@code
207 * ac1.addOffset(ac2).subtractOffset(ac2)} return angular coordinates equal to ac1.
208 * </p>
209 * @param offset offset to subtract
210 * @return new instance, with offset subtracted
211 * @see #addOffset(AngularCoordinates)
212 */
213 @Override
214 public TimeStampedAngularCoordinates subtractOffset(final AngularCoordinates offset) {
215 return addOffset(offset.revert());
216 }
217
218 /** Interpolate angular coordinates.
219 * <p>
220 * The interpolated instance is created by polynomial Hermite interpolation
221 * on Rodrigues vector ensuring rotation rate remains the exact derivative of rotation.
222 * </p>
223 * <p>
224 * This method is based on Sergei Tanygin's paper <a
225 * href="http://www.agi.com/downloads/resources/white-papers/Attitude-interpolation.pdf">Attitude
226 * Interpolation</a>, changing the norm of the vector to match the modified Rodrigues
227 * vector as described in Malcolm D. Shuster's paper <a
228 * href="http://www.ladispe.polito.it/corsi/Meccatronica/02JHCOR/2011-12/Slides/Shuster_Pub_1993h_J_Repsurv_scan.pdf">A
229 * Survey of Attitude Representations</a>. This change avoids the singularity at π.
230 * There is still a singularity at 2π, which is handled by slightly offsetting all rotations
231 * when this singularity is detected.
232 * </p>
233 * <p>
234 * Note that even if first and second time derivatives (rotation rates and acceleration)
235 * from sample can be ignored, the interpolated instance always includes
236 * interpolated derivatives. This feature can be used explicitly to
237 * compute these derivatives when it would be too complex to compute them
238 * from an analytical formula: just compute a few sample points from the
239 * explicit formula and set the derivatives to zero in these sample points,
240 * then use interpolation to add derivatives consistent with the rotations.
241 * </p>
242 * @param date interpolation date
243 * @param filter filter for derivatives from the sample to use in interpolation
244 * @param sample sample points on which interpolation should be done
245 * @return a new position-velocity, interpolated at specified date
246 * @exception OrekitException if the number of point is too small for interpolating
247 */
248 public static TimeStampedAngularCoordinates interpolate(final AbsoluteDate date,
249 final AngularDerivativesFilter filter,
250 final Collection<TimeStampedAngularCoordinates> sample)
251 throws OrekitException {
252
253 // set up safety elements for 2π singularity avoidance
254 final double epsilon = 2 * FastMath.PI / sample.size();
255 final double threshold = FastMath.min(-(1.0 - 1.0e-4), -FastMath.cos(epsilon / 4));
256
257 // set up a linear model canceling mean rotation rate
258 final Vector3D meanRate;
259 if (filter != AngularDerivativesFilter.USE_R) {
260 Vector3D sum = Vector3D.ZERO;
261 for (final TimeStampedAngularCoordinates datedAC : sample) {
262 sum = sum.add(datedAC.getRotationRate());
263 }
264 meanRate = new Vector3D(1.0 / sample.size(), sum);
265 } else {
266 if (sample.size() < 2) {
267 throw new OrekitException(OrekitMessages.NOT_ENOUGH_DATA_FOR_INTERPOLATION,
268 sample.size());
269 }
270 Vector3D sum = Vector3D.ZERO;
271 TimeStampedAngularCoordinates previous = null;
272 for (final TimeStampedAngularCoordinates datedAC : sample) {
273 if (previous != null) {
274 sum = sum.add(estimateRate(previous.getRotation(), datedAC.getRotation(),
275 datedAC.date.durationFrom(previous.date)));
276 }
277 previous = datedAC;
278 }
279 meanRate = new Vector3D(1.0 / (sample.size() - 1), sum);
280 }
281 TimeStampedAngularCoordinates offset =
282 new TimeStampedAngularCoordinates(date, Rotation.IDENTITY, meanRate, Vector3D.ZERO);
283
284 boolean restart = true;
285 for (int i = 0; restart && i < sample.size() + 2; ++i) {
286
287 // offset adaptation parameters
288 restart = false;
289
290 // set up an interpolator taking derivatives into account
291 final HermiteInterpolator interpolator = new HermiteInterpolator();
292
293 // add sample points
294 double sign = +1.0;
295 Rotation previous = Rotation.IDENTITY;
296
297 for (final TimeStampedAngularCoordinates ac : sample) {
298
299 // remove linear offset from the current coordinates
300 final double dt = ac.date.durationFrom(date);
301 final TimeStampedAngularCoordinates fixed = ac.subtractOffset(offset.shiftedBy(dt));
302
303 // make sure all interpolated points will be on the same branch
304 final double dot = MathArrays.linearCombination(fixed.getRotation().getQ0(), previous.getQ0(),
305 fixed.getRotation().getQ1(), previous.getQ1(),
306 fixed.getRotation().getQ2(), previous.getQ2(),
307 fixed.getRotation().getQ3(), previous.getQ3());
308 sign = FastMath.copySign(1.0, dot * sign);
309 previous = fixed.getRotation();
310
311 // check modified Rodrigues vector singularity
312 if (fixed.getRotation().getQ0() * sign < threshold) {
313 // the sample point is close to a modified Rodrigues vector singularity
314 // we need to change the linear offset model to avoid this
315 restart = true;
316 break;
317 }
318
319 final double[][] rodrigues = fixed.getModifiedRodrigues(sign);
320 switch (filter) {
321 case USE_RRA:
322 // populate sample with rotation, rotation rate and acceleration data
323 interpolator.addSamplePoint(dt, rodrigues[0], rodrigues[1], rodrigues[2]);
324 break;
325 case USE_RR:
326 // populate sample with rotation and rotation rate data
327 interpolator.addSamplePoint(dt, rodrigues[0], rodrigues[1]);
328 break;
329 case USE_R:
330 // populate sample with rotation data only
331 interpolator.addSamplePoint(dt, rodrigues[0]);
332 break;
333 default :
334 // this should never happen
335 throw new OrekitInternalError(null);
336 }
337 }
338
339 if (restart) {
340 // interpolation failed, some intermediate rotation was too close to 2π
341 // we need to offset all rotations to avoid the singularity
342 offset = offset.addOffset(new AngularCoordinates(new Rotation(Vector3D.PLUS_I,
343 epsilon,
344 RotationConvention.VECTOR_OPERATOR),
345 Vector3D.ZERO, Vector3D.ZERO));
346 } else {
347 // interpolation succeeded with the current offset
348 final DerivativeStructure zero = new DerivativeStructure(1, 2, 0, 0.0);
349 final DerivativeStructure[] p = interpolator.value(zero);
350 final AngularCoordinates ac = createFromModifiedRodrigues(new double[][] {
351 {
352 p[0].getValue(), p[1].getValue(), p[2].getValue()
353 }, {
354 p[0].getPartialDerivative(1), p[1].getPartialDerivative(1), p[2].getPartialDerivative(1)
355 }, {
356 p[0].getPartialDerivative(2), p[1].getPartialDerivative(2), p[2].getPartialDerivative(2)
357 }
358 });
359 return new TimeStampedAngularCoordinates(offset.getDate(),
360 ac.getRotation(),
361 ac.getRotationRate(),
362 ac.getRotationAcceleration()).addOffset(offset);
363 }
364
365 }
366
367 // this should never happen
368 throw new OrekitInternalError(null);
369
370 }
371
372 }