hpp-bezier-com-traj 4.14.0
Multi contact trajectory generation for the COM using Bezier curves
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waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh
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1#ifndef BEZIER_COM_TRAJ_C0_DC0_DDC0_J0_J1_DDC1_DC1_C1_HH
2#define BEZIER_COM_TRAJ_C0_DC0_DDC0_J0_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_j1_ddc1_dc1_c1 {
13
14static const ConstraintFlag flag = INIT_POS | INIT_VEL | INIT_ACC | END_ACC |
16static const size_t DIM_VAR = 3;
17static const size_t DIM_POINT = 3;
21
30inline coefs_t evaluateCurveAtTime(const std::vector<point_t>& pi, double t) {
31 coefs_t wp;
32 const double t2 = t * t;
33 const double t3 = t2 * t;
34 const double t4 = t3 * t;
35 const double t5 = t4 * t;
36 const double t6 = t5 * t;
37 const double t7 = t6 * t;
38 const double t8 = t7 * t;
39 // equation found with sympy
40 wp.first = 70.0 * t8 - 280.0 * t7 + 420.0 * t6 - 280.0 * t5 + 70.0 * t4;
41 wp.second = 1.0 * pi[8] * t8 - 8.0 * pi[8] * t7 + 28.0 * pi[8] * t6 -
42 56.0 * pi[8] * t5 + 70.0 * pi[8] * t4 - 56.0 * pi[8] * t3 +
43 28.0 * pi[8] * t2 - 8.0 * pi[8] * t + 1.0 * pi[8] -
44 8.0 * pi[1] * t8 + 56.0 * pi[1] * t7 - 168.0 * pi[1] * t6 +
45 280.0 * pi[1] * t5 - 280.0 * pi[1] * t4 + 168.0 * pi[1] * t3 -
46 56.0 * pi[1] * t2 + 8.0 * pi[1] * t + 28.0 * pi[2] * t8 -
47 168.0 * pi[2] * t7 + 420.0 * pi[2] * t6 - 560.0 * pi[2] * t5 +
48 420.0 * pi[2] * t4 - 168.0 * pi[2] * t3 + 28.0 * pi[2] * t2 -
49 56.0 * pi[3] * pow(t, 8) + 280.0 * pi[3] * t7 -
50 560.0 * pi[3] * t6 + 560.0 * pi[3] * t5 - 280.0 * pi[3] * t4 +
51 56.0 * pi[3] * t3 - 56.0 * pi[5] * t8 + 168.0 * pi[5] * t7 -
52 168.0 * pi[5] * t6 + 56.0 * pi[5] * pow(t, 5) +
53 28.0 * pi[6] * t8 - 56.0 * pi[6] * t7 + 28.0 * pi[6] * t6 -
54 8.0 * pi[7] * t8 + 8.0 * pi[7] * t7 + 1.0 * pi[8] * t8;
55 return wp;
56}
57
58inline coefs_t evaluateVelocityCurveAtTime(const std::vector<point_t>& pi,
59 double T, double t) {
60 coefs_t wp;
61 const double alpha = 1. / (T);
62 const double t2 = t * t;
63 const double t3 = t2 * t;
64 const double t4 = t3 * t;
65 const double t5 = t4 * t;
66 const double t6 = t5 * t;
67 const double t7 = t6 * t;
68 // equation found with sympy
69 wp.first =
70 (560.0 * t7 - 1960.0 * t6 + 2520.0 * t5 - 1400.0 * t4 + 280.0 * t3) *
71 alpha;
72 wp.second = (8.0 * pi[8] * t7 - 56.0 * pi[8] * t6 + 168.0 * pi[8] * t5 -
73 280.0 * pi[8] * t4 + 280.0 * pi[8] * t3 - 168.0 * pi[8] * t2 +
74 56.0 * pi[8] * t - 8.0 * pi[8] - 64.0 * pi[1] * t7 +
75 392.0 * pi[1] * t6 - 1008.0 * pi[1] * t5 + 1400.0 * pi[1] * t4 -
