hpp-bezier-com-traj 4.14.0
Multi contact trajectory generation for the COM using Bezier curves
Loading...
Searching...
No Matches
waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh
Go to the documentation of this file.
1#ifndef BEZIER_COM_TRAJ_C0_DC0_DDC0_J0_X3_J1_DDC1_DC1_C1_HH
2#define BEZIER_COM_TRAJ_C0_DC0_DDC0_J0_X3_J1_DDC1_DC1_C1_HH
3
4/*
5 * Copyright 2018, LAAS-CNRS
6 * Author: Pierre Fernbach
7 */
8
10
11namespace bezier_com_traj {
12namespace c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1 {
13
14static const ConstraintFlag flag = INIT_POS | INIT_VEL | INIT_ACC | END_ACC |
17static const size_t DIM_VAR = 9;
18static const size_t DIM_POINT = 3;
22
31// TODO
32inline waypoint_t evaluateCurveWaypointAtTime(const std::vector<point_t>& pi,
33 double t) {
34 waypoint_t wp = initwp(DIM_POINT, DIM_VAR);
35 const double t2 = t * t;
36 const double t3 = t2 * t;
37 const double t4 = t3 * t;
38 const double t5 = t4 * t;
39 const double t6 = t5 * t;
40 const double t7 = t6 * t;
41 const double t8 = t7 * t;
42 const double t9 = t8 * t;
43 const double t10 = t9 * t;
44
45 // equation found with sympy
46 wp.first.block<3, 3>(0, 0) =
47 Matrix3::Identity() *
48 (t4 * 210.0 - t5 * 1260.0 + t6 * 3150.0 - 4200.0 * t7 + 3150.0 * t8 -
49 1260.0 * t9 + 210.0 * t10); // x0
50 wp.first.block<3, 3>(0, 3) =
51 Matrix3::Identity() * (252.0 * t5 - 1260.0 * t6 + 2520.0 * t7 -
52 2520.0 * t8 + 1260.0 * t9 - 252.0 * t10); // x1
53 wp.first.block<3, 3>(0, 6) =
54 Matrix3::Identity() *
55 (210.0 * t6 - 840.0 * t7 + 1260.0 * t8 - 840.0 * t9 + 210.0 * t10); // x2
56 wp.second =
57 1.0 * pi[0] + t * (-10.0 * pi[0] + 10.0 * pi[1]) +
58 t2 * (45.0 * pi[0] - 90.0 * pi[1] + 45.0 * pi[2]) +
59 t3 * (-120.0 * pi[0] + 360.0 * pi[1] - 360.0 * pi[2] + 120.0 * pi[3]) +
60 t4 * (210.0 * pi[0] - 840.0 * pi[1] + 1260.0 * pi[2] - 840.0 * pi[3]) +
61 t5 * (-252.0 * pi[0] + 1260.0 * pi[1] - 2520.0 * pi[2] + 2520.0 * pi[3]) +
62 t6 * (210.0 * pi[0] - 1260.0 * pi[1] + 3150.0 * pi[2] - 4200.0 * pi[3]) +
63 t7 * (-120.0 * pi[0] + 840.0 * pi[1] - 2520.0 * pi[2] + 4200.0 * pi[3] +
64 120.0 * pi[7]) +
65 t8 * (45.0 * pi[0] - 360.0 * pi[1] + 1260.0 * pi[2] - 2520.0 * pi[3] -
66 360.0 * pi[7] + 45.0 * pi[8]) +
67 t9 * (-10.0 * pi[0] + 90.0 * pi[1] - 360.0 * pi[2] + 840.0 * pi[3] +
68 360.0 * pi[7] - 90.0 * pi[8] + 10.0 * pi[9]) +
69 t10 * (1.0 * pi[0] + 1.0 * pi[10] - 10.0 * pi[1] + 45.0 * pi[2] -
