1 /* Copyright 2002-2022 CS GROUP
2 * Licensed to CS GROUP (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.hipparchus.analysis.differentiation.Derivative;
22 import org.hipparchus.analysis.interpolation.HermiteInterpolator;
23 import org.hipparchus.geometry.euclidean.threed.FieldRotation;
24 import org.hipparchus.geometry.euclidean.threed.Rotation;
25 import org.hipparchus.geometry.euclidean.threed.RotationConvention;
26 import org.hipparchus.geometry.euclidean.threed.Vector3D;
27 import org.hipparchus.util.FastMath;
28 import org.hipparchus.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 */
84 public TimeStampedAngularCoordinates(final AbsoluteDate date,
85 final PVCoordinates u1, final PVCoordinates u2,
86 final PVCoordinates v1, final PVCoordinates v2,
87 final double tolerance) {
88 super(u1, u2, v1, v2, tolerance);
89 this.date = date;
90 }
91
92 /** Build one of the rotations that transform one pv coordinates into another one.
93
94 * <p>Except for a possible scale factor, if the instance were
95 * applied to the vector u it will produce the vector v. There is an
96 * infinite number of such rotations, this constructor choose the
97 * one with the smallest associated angle (i.e. the one whose axis
98 * is orthogonal to the (u, v) plane). If u and v are collinear, an
99 * arbitrary rotation axis is chosen.</p>
100
101 * @param date coordinates date
102 * @param u origin vector
103 * @param v desired image of u by the rotation
104 */
105 public TimeStampedAngularCoordinates(final AbsoluteDate date,
106 final PVCoordinates u, final PVCoordinates v) {
107 super(u, v);
108 this.date = date;
109 }
110
111 /** Builds a TimeStampedAngularCoordinates from a {@link FieldRotation}<{@link Derivative}>.
112 * <p>
113 * The rotation components must have time as their only derivation parameter and
114 * have consistent derivation orders.
115 * </p>
116 * @param date coordinates date
117 * @param r rotation with time-derivatives embedded within the coordinates
118 * @param <U> type of the derivative
119 */
120 public <U extends Derivative<U>>TimeStampedAngularCoordinates(final AbsoluteDate date,
121 final FieldRotation<U> r) {
122 super(r);
123 this.date = date;
124 }
125
126 /** {@inheritDoc} */
127 public AbsoluteDate getDate() {
128 return date;
129 }
130
131 /** Revert a rotation/rotation rate pair.
132 * Build a pair which reverse the effect of another pair.
133 * @return a new pair whose effect is the reverse of the effect
134 * of the instance
135 */
136 public TimeStampedAngularCoordinates revert() {
137 return new TimeStampedAngularCoordinates(date,
138 getRotation().revert(),
139 getRotation().applyInverseTo(getRotationRate().negate()),
140 getRotation().applyInverseTo(getRotationAcceleration().negate()));
141 }
142
143 /** Get a time-shifted state.
144 * <p>
145 * The state can be slightly shifted to close dates. This shift is based on
146 * a simple linear model. It is <em>not</em> intended as a replacement for
147 * proper attitude propagation but should be sufficient for either small
148 * time shifts or coarse accuracy.
149 * </p>
150 * @param dt time shift in seconds
151 * @return a new state, shifted with respect to the instance (which is immutable)
152 */
153 public TimeStampedAngularCoordinates shiftedBy(final double dt) {
154 final AngularCoordinates sac = super.shiftedBy(dt);
155 return new TimeStampedAngularCoordinates(date.shiftedBy(dt),
156 sac.getRotation(), sac.getRotationRate(), sac.getRotationAcceleration());
157
158 }
159
160 /** Add an offset from the instance.
161 * <p>
162 * We consider here that the offset rotation is applied first and the
163 * instance is applied afterward. Note that angular coordinates do <em>not</em>
164 * commute under this operation, i.e. {@code a.addOffset(b)} and {@code
165 * b.addOffset(a)} lead to <em>different</em> results in most cases.
166 * </p>
167 * <p>
168 * The two methods {@link #addOffset(AngularCoordinates) addOffset} and
169 * {@link #subtractOffset(AngularCoordinates) subtractOffset} are designed
170 * so that round trip applications are possible. This means that both {@code
171 * ac1.subtractOffset(ac2).addOffset(ac2)} and {@code
172 * ac1.addOffset(ac2).subtractOffset(ac2)} return angular coordinates equal to ac1.