76 1120.0 * pi[1] * t3 + 504.0 * pi[1] * t2 - 112.0 * pi[1] * t +
77 8.0 * pi[1] + 224.0 * pi[2] * t7 - 1176.0 * pi[2] * t6 +
78 2520.0 * pi[2] * t5 - 2800.0 * pi[2] * t4 + 1680.0 * pi[2] * t3 -
79 504.0 * pi[2] * t2 + 56.0 * pi[2] * t - 448.0 * pi[3] * t7 +
80 1960.0 * pi[3] * t6 - 3360.0 * pi[3] * t5 + 2800.0 * pi[3] * t4 -
81 1120.0 * pi[3] * t3 + 168.0 * pi[3] * t2 - 448.0 * pi[5] * t7 +
82 1176.0 * pi[5] * t6 - 1008.0 * pi[5] * t5 + 280.0 * pi[5] * t4 +
83 224.0 * pi[6] * t7 - 392.0 * pi[6] * t6 + 168.0 * pi[6] * t5 -
84 64.0 * pi[7] * t7 + 56.0 * pi[7] * t6 + 8.0 * pi[8] * t7) *
85 alpha;
86 return wp;
87}
88
89inline coefs_t evaluateAccelerationCurveAtTime(const std::vector<point_t>& pi,
90 double T, double t) {
91 coefs_t wp;
92 const double alpha = 1. / (T * T);
93 const double t2 = t * t;
94 const double t3 = t2 * t;
95 const double t4 = t3 * t;
96 const double t5 = t4 * t;
97 const double t6 = t5 * t;
98 // equation found with sympy
99 wp.first =
100 ((3920.0 * t6 - 11760.0 * t5 + 12600.0 * t4 - 5600.0 * t3 + 840.0 * t2)) *
101 alpha;
102 wp.second = (56.0 * pi[8] * t6 - 336.0 * pi[8] * t5 + 840.0 * pi[8] * t4 -
103 1120.0 * pi[8] * t3 + 840.0 * pi[8] * t2 - 336.0 * pi[8] * t +
104 56.0 * pi[8] - 448.0 * pi[1] * t6 + 2352.0 * pi[1] * t5 -
105 5040.0 * pi[1] * t4 + 5600.0 * pi[1] * t3 - 3360.0 * pi[1] * t2 +
106 1008.0 * pi[1] * t - 112.0 * pi[1] + 1568.0 * pi[2] * t6 -
107 7056.0 * pi[2] * t5 + 12600.0 * pi[2] * t4 -
108 11200.0 * pi[2] * t3 + 5040.0 * pi[2] * t2 - 1008.0 * pi[2] * t +
109 56.0 * pi[2] - 3136.0 * pi[3] * t6 + 11760.0 * pi[3] * t5 -
110 16800.0 * pi[3] * t4 + 11200.0 * pi[3] * t3 -
111 3360.0 * pi[3] * t2 + 336.0 * pi[3] * t - 3136.0 * pi[5] * t6 +
112 7056.0 * pi[5] * t5 - 5040.0 * pi[5] * t4 + 1120.0 * pi[5] * t3 +
113 1568.0 * pi[6] * t6 - 2352.0 * pi[6] * t5 + 840.0 * pi[6] * t4 -
114 448.0 * pi[7] * t6 + 336.0 * pi[7] * t5 + 56.0 * pi[8] * t6) *
115 alpha;
116 return wp;
117}
118
119inline coefs_t evaluateJerkCurveAtTime(const std::vector<point_t>& pi, double T,
120 double t) {
121 coefs_t wp;
122 const double alpha = 1. / (T * T * T);
123 const double t2 = t * t;
124 const double t3 = t2 * t;
125 const double t4 = t3 * t;
126 const double t5 = t4 * t;
127 // equation found with sympy
128 wp.first =
129 (23520.0 * t5 - 58800.0 * t4 + 50400.0 * t3 - 16800.0 * t2 + 1680.0 * t) *
130 alpha;
131 wp.second =
132 1.0 *
133 (336.0 * pi[0] * t5 - 1680.0 * pi[0] * t4 + 3360.0 * pi[0] * t3 -
134 3360.0 * pi[0] * t2 + 1680.0 * pi[0] * t - 336.0 * pi[0] -
135 2688.0 * pi[1] * t5 + 11760.0 * pi[1] * t4 - 20160.0 * pi[1] * t3 +
136 16800.0 * pi[1] * t2 - 6720.0 * pi[1] * t + 1008.0 * pi[1] +