70 120.0 * pi[3] - 120.0 * pi[7] + 45.0 * pi[8] - 10.0 * pi[9]);
71 return wp;
72}
73
74// TODO
76 const std::vector<point_t>& pi, double T, double t) {
77 waypoint_t wp = initwp(DIM_POINT, DIM_VAR);
78 const double alpha = 1. / (T);
79 const double t2 = t * t;
80 const double t3 = t2 * t;
81 const double t4 = t3 * t;
82 const double t5 = t4 * t;
83 const double t6 = t5 * t;
84 const double t7 = t6 * t;
85 const double t8 = t7 * t;
86 const double t9 = t8 * t;
87 // equation found with sympy
88 wp.first.block<3, 3>(0, 0) =
89 Matrix3::Identity() * alpha *
90 (1.0 * (2100.0 * t9 - 11340.0 * t8 + 25200.0 * t7 - 29400.0 * t6 +
91 18900.0 * t5 - 6300.0 * t4 + 840.0 * t3)); // x0
92 wp.first.block<3, 3>(0, 3) =
93 Matrix3::Identity() * alpha *
94 (1.0 * (-2520.0 * t9 + 11340.0 * t8 - 20160.0 * t7 + 17640.0 * t6 -
95 7560.0 * t5 + 1260.0 * t4)); // x1
96 wp.first.block<3, 3>(0, 6) =
97 Matrix3::Identity() * alpha *
98 (1.0 * (2100.0 * t9 - 7560.0 * t8 + 10080.0 * t7 - 5880.0 * t6 +
99 1260.0 * t5)); // x2
100 wp.second =
101 (1.0 * (-10.0 * pi[0] + 10.0 * pi[1]) +
102 t * (1.0 * (90.0 * pi[0] - 180.0 * pi[1] + 90.0 * pi[2])) +
103 t2 * (1.0 * (-360.0 * pi[0] + 1080.0 * pi[1] - 1080.0 * pi[2] +
104 360.0 * pi[3])) +
105 t3 * (1.0 *
106 (-90.0 * pi[0] + 810.0 * pi[1] - 3240.0 * pi[2] + 7560.0 * pi[3] +
107 3240.0 * pi[7] - 810.0 * pi[8] + 90.0 * pi[9])) +
108 t4 * (1.0 * (840.0 * pi[0] - 3360.0 * pi[1] + 5040.0 * pi[2] -
109 3360.0 * pi[3])) +
110 t5 * (1.0 * (10.0 * pi[0] + 10.0 * pi[10] - 100.0 * pi[1] +
111 450.0 * pi[2] - 1200.0 * pi[3] - 1200.0 * pi[7] +
112 450.0 * pi[8] - 100.0 * pi[9])) +
113 t6 * (1.0 * (-1260.0 * pi[0] + 6300.0 * pi[1] - 12600.0 * pi[2] +
114 12600.0 * pi[3])) +
115 t7 * (1.0 * (1260.0 * pi[0] - 7560.0 * pi[1] + 18900.0 * pi[2] -
116 25200.0 * pi[3])) +
117 t8 * (1.0 * (-840.0 * pi[0] + 5880.0 * pi[1] - 17640.0 * pi[2] +
118 29400.0 * pi[3] + 840.0 * pi[7])) +
119 t9 * (1.0 * (360.0 * pi[0] - 2880.0 * pi[1] + 10080.0 * pi[2] -
120 20160.0 * pi[3] - 2880.0 * pi[7] + 360.0 * pi[8]))) *
121 alpha;
122 return wp;
123}
124
125// TODO
127 const std::vector<point_t>& pi, double T, double t) {
128 waypoint_t wp = initwp(DIM_POINT, DIM_VAR);
129 const double alpha = 1. / (T * T);
130 const double t2 = t * t;
131 const double t3 = t2 * t;
132 const double t4 = t3 * t;
133 const double t5 = t4 * t;
134 const double t6 = t5 * t;