173 * </p>
174 * @param offset offset to subtract
175 * @return new instance, with offset subtracted
176 * @see #subtractOffset(AngularCoordinates)
177 */
178 @Override
179 public TimeStampedAngularCoordinates addOffset(final AngularCoordinates offset) {
180 final Vector3D rOmega = getRotation().applyTo(offset.getRotationRate());
181 final Vector3D rOmegaDot = getRotation().applyTo(offset.getRotationAcceleration());
182 return new TimeStampedAngularCoordinates(date,
183 getRotation().compose(offset.getRotation(), RotationConvention.VECTOR_OPERATOR),
184 getRotationRate().add(rOmega),
185 new Vector3D( 1.0, getRotationAcceleration(),
186 1.0, rOmegaDot,
187 -1.0, Vector3D.crossProduct(getRotationRate(), rOmega)));
188 }
189
190 /** Subtract an offset from the instance.
191 * <p>
192 * We consider here that the offset rotation is applied first and the
193 * instance is applied afterward. Note that angular coordinates do <em>not</em>
194 * commute under this operation, i.e. {@code a.subtractOffset(b)} and {@code
195 * b.subtractOffset(a)} lead to <em>different</em> results in most cases.
196 * </p>
197 * <p>
198 * The two methods {@link #addOffset(AngularCoordinates) addOffset} and
199 * {@link #subtractOffset(AngularCoordinates) subtractOffset} are designed
200 * so that round trip applications are possible. This means that both {@code
201 * ac1.subtractOffset(ac2).addOffset(ac2)} and {@code
202 * ac1.addOffset(ac2).subtractOffset(ac2)} return angular coordinates equal to ac1.
203 * </p>
204 * @param offset offset to subtract
205 * @return new instance, with offset subtracted
206 * @see #addOffset(AngularCoordinates)
207 */
208 @Override
209 public TimeStampedAngularCoordinates subtractOffset(final AngularCoordinates offset) {
210 return addOffset(offset.revert());
211 }
212
213 /** Interpolate angular coordinates.
214 * <p>
215 * The interpolated instance is created by polynomial Hermite interpolation
216 * on Rodrigues vector ensuring rotation rate remains the exact derivative of rotation.
217 * </p>
218 * <p>
219 * This method is based on Sergei Tanygin's paper <a
220 * href="http://www.agi.com/resources/white-papers/attitude-interpolation">Attitude
221 * Interpolation</a>, changing the norm of the vector to match the modified Rodrigues
222 * vector as described in Malcolm D. Shuster's paper <a
223 * href="http://www.ladispe.polito.it/corsi/Meccatronica/02JHCOR/2011-12/Slides/Shuster_Pub_1993h_J_Repsurv_scan.pdf">A
224 * Survey of Attitude Representations</a>. This change avoids the singularity at π.
225 * There is still a singularity at 2π, which is handled by slightly offsetting all rotations
226 * when this singularity is detected. Another change is that the mean linear motion
227 * is first removed before interpolation and added back after interpolation. This allows
228 * to use interpolation even when the sample covers much more than one turn and even
229 * when sample points are separated by more than one turn.
230 * </p>
231 * <p>
232 * Note that even if first and second time derivatives (rotation rates and acceleration)
233 * from sample can be ignored, the interpolated instance always includes
234 * interpolated derivatives. This feature can be used explicitly to
235 * compute these derivatives when it would be too complex to compute them
236 * from an analytical formula: just compute a few sample points from the
237 * explicit formula and set the derivatives to zero in these sample points,
238 * then use interpolation to add derivatives consistent with the rotations.
