6#ifndef BEZIER_COM_TRAJ_c0_dc0_ddc0_ddc1_dc1_c1_H
7#define BEZIER_COM_TRAJ_c0_dc0_ddc0_ddc1_dc1_c1_H
12namespace c0_dc0_ddc0_ddc1_dc1_c1 {
14static const ConstraintFlag flag =
36 wp.first = -20.0 * t6 + 60.0 * t5 - 60.0 * t4 + 20.0 * t3;
37 wp.second = 1.0 * pi[0] * t6 - 6.0 * pi[0] * t5 + 15.0 * pi[0] * t4 -
38 20.0 * pi[0] * t3 + 15.0 * pi[0] * t2 - 6.0 * pi[0] * t +
39 1.0 * pi[0] - 6.0 * pi[1] * t6 + 30.0 * pi[1] * t5 -
40 60.0 * pi[1] * t4 + 60.0 * pi[1] * t3 - 30.0 * pi[1] * t2 +
41 6.0 * pi[1] * t + 15.0 * pi[2] * t6 - 60.0 * pi[2] * t5 +
42 90.0 * pi[2] * t4 - 60.0 * pi[2] * t3 + 15.0 * pi[2] * t2 +
43 15.0 * pi[4] * t6 - 30.0 * pi[4] * t5 + 15.0 * pi[4] * t4 -
44 6.0 * pi[5] * t6 + 6.0 * pi[5] * t5 + 1.0 * pi[6] * t6;
51 double alpha = 1. / (T * T);
56 wp.first = 1.0 * (-600.0 * t4 + 1200.0 * t3 - 720.0 * t2 + 120.0 * t) * alpha;
58 (30.0 * pi[0] * t4 - 120.0 * pi[0] * t3 + 180.0 * pi[0] * t2 -
59 120.0 * pi[0] * t + 30.0 * pi[0] - 180.0 * pi[1] * t4 +
60 600.0 * pi[1] * t3 - 720.0 * pi[1] * t2 + 360.0 * pi[1] * t -
61 60.0 * pi[1] + 450.0 * pi[2] * t4 - 1200.0 * pi[2] * t3 +
62 1080.0 * pi[2] * t2 - 360.0 * pi[2] * t + 30.0 * pi[2] +
63 450.0 * pi[4] * t4 - 600.0 * pi[4] * t3 + 180.0 * pi[4] * t2 -
64 180.0 * pi[5] * t4 + 120.0 * pi[5] * t3 + 30.0 * pi[6] * t4) *
75 std::vector<point_t> pi;
76 pi.push_back(pData.
c0_);
77 pi.push_back((pData.
dc0_ * T / n) + pData.
c0_);
78 pi.push_back((pData.
ddc0_ * T * T / (n * (n - 1))) +
79 (2. * pData.
dc0_ * T / n) + pData.
c0_);
80 pi.push_back(point_t::Zero());
81 pi.push_back((pData.
ddc1_ * T * T / (n * (n - 1))) -
82 (2 * pData.
dc1_ * T / n) + pData.
c1_);
83 pi.push_back((-pData.
dc1_ * T / n) + pData.
c1_);
84 pi.push_back(pData.