135 const double t7 = t6 * t;
136 const double t8 = t7 * t;
137 // equation found with sympy
138 wp.first.block<3, 3>(0, 0) =
139 Matrix3::Identity() * alpha *
140 (1.0 * (18900.0 * t8 - 90720.0 * t7 + 176400.0 * t6 - 176400.0 * t5 +
141 94500.0 * t4 - 25200.0 * t3 + 2520.0 * t2)); // x0
142 wp.first.block<3, 3>(0, 3) =
143 Matrix3::Identity() * alpha *
144 (1.0 * (-22680.0 * t8 + 90720.0 * t7 - 141120.0 * t6 + 105840.0 * t5 -
145 37800.0 * t4 + 5040.0 * t3)); // x1
146 wp.first.block<3, 3>(0, 6) =
147 Matrix3::Identity() * alpha *
148 (1.0 * (18900.0 * t8 - 60480.0 * t7 + 70560.0 * t6 - 35280.0 * t5 +
149 6300.0 * t4)); // x2
150 wp.second =
151 (1.0 * (90.0 * pi[0] - 180.0 * pi[1] + 90.0 * pi[2]) +
152 t * (1.0 * (-720.0 * pi[0] + 2160.0 * pi[1] - 2160.0 * pi[2] +
153 720.0 * pi[3])) +
154 t2 * (1.0 * (2520.0 * pi[0] - 10080.0 * pi[1] + 15120.0 * pi[2] -
155 10080.0 * pi[3])) +
156 t3 * (1.0 * (90.0 * pi[0] + 90.0 * pi[10] - 900.0 * pi[1] +
157 4050.0 * pi[2] - 10800.0 * pi[3] - 10800.0 * pi[7] +
158 4050.0 * pi[8] - 900.0 * pi[9])) +
159 t4 * (1.0 * (-5040.0 * pi[0] + 25200.0 * pi[1] - 50400.0 * pi[2] +
160 50400.0 * pi[3])) +
161 t5 * (1.0 * (6300.0 * pi[0] - 37800.0 * pi[1] + 94500.0 * pi[2] -
162 126000.0 * pi[3])) +
163 t6 * (1.0 * (-5040.0 * pi[0] + 35280.0 * pi[1] - 105840.0 * pi[2] +
164 176400.0 * pi[3] + 5040.0 * pi[7])) +
165 t7 * (1.0 * (2520.0 * pi[0] - 20160.0 * pi[1] + 70560.0 * pi[2] -
166 141120.0 * pi[3] - 20160.0 * pi[7] + 2520.0 * pi[8])) +
167 t8 * (1.0 * (-720.0 * pi[0] + 6480.0 * pi[1] - 25920.0 * pi[2] +
168 60480.0 * pi[3] + 25920.0 * pi[7] - 6480.0 * pi[8] +
169 720.0 * pi[9]))) *
170 alpha;
171 return wp;
172}
173
174// TODO
176 const std::vector<point_t>& pi, double T, double t) {
177 waypoint_t wp = initwp(DIM_POINT, DIM_VAR);
178 const double alpha = 1. / (T * T * T);
179 const double t2 = t * t;
180 const double t3 = t2 * t;
181 const double t4 = t3 * t;
182 const double t5 = t4 * t;
183 const double t6 = t5 * t;
184 const double t7 = t6 * t;
185 // equation found with sympy
186 wp.first.block<3, 3>(0, 0) =
187 Matrix3::Identity() * alpha *
188 (1.0 * (151200.0 * t7 - 635040.0 * t6 + 1058400.0 * t5 - 882000.0 * t4 +
189 378000.0 * t3 - 75600.0 * t2 + 5040.0 * t)); // x0
190 wp.first.block<3, 3>(0, 3) =
191 Matrix3::Identity() * alpha *
192 (1.0 * (-181440.0 * t7 + 635040.0 * t6 - 846720.0 * t5 + 529200.0 * t4 -
193 151200.0 * t3 + 15120.0 * t2)); // x1