239 * </p>
240 * @param date interpolation date
241 * @param filter filter for derivatives from the sample to use in interpolation
242 * @param sample sample points on which interpolation should be done
243 * @return a new position-velocity, interpolated at specified date
244 */
245 public static TimeStampedAngularCoordinates interpolate(final AbsoluteDate date,
246 final AngularDerivativesFilter filter,
247 final Collection<TimeStampedAngularCoordinates> sample) {
248
249 // set up safety elements for 2π singularity avoidance
250 final double epsilon = 2 * FastMath.PI / sample.size();
251 final double threshold = FastMath.min(-(1.0 - 1.0e-4), -FastMath.cos(epsilon / 4));
252
253 // set up a linear model canceling mean rotation rate
254 final Vector3D meanRate;
255 if (filter != AngularDerivativesFilter.USE_R) {
256 Vector3D sum = Vector3D.ZERO;
257 for (final TimeStampedAngularCoordinates datedAC : sample) {
258 sum = sum.add(datedAC.getRotationRate());
259 }
260 meanRate = new Vector3D(1.0 / sample.size(), sum);
261 } else {
262 if (sample.size() < 2) {
263 throw new OrekitException(OrekitMessages.NOT_ENOUGH_DATA_FOR_INTERPOLATION,
264 sample.size());
265 }
266 Vector3D sum = Vector3D.ZERO;
267 TimeStampedAngularCoordinates previous = null;
268 for (final TimeStampedAngularCoordinates datedAC : sample) {
269 if (previous != null) {
270 sum = sum.add(estimateRate(previous.getRotation(), datedAC.getRotation(),
271 datedAC.date.durationFrom(previous.date)));
272 }
273 previous = datedAC;
274 }
275 meanRate = new Vector3D(1.0 / (sample.size() - 1), sum);
276 }
277 TimeStampedAngularCoordinates offset =
278 new TimeStampedAngularCoordinates(date, Rotation.IDENTITY, meanRate, Vector3D.ZERO);
279
280 boolean restart = true;
281 for (int i = 0; restart && i < sample.size() + 2; ++i) {
282
283 // offset adaptation parameters
284 restart = false;
285
286 // set up an interpolator taking derivatives into account
287 final HermiteInterpolator interpolator = new HermiteInterpolator();
288
289 // add sample points
290 double sign = +1.0;
291 Rotation previous = Rotation.IDENTITY;
292
293 for (final TimeStampedAngularCoordinates ac : sample) {
294
295 // remove linear offset from the current coordinates
296 final double dt = ac.date.durationFrom(date);
297 final TimeStampedAngularCoordinates fixed = ac.subtractOffset(offset.shiftedBy(dt));
298
299 // make sure all interpolated points will be on the same branch
300 final double dot = MathArrays.linearCombination(fixed.getRotation().getQ0(), previous.getQ0(),
301 fixed.getRotation().getQ1(), previous.getQ1(),
302 fixed.getRotation().getQ2(), previous.getQ2(),
303 fixed.getRotation().getQ3(), previous.getQ3());
304 sign = FastMath.copySign(1.0, dot * sign);
305 previous = fixed.getRotation();
306
307 // check modified Rodrigues vector singularity
308 if (fixed.getRotation().getQ0() * sign < threshold) {
309 // the sample point is close to a modified Rodrigues vector singularity
310 // we need to change the linear offset model to avoid this
311 restart = true;
312 break;
313 }
314
315 final double[][] rodrigues = fixed.getModifiedRodrigues(sign);
316 switch (filter) {
317 case USE_RRA:
318 // populate sample with rotation, rotation rate and acceleration data
319 interpolator.addSamplePoint(dt, rodrigues[0], rodrigues[1], rodrigues[2]);
320 break;
321 case USE_RR:
322 // populate sample with rotation and rotation rate data
323 interpolator.addSamplePoint(dt, rodrigues[0], rodrigues[1]);
324 break;
325 case USE_R:
326 // populate sample with rotation data only
327 interpolator.addSamplePoint(dt, rodrigues[0]);
328 break;
329 default :
330 // this should never happen
331 throw new OrekitInternalError(null);
332 }
333 }
334
335 if (restart) {
336 // interpolation failed, some intermediate rotation was too close to 2π
337 // we need to offset all rotations to avoid the singularity
338 offset = offset.addOffset(new AngularCoordinates(new Rotation(Vector3D.PLUS_I,
339 epsilon,
340 RotationConvention.VECTOR_OPERATOR),
341 Vector3D.ZERO, Vector3D.ZERO));
342 } else {
343 // interpolation succeeded with the current offset
344 final double[][] p = interpolator.derivatives(0.0, 2);
345 final AngularCoordinates ac = createFromModifiedRodrigues(p);
346 return new TimeStampedAngularCoordinates(offset.getDate(),
347 ac.getRotation(),
348 ac.getRotationRate(),
349 ac.getRotationAcceleration()).addOffset(offset);
350 }
351
352 }
353
354 // this should never happen
355 throw new OrekitInternalError(null);
356
357 }
358
359 }