137 9408.0 * pi[2] * t5 - 35280.0 * pi[2] * t4 + 50400.0 * pi[2] * t3 -
138 33600.0 * pi[2] * t2 + 10080.0 * pi[2] * t - 1008.0 * pi[2] -
139 18816.0 * pi[3] * t5 + 58800.0 * pi[3] * t4 - 67200.0 * pi[3] * t3 +
140 33600.0 * pi[3] * t2 - 6720.0 * pi[3] * t + 336.0 * pi[3] -
141 18816.0 * pi[5] * t5 + 35280.0 * pi[5] * t4 - 20160.0 * pi[5] * t3 +
142 3360.0 * pi[5] * t2 + 9408.0 * pi[6] * t5 - 11760.0 * pi[6] * t4 +
143 3360.0 * pi[6] * t3 - 2688.0 * pi[7] * t5 + 1680.0 * pi[7] * t4 +
144 336.0 * pi[8] * t5) *
145 alpha;
146 return wp;
147}
148inline waypoint_t evaluateCurveWaypointAtTime(const std::vector<point_t>& pi,
149 double t) {
150 coefs_t coef = evaluateCurveAtTime(pi, t);
151 waypoint_t wp;
152 wp.first = Matrix3::Identity() * coef.first;
153 wp.second = coef.second;
154 return wp;
155}
157 const std::vector<point_t>& pi, double T, double t) {
158 coefs_t coef = evaluateVelocityCurveAtTime(pi, T, t);
159 waypoint_t wp;
160 wp.first = Matrix3::Identity() * coef.first;
161 wp.second = coef.second;
162 return wp;
163}
165 const std::vector<point_t>& pi, double T, double t) {
167 waypoint_t wp;
168 wp.first = Matrix3::Identity() * coef.first;
169 wp.second = coef.second;
170 return wp;
171}
172
174 const std::vector<point_t>& pi, double T, double t) {
175 coefs_t coef = evaluateJerkCurveAtTime(pi, T, t);
176 waypoint_t wp;
177 wp.first = Matrix3::Identity() * coef.first;
178 wp.second = coef.second;
179 return wp;
180}
181
182inline std::vector<point_t> computeConstantWaypoints(const ProblemData& pData,
183 double T) {
184 // equation for constraint on initial and final position and velocity and
185 // initial acceleration(degree 5, 5 constant waypoint and one free (pi[3]))
186 // first, compute the constant waypoints that only depend on pData :
187 double n = 8.;
188 std::vector<point_t> pi;
189 pi.push_back(pData.c0_);
190 pi.push_back((pData.dc0_ * T / n) + pData.c0_);
191 pi.push_back((pData.ddc0_ * T * T / (n * (n - 1))) +
192 (2 * pData.dc0_ * T / n) +
193 pData.c0_); // * T because derivation make a T appear
194 pi.push_back((pData.j0_ * T * T * T / (n * (n - 1) * (n - 2))) +
195 (3 * pData.ddc0_ * T * T / (n * (n - 1))) +
196 (3 * pData.dc0_ * T / n) + pData.c0_);
197 pi.push_back(point_t::Zero());
198 pi.push_back((-pData.j1_ * T * T * T / (n * (n - 1) * (n - 2))) +
199 (3 * pData.ddc1_ * T * T / (n * (n - 1))) -
200 (3 * pData.dc1_ * T / n) + pData.c1_); // * T ??
201 pi.push_back((pData.ddc1_ * T * T / (n * (n - 1))) -
202 (2 * pData.dc1_ * T / n) + pData.c1_); // * T ??
203 pi.push_back((-pData.dc1_ * T / n) + pData.c1_); // * T ?