194 wp.first.block<3, 3>(0, 6) =
195 Matrix3::Identity() * alpha *
196 (1.0 * (151200.0 * t7 - 423360.0 * t6 + 423360.0 * t5 - 176400.0 * t4 +
197 25200.0 * t3)); // x2
198 wp.second =
199 (1.0 *
200 (-720.0 * pi[0] + 2160.0 * pi[1] - 2160.0 * pi[2] + 720.0 * pi[3]) +
201 t * (1.0 * (5040.0 * pi[0] - 20160.0 * pi[1] + 30240.0 * pi[2] -
202 20160.0 * pi[3])) +
203 t2 * (1.0 * (-15120.0 * pi[0] + 75600.0 * pi[1] - 151200.0 * pi[2] +
204 151200.0 * pi[3])) +
205 t3 * (1.0 * (25200.0 * pi[0] - 151200.0 * pi[1] + 378000.0 * pi[2] -
206 504000.0 * pi[3])) +
207 t4 * (1.0 * (-25200.0 * pi[0] + 176400.0 * pi[1] - 529200.0 * pi[2] +
208 882000.0 * pi[3] + 25200.0 * pi[7])) +
209 t5 * (1.0 * (15120.0 * pi[0] - 120960.0 * pi[1] + 423360.0 * pi[2] -
210 846720.0 * pi[3] - 120960.0 * pi[7] + 15120.0 * pi[8])) +
211 t6 * (1.0 * (-5040.0 * pi[0] + 45360.0 * pi[1] - 181440.0 * pi[2] +
212 423360.0 * pi[3] + 181440.0 * pi[7] - 45360.0 * pi[8] +
213 5040.0 * pi[9])) +
214 t7 * (1.0 * (720.0 * pi[0] + 720.0 * pi[10] - 7200.0 * pi[1] +
215 32400.0 * pi[2] - 86400.0 * pi[3] - 86400.0 * pi[7] +
216 32400.0 * pi[8] - 7200.0 * pi[9]))) *
217 alpha;
218 return wp;
219}
220
221inline std::vector<point_t> computeConstantWaypoints(const ProblemData& pData,
222 double T) {
223 // equation for constraint on initial and final position and velocity and
224 // initial acceleration(degree 5, 5 constant waypoint and one free (pi[3]))
225 // first, compute the constant waypoints that only depend on pData :
226 double n = 10.;
227 std::vector<point_t> pi;
228 pi.push_back(pData.c0_);
229 pi.push_back((pData.dc0_ * T / n) + pData.c0_);
230 pi.push_back((pData.ddc0_ * T * T / (n * (n - 1))) +
231 (2 * pData.dc0_ * T / n) +
232 pData.c0_); // * T because derivation make a T appear
233 pi.push_back((pData.j0_ * T * T * T / (n * (n - 1) * (n - 2))) +
234 (3 * pData.ddc0_ * T * T / (n * (n - 1))) +
235 (3 * pData.dc0_ * T / n) + pData.c0_);
236 pi.push_back(point_t::Zero());
237 pi.push_back(point_t::Zero());
238 pi.push_back(point_t::Zero());
239 pi.push_back((-pData.j1_ * T * T * T / (n * (n - 1) * (n - 2))) +
240 (3 * pData.ddc1_ * T * T / (n * (n - 1))) -
241 (3 * pData.dc1_ * T / n) + pData.c1_); // * T ??
242 pi.push_back((pData.ddc1_ * T * T / (n * (n - 1))) -
243 (2 * pData.dc1_ * T / n) + pData.c1_); // * T ??
244 pi.push_back((-pData.dc1_ * T / n) + pData.c1_); // * T ?