c1_);
90 bezier_wp_t::t_point_t wps;
92 const int DIM_VAR = 3;
94 std::vector<Matrix3> Cpi;
95 for (std::size_t i = 0; i < pi.size(); ++i) {
96 Cpi.push_back(
skew(pi[i]));
100 const double T2 = T * T;
101 const double alpha = 1 / (T2);
105 w0.second.head<3>() = (30 * pi[0] - 60 * pi[1] + 30 * pi[2]) * alpha;
106 w0.second.tail<3>() =
108 (1.0 * Cg * T2 * pi[0] - 60.0 * Cpi[0] * pi[1] + 30.0 * Cpi[0] * pi[2]) *
112 w1.first.block<3, 3>(0, 0) = 13.3333333333333 * alpha * Matrix3::Identity();
113 w1.first.block<3, 3>(3, 0) = 13.3333333333333 * Cpi[0] * alpha;
114 w1.second.head<3>() =
115 1.0 * (16.6666666666667 * pi[0] - 20.0 * pi[1] - 10.0 * pi[2]) * alpha;
116 w1.second.tail<3>() = 1.0 *
117 (0.333333333333333 * Cg * T2 * pi[0] +
118 0.666666666666667 * Cg * T2 * pi[1] -
119 30.0 * Cpi[0] * pi[2] + 20.0 * Cpi[1] * pi[2]) *
123 w2.first.block<3, 3>(0, 0) = 6.66666666666667 * alpha * Matrix3::Identity();
124 w2.first.block<3, 3>(3, 0) =
125 1.0 * (-13.3333333333333 * Cpi[0] + 20.0 * Cpi[1]) * alpha;
126 w2.second.head<3>() =
127 1.0 * (8.33333333333333 * pi[0] - 20.0 * pi[2] + 5.0 * pi[4]) * alpha;
128 w2.second.tail<3>() =
130 (0.0833333333333334 * Cg * T2 * pi[0] + 0.5 * Cg * T2 * pi[1] +
131 0.416666666666667 * Cg * T2 * pi[2] + 5.0 * Cpi[0] * pi[4] -
132 20.0 * Cpi[1] * pi[2]) *
136 w3.first.block<3, 3>(0, 0) = -5.71428571428572 * alpha * Matrix3::Identity();
137 w3.first.block<3, 3>(3, 0) = 1.0 *
138 (0.238095238095238 * Cg * T2 - 20.0 * Cpi[1] +
139 14.2857142857143 * Cpi[2]) *
141 w3.second.head<3>() = 1.0 *
142 (3.57142857142857 * pi[0] + 7.14285714285714 * pi[1] -
143 14.2857142857143 * pi[2] + 7.85714285714286 * pi[4] +
144 1.42857142857143 * pi[5]) *
146 w3.second.tail<3>() =
148 (0.0119047619047619 * Cg * T2 * pi[0] +
149 0.214285714285714 * Cg * T2 * pi[1] +
150 0.535714285714286 * Cg * T2 * pi[2] - 5.0 * Cpi[0] * pi[4] +
151 1.42857142857143 * Cpi[0] * pi[5] + 12.8571428571429 * Cpi[1] * pi[4]) *
155 w4.first.block<3, 3>(0, 0) = -14.2857142857143 * alpha * Matrix3::Identity();
156 w4.first.block<3, 3>(3, 0) =
157 1.0 * (0.476190476190476 * Cg * T2 - 14.2857142857143 * Cpi[2]) * alpha;
158 w4.second.head<3>() = 1.0 *
159 (1.19047619047619 * pi[0] + 7.14285714285714 * pi[1] -
160 3.57142857142857 * pi[2] + 5.0 * pi[4] +
161 4.28571428571429 * pi[5] + 0.238095238095238 * pi[6]) *
163 w4.second.tail<3>() =
165 (0.0476190476190471 * Cg * T2 * pi[1] +
166 0.357142857142857 * Cg * T2 * pi[2] +
167 0.119047619047619 * Cg * T2 * pi[4] - 1.42857142857143 * Cpi[0] * pi[5] +
168 0.238095238095238 * Cpi[0] * pi[6] - 12.8571428571429 * Cpi[1] * pi[4] +
169 5.71428571428571 * Cpi[1] * pi[5] + 17.8571428571429 * Cpi[2] * pi[4]) *
173 w5.
first.block<3, 3>(0, 0) = -14.2857142857143 * alpha * Matrix3::Identity();
174 w5.
first.block<3, 3>(3, 0) =
175 1.0 * (0.476190476190476 * Cg * T2 - 14.2857142857143 * Cpi[4]) * alpha;
176 w5.