204 pi.push_back(pData.c1_);
205 return pi;
206}
207
208inline bezier_wp_t::t_point_t computeWwaypoints(const ProblemData& pData,
209 double T) {
210 bezier_wp_t::t_point_t wps;
211 const int DIM_POINT = 6;
212 const int DIM_VAR = 3;
213 std::vector<point_t> pi = computeConstantWaypoints(pData, T);
214 std::vector<Matrix3> Cpi;
215 for (std::size_t i = 0; i < pi.size(); ++i) {
216 Cpi.push_back(skew(pi[i]));
217 }
218 const Vector3 g = pData.contacts_.front().contactPhase_->m_gravity;
219 const Matrix3 Cg = skew(g);
220 const double T2 = T * T;
221 const double alpha = 1 / (T2);
222
223 // equation of waypoints for curve w found with sympy
224 waypoint_t w0 = initwp(DIM_POINT, DIM_VAR);
225 w0.second.head<3>() = (30 * pi[0] - 60 * pi[1] + 30 * pi[2]) * alpha;
226 w0.second.tail<3>() =
227 1.0 *
228 (1.0 * Cg * T2 * pi[0] - 60.0 * Cpi[0] * pi[1] + 30.0 * Cpi[0] * pi[2]) *
229 alpha;
230 wps.push_back(w0);
231 waypoint_t w1 = initwp(DIM_POINT, DIM_VAR);
232 w1.first.block<3, 3>(0, 0) = 13.3333333333333 * alpha * Matrix3::Identity();
233 w1.first.block<3, 3>(3, 0) = 13.3333333333333 * Cpi[0] * alpha;
234 w1.second.head<3>() =
235 1.0 * (16.6666666666667 * pi[0] - 20.0 * pi[1] - 10.0 * pi[2]) * alpha;
236 w1.second.tail<3>() = 1.0 *
237 (0.333333333333333 * Cg * T2 * pi[0] +
238 0.666666666666667 * Cg * T2 * pi[1] -
239 30.0 * Cpi[0] * pi[2] + 20.0 * Cpi[1] * pi[2]) *
240 alpha;
241 wps.push_back(w1);
242 waypoint_t w2 = initwp(DIM_POINT, DIM_VAR);
243 w2.first.block<3, 3>(0, 0) = 6.66666666666667 * alpha * Matrix3::Identity();
244 w2.first.block<3, 3>(3, 0) =
245 1.0 * (-13.3333333333333 * Cpi[0] + 20.0 * Cpi[1]) * alpha;
246 w2.second.head<3>() =
247 1.0 * (8.33333333333333 * pi[0] - 20.0 * pi[2] + 5.0 * pi[4]) * alpha;
248 w2.second.tail<3>() =
249 1.0 *
250 (0.0833333333333334 * Cg * T2 * pi[0] + 0.5 * Cg * T2 * pi[1] +
251 0.416666666666667 * Cg * T2 * pi[2] + 5.0 * Cpi[0] * pi[4] -
252 20.0 * Cpi[1] * pi[2]) *
253 alpha;
254 wps.push_back(w2);
255 waypoint_t w3 = initwp(DIM_POINT, DIM_VAR);
256 w3.first.block<3, 3>(0, 0) = -5.71428571428572 * alpha * Matrix3::Identity();
257 w3.first.block<3, 3>(3, 0) = 1.0 *
258 (0.238095238095238 * Cg * T2 - 20.0 * Cpi[1] +
259 14.2857142857143 * Cpi[2]) *
260 alpha;
261 w3.second.head<3>() = 1.0 *
262 (3.57142857142857 * pi[0] + 7.14285714285714 * pi[1] -
263 14.2857142857143 * pi[2] + 7.85714285714286 * pi[4] +
264 1.42857142857143 * pi[5]) *
265 alpha;
266 w3.second.tail<3>() =
267 1.0 *
268 (0.0119047619047619 * Cg * T2 * pi[0] +
269 0.214285714285714 * Cg * T2 * pi[1] +
270 0.535714285714286 * Cg * T2 * pi[2] - 5.0 * Cpi[0] * pi[4] +
271 1.42857142857143 * Cpi[0] * pi[5] + 12.8571428571429 * Cpi[1] * pi[4]) *
272 alpha;
273 wps.push_back(w3);
274 waypoint_t w4 = initwp(DIM_POINT, DIM_VAR);
275 w4.first.block<3, 3>(0, 0) = -14.2857142857143 * alpha * Matrix3::Identity();
276 w4.first.block<3, 3>(3, 0) =
277 1.0 * (0.476190476190476 * Cg * T2 - 14.2857142857143 * Cpi[2]) * alpha;