245 pi.push_back(pData.c1_);
246 return pi;
247}
248
249// TODO
250inline bezier_wp_t::t_point_t computeWwaypoints(const ProblemData& pData,
251 double T) {
252 bezier_wp_t::t_point_t wps;
253 // const int DIM_POINT = 6;
254 // const int DIM_VAR = 9;
255 std::vector<point_t> pi = computeConstantWaypoints(pData, T);
256 std::vector<Matrix3> Cpi;
257 for (std::size_t i = 0; i < pi.size(); ++i) {
258 Cpi.push_back(skew(pi[i]));
259 }
260 // const Vector3 g = pData.contacts_.front().contactPhase_->m_gravity;
261 // const Matrix3 Cg = skew(g);
262 // const double T2 = T * T;
263 // const double alpha = 1 / (T2);
264 std::cout << "NOT IMPLEMENTED YET" << std::endl;
265 return wps;
266}
267
268std::vector<waypoint_t> computeVelocityWaypoints(
269 const ProblemData& pData, const double T,
270 std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) {
271 if (pi.size() == 0) pi = computeConstantWaypoints(pData, T);
272
273 std::vector<waypoint_t> wps;
274 assert(pi.size() == 11);
275
276 double alpha = 1. / (T);
277 waypoint_t w = initwp(DIM_POINT, DIM_VAR);
278
279 // assign w0:
280 w.second = alpha * 10 * (-pi[0] + pi[1]);
281 wps.push_back(w);
282 w = initwp(DIM_POINT, DIM_VAR);
283 // assign w1:
284 w.second = alpha * 10 * (-pi[1] + pi[2]);
285 wps.push_back(w);
286 w = initwp(DIM_POINT, DIM_VAR);
287 // assign w2:
288 w.second = alpha * 10 * (-pi[2] + pi[3]);
289 wps.push_back(w);
290 w = initwp(DIM_POINT, DIM_VAR);
291 // assign w3:
292 w.first.block<3, 3>(0, 0) = 10 * alpha * Matrix3::Identity(); // x0
293 w.second = alpha * 10 * (-pi[3]);
294 wps.push_back(w);
295 w = initwp(DIM_POINT, DIM_VAR);
296 // assign w4:
297 w.first.block<3, 3>(0, 0) = -10 * alpha * Matrix3::Identity(); // x0
298 w.first.block<3, 3>(0, 3) = 10 * alpha * Matrix3::Identity(); // x1
299 wps.push_back(w);
300 w = initwp(DIM_POINT, DIM_VAR);
301 // assign w5:
302 w.first.block<3, 3>(0, 3) = -10 * alpha * Matrix3::Identity(); // x1
303 w.first.block<3, 3>(0, 6) = 10 * alpha * Matrix3::Identity(); // x2
304 wps.push_back(w);
305 w = initwp(DIM_POINT, DIM_VAR);
306 // assign w6:
307 w.first.block<3, 3>(0, 6) = -10 * alpha * Matrix3::Identity(); // x2
308 w.second = alpha * 10 * pi[7];
309 wps.push_back(w);
310 w = initwp(DIM_POINT, DIM_VAR);
311 // assign w7:
312 w.second = alpha * 10 * (-pi[7] + pi[8]);
313 wps.push_back(w);
314 w = initwp(DIM_POINT, DIM_VAR);
315 // assign w8:
316 w.second = alpha * 10 * (-pi[8] + pi[9]);
317 wps.push_back(w);
318 w = initwp(DIM_POINT, DIM_VAR);
319 // assign w9:
320 w.second = alpha * 10 * (pi[10] - pi[9]);
321 wps.push_back(w);
322 return wps;
323}
324
325std::vector<waypoint_t> computeAccelerationWaypoints(
326 const ProblemData& pData, const double T,
327 std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) {
328 if (pi.size() == 0) pi = computeConstantWaypoints(pData, T);
329
330 std::vector<waypoint_t> wps;
331 assert(pi.size() == 11);
332 double alpha = 1. / (T * T);
333
334 waypoint_t w = initwp(DIM_POINT, DIM_VAR);
335
336 // assign w0:
337 w.second = alpha * 90 * (pi[0] - 2 * pi[1] + pi[2]);
338 wps.push_back(w);
339 w = initwp(DIM_POINT, DIM_VAR);
340 // assign w1:
