| Directory: | ./ |
|---|---|
| File: | unittest/contact-dynamics.cpp |
| Date: | 2025-02-12 21:03:38 |
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| Lines: | 220 | 220 | 100.0% |
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| 1 | // | ||
| 2 | // Copyright (c) 2016-2020 CNRS INRIA | ||
| 3 | // | ||
| 4 | |||
| 5 | #include "pinocchio/spatial/se3.hpp" | ||
| 6 | #include "pinocchio/multibody/model.hpp" | ||
| 7 | #include "pinocchio/multibody/data.hpp" | ||
| 8 | #include "pinocchio/algorithm/jacobian.hpp" | ||
| 9 | #include "pinocchio/algorithm/contact-dynamics.hpp" | ||
| 10 | #include "pinocchio/algorithm/joint-configuration.hpp" | ||
| 11 | #include "pinocchio/multibody/sample-models.hpp" | ||
| 12 | #include "pinocchio/utils/timer.hpp" | ||
| 13 | |||
| 14 | #include <iostream> | ||
| 15 | |||
| 16 | #include <boost/test/unit_test.hpp> | ||
| 17 | #include <boost/utility/binary.hpp> | ||
| 18 | |||
| 19 | BOOST_AUTO_TEST_SUITE(BOOST_TEST_MODULE) | ||
| 20 | |||
| 21 |
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|
4 | BOOST_AUTO_TEST_CASE(test_FD) |
| 22 | { | ||
| 23 | using namespace Eigen; | ||
| 24 | using namespace pinocchio; | ||
| 25 | |||
| 26 |
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2 | pinocchio::Model model; |
| 27 |
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2 | pinocchio::buildModels::humanoidRandom(model, true); |
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2 | pinocchio::Data data(model); |
| 29 | |||
| 30 |
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2 | VectorXd q = VectorXd::Ones(model.nq); |
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2 | q.segment<4>(3).normalize(); |
| 32 | |||
| 33 |
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2 | pinocchio::computeJointJacobians(model, data, q); |
| 34 | |||
| 35 |
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2 | VectorXd v = VectorXd::Ones(model.nv); |
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2 | VectorXd tau = VectorXd::Zero(model.nv); |
| 37 | |||
| 38 |
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2 | const std::string RF = "rleg6_joint"; |
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2 | const std::string LF = "lleg6_joint"; |
| 40 | |||
| 41 |
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2 | Data::Matrix6x J_RF(6, model.nv); |
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2 | J_RF.setZero(); |
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2 | getJointJacobian(model, data, model.getJointId(RF), LOCAL, J_RF); |
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2 | Data::Matrix6x J_LF(6, model.nv); |
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2 | J_LF.setZero(); |
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2 | getJointJacobian(model, data, model.getJointId(LF), LOCAL, J_LF); |
| 47 | |||
| 48 |
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2 | Eigen::MatrixXd J(12, model.nv); |
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2 | J.setZero(); |
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2 | J.topRows<6>() = J_RF; |
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2 | J.bottomRows<6>() = J_LF; |
| 52 | |||
| 53 |
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2 | Eigen::VectorXd gamma(VectorXd::Ones(12)); |
| 54 | |||
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2 | Eigen::MatrixXd H(J.transpose()); |
| 56 | |||
| 57 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 58 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_DEPRECECATED_DECLARATIONS | ||
| 59 |
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2 | pinocchio::forwardDynamics(model, data, q, v, tau, J, gamma, 0.); |
| 60 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 61 | |||
| 62 |
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2 | data.M.triangularView<Eigen::StrictlyLower>() = |
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4 | data.M.transpose().triangularView<Eigen::StrictlyLower>(); |
| 64 | |||
| 65 |
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2 | MatrixXd Minv(data.M.inverse()); |
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2 | MatrixXd JMinvJt(J * Minv * J.transpose()); |
| 67 | |||
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2 | Eigen::MatrixXd G_ref(J.transpose()); |
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2 | cholesky::Uiv(model, data, G_ref); |
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66 | for (int k = 0; k < model.nv; ++k) |
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64 | G_ref.row(k) /= sqrt(data.D[k]); |
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2 | Eigen::MatrixXd H_ref(G_ref.transpose() * G_ref); |
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2 | BOOST_CHECK(H_ref.isApprox(JMinvJt, 1e-12)); |
| 74 | |||
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2 | VectorXd lambda_ref = -JMinvJt.inverse() * (J * Minv * (tau - data.nle) + gamma); |
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2 | BOOST_CHECK(data.lambda_c.isApprox(lambda_ref, 1e-12)); |
| 77 | |||
| 78 |
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2 | VectorXd a_ref = Minv * (tau - data.nle + J.transpose() * lambda_ref); |
| 79 | |||
| 80 | Eigen::VectorXd dynamics_residual_ref( | ||
| 81 |
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2 | data.M * a_ref + data.nle - tau - J.transpose() * lambda_ref); |
| 82 |
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2 | BOOST_CHECK( |
| 83 | dynamics_residual_ref.norm() | ||
| 84 | <= 1e-11); // previously 1e-12, may be due to numerical approximations, i obtain 2.03e-12 | ||
| 85 | |||
| 86 |
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2 | Eigen::VectorXd constraint_residual(J * data.ddq + gamma); |
| 87 |
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2 | BOOST_CHECK(constraint_residual.norm() <= 1e-12); |
| 88 | |||
| 89 | Eigen::VectorXd dynamics_residual( | ||
| 90 |