278 w4.second.head<3>() = 1.0 *
279 (1.19047619047619 * pi[0] + 7.14285714285714 * pi[1] -
280 3.57142857142857 * pi[2] + 5.0 * pi[4] +
281 4.28571428571429 * pi[5] + 0.238095238095238 * pi[6]) *
282 alpha;
283 w4.second.tail<3>() =
284 1.0 *
285 (0.0476190476190471 * Cg * T2 * pi[1] +
286 0.357142857142857 * Cg * T2 * pi[2] +
287 0.119047619047619 * Cg * T2 * pi[4] - 1.42857142857143 * Cpi[0] * pi[5] +
288 0.238095238095238 * Cpi[0] * pi[6] - 12.8571428571429 * Cpi[1] * pi[4] +
289 5.71428571428571 * Cpi[1] * pi[5] + 17.8571428571429 * Cpi[2] * pi[4]) *
290 alpha;
291 wps.push_back(w4);
292 waypoint_t w5 = initwp(DIM_POINT, DIM_VAR);
293 w5.first.block<3, 3>(0, 0) = -14.2857142857143 * alpha * Matrix3::Identity();
294 w5.first.block<3, 3>(3, 0) =
295 1.0 * (0.476190476190476 * Cg * T2 - 14.2857142857143 * Cpi[4]) * alpha;
296 w5.second.head<3>() = 1.0 *
297 (0.238095238095238 * pi[0] + 4.28571428571429 * pi[1] +
298 5.0 * pi[2] - 3.57142857142857 * pi[4] +
299 7.14285714285714 * pi[5] + 1.19047619047619 * pi[6]) *
300 alpha;
301 w5.second.tail<3>() =
302 1.0 *
303 (+0.11904761904762 * Cg * T2 * pi[2] +
304 0.357142857142857 * Cg * T2 * pi[4] +
305 0.0476190476190476 * Cg * T2 * pi[5] -
306 0.238095238095238 * Cpi[0] * pi[6] - 5.71428571428572 * Cpi[1] * pi[5] +
307 1.42857142857143 * Cpi[1] * pi[6] - 17.8571428571429 * Cpi[2] * pi[4] +
308 12.8571428571429 * Cpi[2] * pi[5]) *
309 alpha;
310 wps.push_back(w5);
311 waypoint_t w6 = initwp(DIM_POINT, DIM_VAR);
312 w6.first.block<3, 3>(0, 0) = -5.71428571428571 * alpha * Matrix3::Identity();
313 w6.first.block<3, 3>(3, 0) = 1.0 *
314 (0.238095238095238 * Cg * T2 +
315 14.2857142857143 * Cpi[4] - 20.0 * Cpi[5]) *
316 alpha;
317 w6.second.head<3>() = 1.0 *
318 (1.42857142857143 * pi[1] + 7.85714285714286 * pi[2] -
319 14.2857142857143 * pi[4] + 7.14285714285715 * pi[5] +
320 3.57142857142857 * pi[6]) *
321 alpha;
322 w6.second.tail<3>() =
323 1.0 *
324 (0.535714285714286 * Cg * T2 * pi[4] +
325 0.214285714285714 * Cg * T2 * pi[5] +
326 0.0119047619047619 * Cg * T2 * pi[6] -
327 1.42857142857143 * Cpi[1] * pi[6] - 12.8571428571429 * Cpi[2] * pi[5] +
328 5.0 * Cpi[2] * pi[6]) *
329 alpha;
330 wps.push_back(w6);
331 waypoint_t w7 = initwp(DIM_POINT, DIM_VAR);
332 w7.first.block<3, 3>(0, 0) = 6.66666666666667 * alpha * Matrix3::Identity();
333 w7.first.block<3, 3>(3, 0) =
334 1.0 * (20.0 * Cpi[5] - 13.3333333333333 * Cpi[6]) * alpha;
335 w7.second.head<3>() =
336 1.0 * (5.0 * pi[2] - 20.0 * pi[4] + 8.33333333333333 * pi[6]) * alpha;
337 w7.second.tail<3>() =
338 1.0 *
339 (0.416666666666667 * Cg * T2 * pi[4] + 0.5 * Cg * T2 * pi[5] +
340 0.0833333333333333 * Cg * T2 * pi[6] - 5.0 * Cpi[2] * pi[6] +
341 20.0 * Cpi[4] * pi[5]) *
342 alpha;
343 wps.push_back(w7);
344 waypoint_t w8 = initwp(DIM_POINT, DIM_VAR);
345 w8.first.block<3, 3>(0, 0) = 13.3333333333333 * alpha * Matrix3::Identity();
346 w8.first.block<3, 3>(3, 0) = 1.0 * (13.3333333333333 * Cpi[6]) * alpha;