341 w.second = alpha * 90 * (pi[1] - 2 * pi[2] + pi[3]);
342 wps.push_back(w);
343 w = initwp(DIM_POINT, DIM_VAR);
344 // assign w2:
345 w.first.block<3, 3>(0, 0) = 90 * alpha * Matrix3::Identity(); // x0
346 w.second = alpha * 90 * (pi[2] - pi[3]);
347 wps.push_back(w);
348 w = initwp(DIM_POINT, DIM_VAR);
349 // assign w3:
350 w.first.block<3, 3>(0, 0) = -180 * alpha * Matrix3::Identity(); // x0
351 w.first.block<3, 3>(0, 3) = 90 * alpha * Matrix3::Identity(); // x1
352 w.second = alpha * 90 * pi[3];
353 wps.push_back(w);
354 w = initwp(DIM_POINT, DIM_VAR);
355 // assign w4:
356 w.first.block<3, 3>(0, 0) = 90 * alpha * Matrix3::Identity(); // x0
357 w.first.block<3, 3>(0, 3) = -180 * alpha * Matrix3::Identity(); // x1
358 w.first.block<3, 3>(0, 6) = 90 * alpha * Matrix3::Identity(); // x2
359 wps.push_back(w);
360 w = initwp(DIM_POINT, DIM_VAR);
361 // assign w5:
362 w.first.block<3, 3>(0, 3) = 90 * alpha * Matrix3::Identity(); // x1
363 w.first.block<3, 3>(0, 6) = -180 * alpha * Matrix3::Identity(); // x2
364 w.second = alpha * 90 * pi[7];
365 wps.push_back(w);
366 w = initwp(DIM_POINT, DIM_VAR);
367 // assign w6:
368 w.first.block<3, 3>(0, 6) = 90 * alpha * Matrix3::Identity(); // x2
369 w.second = alpha * 90 * (-2 * pi[7] + pi[8]);
370 wps.push_back(w);
371 w = initwp(DIM_POINT, DIM_VAR);
372 // assign w7:
373 w.second = alpha * 90 * (pi[7] - 2 * pi[8] + pi[9]);
374 wps.push_back(w);
375 wps.push_back(w);
376 w = initwp(DIM_POINT, DIM_VAR);
377 // assign w8:
378 w.second = alpha * 90 * (pi[10] + pi[8] - 2 * pi[9]);
379 wps.push_back(w);
380 return wps;
381}
382
383std::vector<waypoint_t> computeJerkWaypoints(
384 const ProblemData& pData, const double T,
385 std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) {
386 if (pi.size() == 0) pi = computeConstantWaypoints(pData, T);
387
388 std::vector<waypoint_t> wps;
389 assert(pi.size() == 11);
390
391 double alpha = 1. / (T * T * T);
392
393 waypoint_t w = initwp(DIM_POINT, DIM_VAR);
394
395 // assign w0:
396 w.second = alpha * 720 * (-pi[0] + 3 * pi[1] - 3 * pi[2] + pi[3]);
397 wps.push_back(w);
398 w = initwp(DIM_POINT, DIM_VAR);
399 // assign w1:
400 w.first.block<3, 3>(0, 0) = 720 * alpha * Matrix3::Identity(); // x0
401 w.second = alpha * 720 * (-pi[1] + 3 * pi[2] - 3 * pi[3]);
402 wps.push_back(w);
403 w = initwp(DIM_POINT, DIM_VAR);
404 // assign w2:
405 w.first.block<3, 3>(0, 0) = 720 * -3 * alpha * Matrix3::Identity(); // x0
406 w.first.block<3, 3>(0, 3) = 720 * alpha * Matrix3::Identity(); // x1
407 w.second = alpha * 720 * (-pi[2] + 3 * pi[3]);
408 wps.push_back(w);
409 w = initwp(DIM_POINT, DIM_VAR);
410 // assign w3:
411 w.first.block<3, 3>(0, 0) = 720 * 3 * alpha * Matrix3::Identity(); // x0
412 w.first.block<3, 3>(0, 3) = 720 * -3 * alpha * Matrix3::Identity(); // x1
413 w.first.block<3, 3>(0, 6) = 720 * alpha * Matrix3::Identity(); // x2
414 w.second = alpha * 720 * (-pi[3]);
415 wps.push_back(w);
416 w = initwp(DIM_POINT, DIM_VAR);
417 // assign w4:
418 w.first.block<3, 3>(0, 0) = -720 * alpha * Matrix3::Identity(); // x0
419 w.first.block<3, 3>(0, 3) = 720 * 3 * alpha * Matrix3::Identity(); // x1