second.head<3>() = 1.0 *
177 (0.238095238095238 * pi[0] + 4.28571428571429 * pi[1] +
178 5.0 * pi[2] - 3.57142857142857 * pi[4] +
179 7.14285714285714 * pi[5] + 1.19047619047619 * pi[6]) *
183 (+0.11904761904762 * Cg * T2 * pi[2] +
184 0.357142857142857 * Cg * T2 * pi[4] +
185 0.0476190476190476 * Cg * T2 * pi[5] -
186 0.238095238095238 * Cpi[0] * pi[6] - 5.71428571428572 * Cpi[1] * pi[5] +
187 1.42857142857143 * Cpi[1] * pi[6] - 17.8571428571429 * Cpi[2] * pi[4] +
188 12.8571428571429 * Cpi[2] * pi[5]) *
192 w6.
first.block<3, 3>(0, 0) = -5.71428571428571 * alpha * Matrix3::Identity();
193 w6.
first.block<3, 3>(3, 0) = 1.0 *
194 (0.238095238095238 * Cg * T2 +
195 14.2857142857143 * Cpi[4] - 20.0 * Cpi[5]) *
197 w6.
second.head<3>() = 1.0 *
198 (1.42857142857143 * pi[1] + 7.85714285714286 * pi[2] -
199 14.2857142857143 * pi[4] + 7.14285714285715 * pi[5] +
200 3.57142857142857 * pi[6]) *
204 (0.535714285714286 * Cg * T2 * pi[4] +
205 0.214285714285714 * Cg * T2 * pi[5] +
206 0.0119047619047619 * Cg * T2 * pi[6] -
207 1.42857142857143 * Cpi[1] * pi[6] - 12.8571428571429 * Cpi[2] * pi[5] +
208 5.0 * Cpi[2] * pi[6]) *
212 w7.
first.block<3, 3>(0, 0) = 6.66666666666667 * alpha * Matrix3::Identity();
213 w7.
first.block<3, 3>(3, 0) =
214 1.0 * (20.0 * Cpi[5] - 13.3333333333333 * Cpi[6]) * alpha;
216 1.0 * (5.0 * pi[2] - 20.0 * pi[4] + 8.33333333333333 * pi[6]) * alpha;
219 (0.416666666666667 * Cg * T2 * pi[4] + 0.5 * Cg * T2 * pi[5] +
220 0.0833333333333333 * Cg * T2 * pi[6] - 5.0 * Cpi[2] * pi[6] +
221 20.0 * Cpi[4] * pi[5]) *
225 w8.
first.block<3, 3>(0, 0) = 13.3333333333333 * alpha * Matrix3::Identity();
226 w8.
first.block<3, 3>(3, 0) = 1.0 * (13.3333333333333 * Cpi[6]) * alpha;
229 (-9.99999999999999 * pi[4] - 20.0 * pi[5] + 16.6666666666667 * pi[6]) *
231 w8.
second.tail<3>() = 1.0 *
232 (0.666666666666667 * Cg * T2 * pi[5] +
233 0.333333333333333 * Cg * T2 * pi[6] -
234 20.0 * Cpi[4] * pi[5] + 30.0 * Cpi[4] * pi[6]) *
238 w9.
second.head<3>() = (30 * pi[4] - 60 * pi[5] + 30 * pi[6]) * alpha;
241 (1.0 * Cg * T2 * pi[6] - 30.0 * Cpi[4] * pi[6] + 60.0 * Cpi[5] * pi[6]) *
252 v.second = (-6.0 * pi[5] + 6.0 * pi[6]) / T;
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
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_ddc1_dc1_c1.hh:28
coefs_t computeFinalVelocityPoint(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_ddc0_ddc1_dc1_c1.hh:247
bezier_wp_t::t_point_t computeWwaypoints(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_ddc0_ddc1_dc1_c1.hh:88
std::vector< point_t > computeConstantWaypoints(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_ddc0_ddc1_dc1_c1.hh:69
coefs_t evaluateAccelerationCurveAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_ddc0_ddc1_dc1_c1.hh:48
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
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
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 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 c0_
Definition: data.hh:107
point_t c1_
Definition: data.hh:107
VectorX second
Definition: utils.hh:27
MatrixXX first
Definition: utils.hh:26