347 w8.second.head<3>() =
348 1.0 *
349 (-9.99999999999999 * pi[4] - 20.0 * pi[5] + 16.6666666666667 * pi[6]) *
350 alpha;
351 w8.second.tail<3>() = 1.0 *
352 (0.666666666666667 * Cg * T2 * pi[5] +
353 0.333333333333333 * Cg * T2 * pi[6] -
354 20.0 * Cpi[4] * pi[5] + 30.0 * Cpi[4] * pi[6]) *
355 alpha;
356 wps.push_back(w8);
357 waypoint_t w9 = initwp(DIM_POINT, DIM_VAR);
358 w9.second.head<3>() = (30 * pi[4] - 60 * pi[5] + 30 * pi[6]) * alpha;
359 w9.second.tail<3>() =
360 1.0 *
361 (1.0 * Cg * T2 * pi[6] - 30.0 * Cpi[4] * pi[6] + 60.0 * Cpi[5] * pi[6]) *
362 alpha;
363 wps.push_back(w9);
364 return wps;
365}
366
367std::vector<waypoint_t> computeVelocityWaypoints(
368 const ProblemData& pData, const double T,
369 std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) {
370 if (pi.size() == 0) pi = computeConstantWaypoints(pData, T);
371
372 std::vector<waypoint_t> wps;
373 assert(pi.size() == 9);
374
375 double alpha = 1. / (T);
376 waypoint_t w = initwp(DIM_POINT, DIM_VAR);
377 // assign w0:
378 w.second = alpha * 8 * (-pi[0] + pi[1]);
379 wps.push_back(w);
380 w = initwp(DIM_POINT, DIM_VAR);
381 // assign w1:
382 w.second = alpha * 8 * (-pi[1] + pi[2]);
383 wps.push_back(w);
384 w = initwp(DIM_POINT, DIM_VAR);
385 // assign w2:
386 w.second = alpha * 8 * (-pi[2] + pi[3]);
387 wps.push_back(w);
388 w = initwp(DIM_POINT, DIM_VAR);
389 // assign w3:
390 w.first = 8 * alpha * Matrix3::Identity();
391 w.second = alpha * -8 * pi[3];
392 wps.push_back(w);
393 w = initwp(DIM_POINT, DIM_VAR);
394 // assign w4:
395 w.first = -8 * alpha * Matrix3::Identity();
396 w.second = alpha * 8 * pi[5];
397 wps.push_back(w);
398 w = initwp(DIM_POINT, DIM_VAR);
399 // assign w5:
400 w.second = alpha * 8 * (-pi[5] + pi[6]);
401 wps.push_back(w);
402 w = initwp(DIM_POINT, DIM_VAR);
403 // assign w6:
404 w.second = alpha * 8 * (-pi[6] + pi[7]);
405 wps.push_back(w);
406 w = initwp(DIM_POINT, DIM_VAR);
407 // assign w7:
408 w.second = alpha * 8 * (-pi[7] + pi[8]);
409 wps.push_back(w);
410 return wps;
411}
412
413std::vector<waypoint_t> computeAccelerationWaypoints(
414 const ProblemData& pData, const double T,
415 std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) {
416 if (pi.size() == 0) pi = computeConstantWaypoints(pData, T);
417
418 std::vector<waypoint_t> wps;
419 assert(pi.size() == 9);
420 double alpha = 1. / (T * T);
421
422 waypoint_t w = initwp(DIM_POINT, DIM_VAR);
423
424 // assign w0:
425 w.second = 56 * alpha * (pi[0] - 2 * pi[1] + pi[2]);
426 wps.push_back(w);
427 w = initwp(DIM_POINT, DIM_VAR);
428 // assign w1:
429 w.second = 56 * alpha * (pi[1] - 2 * pi[2] + pi[3]);
430 wps.push_back(w);
431 w = initwp(DIM_POINT, DIM_VAR);
432 // assign w2:
433 w.first = 56 * alpha * Matrix3::Identity();
434 w.second = (56 * pi[2] - 112 * pi[3]) * alpha;
435 wps.push_back(w);
436 w = initwp(DIM_POINT, DIM_VAR);
437 // assign w3:
438 w.first = -112 * alpha * Matrix3::Identity();