420 w.first.block<3, 3>(0, 6) = 720 * -3 * alpha * Matrix3::Identity(); // x2
421 w.second = alpha * 720 * pi[7];
422 wps.push_back(w);
423 w = initwp(DIM_POINT, DIM_VAR);
424 // assign w5:
425 w.first.block<3, 3>(0, 3) = -720 * alpha * Matrix3::Identity(); // x1
426 w.first.block<3, 3>(0, 6) = 720 * 3 * alpha * Matrix3::Identity(); // x2
427 w.second = alpha * 720 * (-3 * pi[7] + pi[8]);
428 wps.push_back(w);
429 w = initwp(DIM_POINT, DIM_VAR);
430 // assign w5:
431 w.first.block<3, 3>(0, 6) = -720 * alpha * Matrix3::Identity(); // x2
432 w.second = alpha * 720 * (3 * pi[7] - 3 * pi[8] + pi[9]);
433 wps.push_back(w);
434 w = initwp(DIM_POINT, DIM_VAR);
435 // assign w6:
436 w.second = alpha * 720 * (pi[10] - pi[7] + 3 * pi[8] - 3 * pi[9]);
437 wps.push_back(w);
438 return wps;
439}
440
441// TODO
442inline coefs_t computeFinalVelocityPoint(const ProblemData& pData, double T) {
443 coefs_t v;
444 std::vector<point_t> pi = computeConstantWaypoints(pData, T);
445 // equation found with sympy
446 v.first = 0.;
447 v.second = (-6.0 * pi[5] + 6.0 * pi[6]) / T;
448 return v;
449}
450
451inline std::pair<MatrixXX, VectorX> computeVelocityCost(
452 const ProblemData& pData, double T,
453 std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) {
454 MatrixXX H = MatrixXX::Zero(9, 9);
455 VectorX g = VectorX::Zero(9);
456 if (pi.size() == 0) pi = computeConstantWaypoints(pData, T);
457
458 g.segment<3>(0) = (-12.352941184069 * pi[0] - 2.03619909502433 * pi[10] -
459 10.5882353430148 * pi[1] + 1.2217194516605 * pi[2] +
460 12.2171947000329 * pi[3] - 4.66474701697538 * pi[7] -
461 7.21925133730399 * pi[8] - 5.42986425333795 * pi[9]) /
462 (2 * T); // x0
463 g.segment<3>(3) = (-5.29411764601331 * pi[0] - 5.29411764705762 * pi[10] -
464 8.95927605247282 * pi[1] - 6.10859723220821 * pi[2] +
465 2.2213080007358 * pi[3] + 2.22130810120924 * pi[7] -
466 6.10859728485633 * pi[8] - 8.95927601808432 * pi[9]) /
467 (2 * T); // x1
468 g.segment<3>(6) = (-2.03619909557297 * pi[0] - 12.3529411764706 * pi[10] -
469 5.42986425052241 * pi[1] - 7.21925133714926 * pi[2] -
470 4.66474700749421 * pi[3] + 12.2171945706055 * pi[7] +
471 1.22171945695766 * pi[8] - 10.5882352941172 * pi[9]) /
472 (2 * T); // x2
473
474 H.block<3, 3>(0, 0) = Matrix3::Identity() * 7.77457833646806 / (T); // x0^2
475 H.block<3, 3>(3, 3) = Matrix3::Identity() * 7.25627312788583 / (T); // x1^2
476 H.block<3, 3>(6, 6) = Matrix3::Identity() * 7.77457836216558 / (T); // x2^2
477 H.block<3, 3>(0, 3) =
478 Matrix3::Identity() * 10.8844097406652 / (2 * T); // x0*x1 / 2
479 H.block<3, 3>(3, 0) =
480 Matrix3::Identity() * 10.8844097406652 / (2 * T); // x0*x1 / 2
481 H.block<3, 3>(0, 6) =
482 Matrix3::Identity() * 2.41875768460934 / (2 * T); // x0*x2 / 2
483 H.block<3, 3>(6, 0) =
484 Matrix3::Identity() * 2.41875768460934 / (2 * T); // x0*x2 / 2
485 H.block<3, 3>(3, 6) =
486 Matrix3::Identity() * 10.8844097036619 / (2 * T); // x1*x2 / 2
487 H.block<3, 3>(6, 3) =
488 Matrix3::Identity() * 10.8844097036619 / (2 * T); // x1*x2 / 2
489
490 double norm = H.norm();
491 H /= norm;
492 g /= norm;
493
494 return std::make_pair(H, g);
495}
496