439 w.second = (56 * pi[3] + 56 * pi[8]) * alpha;
440 wps.push_back(w);
441 w = initwp(DIM_POINT, DIM_VAR);
442 // assign w4:
443 w.first = 56 * alpha * Matrix3::Identity();
444 w.second = (-112 * pi[5] + 56 * pi[6]) * alpha;
445 wps.push_back(w);
446 w = initwp(DIM_POINT, DIM_VAR);
447 // assign w5:
448 w.second = 56 * alpha * (pi[5] - 2 * pi[6] + pi[7]);
449 wps.push_back(w);
450 w = initwp(DIM_POINT, DIM_VAR);
451 // assign w5:
452 w.second = 56 * alpha * (pi[6] - 2 * pi[7] + pi[8]);
453 wps.push_back(w);
454 return wps;
455}
456
457std::vector<waypoint_t> computeJerkWaypoints(
458 const ProblemData& pData, const double T,
459 std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) {
460 if (pi.size() == 0) pi = computeConstantWaypoints(pData, T);
461
462 std::vector<waypoint_t> wps;
463 assert(pi.size() == 9);
464
465 double alpha = 1. / (T * T * T);
466
467 waypoint_t w = initwp(DIM_POINT, DIM_VAR);
468
469 // assign w0:
470 w.second = 336 * (-pi[0] + 3 * pi[1] - 3 * pi[2] + pi[3]) * alpha;
471 wps.push_back(w);
472 w = initwp(DIM_POINT, DIM_VAR);
473 // assign w1:
474 w.first = 336 * alpha * Matrix3::Identity();
475 w.second = 336 * (-pi[1] + 3 * pi[2] - 3 * pi[3]) * alpha;
476 wps.push_back(w);
477 w = initwp(DIM_POINT, DIM_VAR);
478 // assign w2:
479 w.first = -3 * 336 * alpha * Matrix3::Identity();
480 w.second = 336 * (-pi[2] + 3 * pi[3] + pi[5]) * alpha;
481 wps.push_back(w);
482 w = initwp(DIM_POINT, DIM_VAR);
483 // assign w3:
484 w.first = 3 * 336 * alpha * Matrix3::Identity();
485 w.second = 336 * (-pi[3] - 3 * pi[5] + pi[6]) * alpha;
486 wps.push_back(w);
487 w = initwp(DIM_POINT, DIM_VAR);
488 // assign w4:
489 w.first = -336 * alpha * Matrix3::Identity();
490 w.second = 336 * (3 * pi[5] - 3 * pi[6] + pi[7]) * alpha;
491 wps.push_back(w);
492 w = initwp(DIM_POINT, DIM_VAR);
493 // assign w5:
494 w.second = 336 * (-pi[5] + 3 * pi[6] - 3 * pi[7] + pi[8]) * alpha;
495 wps.push_back(w);
496 return wps;
497}
498
499inline coefs_t computeFinalVelocityPoint(const ProblemData& pData, double T) {
500 coefs_t v;
501 std::vector<point_t> pi = computeConstantWaypoints(pData, T);
502 // equation found with sympy
503 v.first = 0.;
504 v.second = (-6.0 * pi[5] + 6.0 * pi[6]) / T;
505 return v;
506}
507
508inline std::pair<MatrixXX, VectorX> computeVelocityCost(
509 const ProblemData& pData, double T,
510 std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) {
511 MatrixXX H = MatrixXX::Zero(3, 3);
512 VectorX g = VectorX::Zero(3);
513 if (pi.size() == 0) pi = computeConstantWaypoints(pData, T);
514
515 g = (-7.8321678321748 * pi[0] - 7.83216783237586 * pi[1] +
516 9.13752913728184 * pi[3] + 9.13752913758454 * pi[5] -
517 7.83216783216697 * pi[7] - 7.83216783216777 * pi[8]) /
518 (2 * T);
519 H = Matrix3::Identity() * 6.52680652684107 / (T);
520
521 double norm = H.norm();
522 H /= norm;
523 g /= norm;
524
525 return std::make_pair(H, g);
526}
527
528} // namespace c0_dc0_ddc0_j0_j1_ddc1_dc1_c1
529
530} // namespace bezier_com_traj
531
532#endif // WAYPOINTS_C0_DC0_DDC0_J0_J1_DDC1_DC1_C1_HH
END_ACC
Definition: flags.hh:25
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
coefs_t evaluateJerkCurveAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:119
coefs_t evaluateCurveAtTime(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_j1_ddc1_dc1_c1.hh:30
waypoint_t evaluateCurveWaypointAtTime(const std::vector< point_t > &pi, double t)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:148
coefs_t evaluateAccelerationCurveAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:89
bezier_wp_t::t_point_t computeWwaypoints(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:208
waypoint_t evaluateJerkCurveWaypointAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:173
std::vector< point_t > computeConstantWaypoints(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:182
coefs_t evaluateVelocityCurveAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:58
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_j1_ddc1_dc1_c1.hh:367
waypoint_t evaluateAccelerationCurveWaypointAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:164
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_j1_ddc1_dc1_c1.hh:413
waypoint_t evaluateVelocityCurveWaypointAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:156
coefs_t computeFinalVelocityPoint(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_ddc0_j0_j1_ddc1_dc1_c1.hh:499
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_j1_ddc1_dc1_c1.hh:508
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_j1_ddc1_dc1_c1.hh:457
Definition: common_solve_methods.hh:15
waypoint6_t w0(point_t_tC p0, point_t_tC p1, point_t_tC g, const Matrix3 &p0X, const Matrix3 &, const Matrix3 &, const double alpha)
Definition: solve_0_step.cpp:12
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
Eigen::Matrix< value_type, 3, 3 > Matrix3
Definition: definitions.hh:17
const int DIM_POINT
Definition: solve_end_effector.hh:15
centroidal_dynamics::Vector3 Vector3
Definition: definitions.hh:22
waypoint6_t w3(point_t_tC p0, point_t_tC p1, point_t_tC g, const Matrix3 &, const Matrix3 &, const Matrix3 &, const double alpha)
Definition: solve_0_step.cpp:45
std::pair< double, point3_t > coefs_t
Definition: definitions.hh:62
waypoint6_t w1(point_t_tC p0, point_t_tC p1, point_t_tC, const Matrix3 &, const Matrix3 &, const Matrix3 &gX, const double alpha)
Definition: solve_0_step.cpp:23
waypoint6_t w4(point_t_tC, point_t_tC p1, point_t_tC g, const Matrix3 &, const Matrix3 &, const Matrix3 &, const double alpha)
Definition: solve_0_step.cpp:56
waypoint6_t w2(point_t_tC p0, point_t_tC p1, point_t_tC g, const Matrix3 &, const Matrix3 &, const Matrix3 &gX, const double alpha)
Definition: solve_0_step.cpp:34
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
std::vector< ContactData > contacts_
Definition: data.hh:106
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