497} // namespace c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1
498
499} // namespace bezier_com_traj
500
501#endif // WAYPOINTS_C0_DC0_DDC0_J0_J1_DDC1_DC1_C1_HH
END_ACC
Definition: flags.hh:25
THREE_FREE_VAR
Definition: flags.hh:30
INIT_VEL
Definition: flags.hh:21
END_VEL
Definition: flags.hh:24
END_POS
Definition: flags.hh:23
INIT_ACC
Definition: flags.hh:22
INIT_POS
Definition: flags.hh:20
INIT_JERK
Definition: flags.hh:26
END_JERK
Definition: flags.hh:27
std::pair< MatrixXX, VectorX > computeVelocityCost(const ProblemData &pData, double T, std::vector< bezier_t::point_t > pi=std::vector< bezier_t::point_t >())
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:451
std::vector< waypoint_t > computeAccelerationWaypoints(const ProblemData &pData, const double T, std::vector< bezier_t::point_t > pi=std::vector< bezier_t::point_t >())
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:325
waypoint_t evaluateCurveWaypointAtTime(const std::vector< point_t > &pi, double t)
evaluateCurveAtTime compute the expression of the point on the curve at t, defined by the waypoint pi...
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:32
coefs_t computeFinalVelocityPoint(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:442
bezier_wp_t::t_point_t computeWwaypoints(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:250
std::vector< point_t > computeConstantWaypoints(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:221
waypoint_t evaluateJerkCurveWaypointAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:175
waypoint_t evaluateVelocityCurveWaypointAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:75
waypoint_t evaluateAccelerationCurveWaypointAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:126
std::vector< waypoint_t > computeVelocityWaypoints(const ProblemData &pData, const double T, std::vector< bezier_t::point_t > pi=std::vector< bezier_t::point_t >())
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:268
std::vector< waypoint_t > computeJerkWaypoints(const ProblemData &pData, const double T, std::vector< bezier_t::point_t > pi=std::vector< bezier_t::point_t >())
Definition: waypoints_c0_dc0_ddc0_j0_x3_j1_ddc1_dc1_c1.hh:383
Definition: common_solve_methods.hh:15
centroidal_dynamics::VectorX VectorX
Definition: definitions.hh:24
BEZIER_COM_TRAJ_DLLAPI Matrix3 skew(point_t_tC x)
skew symmetric matrix
Definition: utils.cpp:62
const int DIM_POINT
Definition: solve_end_effector.hh:15
std::pair< double, point3_t > coefs_t
Definition: definitions.hh:62
Eigen::Matrix< value_type, Eigen::Dynamic, Eigen::Dynamic > MatrixXX
Definition: definitions.hh:21
Defines all the inputs of the problem: Initial and terminal constraints, as well as selected cost fun...
Definition: data.hh:92
point_t ddc1_
Definition: data.hh:107
point_t j1_
Definition: data.hh:107
point_t dc0_
Definition: data.hh:107
point_t ddc0_
Definition: data.hh:107
point_t dc1_
Definition: data.hh:107
point_t j0_
Definition: data.hh:107
point_t c0_
Definition: data.hh:107
point_t c1_
Definition: data.hh:107
Definition: utils.hh:25
VectorX second
Definition: utils.hh:27
MatrixXX first
Definition: utils.hh:26