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2 | data.M * data.ddq + data.nle - tau - J.transpose() * data.lambda_c); |
| 91 |
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2 | BOOST_CHECK(dynamics_residual.norm() <= 1e-12); |
| 92 | 2 | } | |
| 93 | |||
| 94 |
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4 | BOOST_AUTO_TEST_CASE(test_computeKKTMatrix) |
| 95 | { | ||
| 96 | using namespace Eigen; | ||
| 97 | using namespace pinocchio; | ||
| 98 |
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2 | pinocchio::Model model; |
| 99 |
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2 | pinocchio::buildModels::humanoidRandom(model, true); |
| 100 |
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2 | pinocchio::Data data(model), data_ref(model); |
| 101 | |||
| 102 |
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2 | VectorXd q = VectorXd::Ones(model.nq); |
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2 | q.segment<4>(3).normalize(); |
| 104 | |||
| 105 |
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2 | pinocchio::computeJointJacobians(model, data_ref, q); |
| 106 | |||
| 107 |
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2 | const std::string RF = "rleg6_joint"; |
| 108 |
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2 | const std::string LF = "lleg6_joint"; |
| 109 | |||
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2 | Data::Matrix6x J_RF(6, model.nv); |
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2 | J_RF.setZero(); |
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2 | getJointJacobian(model, data_ref, model.getJointId(RF), LOCAL, J_RF); |
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2 | Data::Matrix6x J_LF(6, model.nv); |
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2 | J_LF.setZero(); |
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2 | getJointJacobian(model, data_ref, model.getJointId(LF), LOCAL, J_LF); |
| 116 | |||
| 117 |
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2 | Eigen::MatrixXd J(12, model.nv); |
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2 | J.setZero(); |
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2 | J.topRows<6>() = J_RF; |
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2 | J.bottomRows<6>() = J_LF; |
| 121 | |||
| 122 | // Check Forward Dynamics | ||
| 123 |
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2 | pinocchio::crba(model, data_ref, q, pinocchio::Convention::WORLD); |
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2 | data_ref.M.triangularView<Eigen::StrictlyLower>() = |
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4 | data_ref.M.transpose().triangularView<Eigen::StrictlyLower>(); |
| 126 | |||
| 127 |
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2 | Eigen::MatrixXd MJtJ(model.nv + 12, model.nv + 12); |
| 128 |
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2 | MJtJ << data_ref.M, J.transpose(), J, Eigen::MatrixXd::Zero(12, 12); |
| 129 | |||
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2 | Eigen::MatrixXd KKTMatrix_inv(model.nv + 12, model.nv + 12); |
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2 | computeKKTContactDynamicMatrixInverse(model, data, q, J, KKTMatrix_inv); |
| 132 | |||
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2 | BOOST_CHECK(KKTMatrix_inv.isApprox(MJtJ.inverse())); |
| 134 | 2 | } | |
| 135 | |||
| 136 |
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4 | BOOST_AUTO_TEST_CASE(test_getKKTMatrix) |
| 137 | { | ||
| 138 | using namespace Eigen; | ||
| 139 | using namespace pinocchio; | ||
| 140 |
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2 | pinocchio::Model model; |
| 141 |
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2 | pinocchio::buildModels::humanoidRandom(model, true); |
| 142 |
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2 | pinocchio::Data data(model); |
| 143 | |||
| 144 |
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2 | VectorXd q = VectorXd::Ones(model.nq); |
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2 | q.segment<4>(3).normalize(); |
| 146 | |||
| 147 |
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2 | pinocchio::computeJointJacobians(model, data, q); |
| 148 | |||
| 149 |
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2 | VectorXd v = VectorXd::Ones(model.nv); |
| 150 |
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2 | VectorXd tau = VectorXd::Zero(model.nv); |
| 151 | |||
| 152 |
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2 | const std::string RF = "rleg6_joint"; |
| 153 |
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2 | const std::string LF = "lleg6_joint"; |
| 154 | |||
| 155 |
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2 | Data::Matrix6x J_RF(6, model.nv); |
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2 | J_RF.setZero(); |
| 157 |
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2 | getJointJacobian(model, data, model.getJointId(RF), LOCAL, J_RF); |
| 158 |
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2 | Data::Matrix6x J_LF(6, model.nv); |
| 159 |
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2 | J_LF.setZero(); |
| 160 |
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2 | getJointJacobian(model, data, model.getJointId(LF), LOCAL, J_LF); |
| 161 | |||
| 162 |
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2 | Eigen::MatrixXd J(12, model.nv); |
| 163 |
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2 | J.setZero(); |
| 164 |
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2 | J.topRows<6>() = J_RF; |
| 165 |
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2 | J.bottomRows<6>() = J_LF; |
| 166 | |||
| 167 |
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2 | Eigen::VectorXd gamma(VectorXd::Ones(12)); |
| 168 | |||
| 169 |
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2 | Eigen::MatrixXd H(J.transpose()); |
| 170 | |||
| 171 | // Check Forward Dynamics | ||
| 172 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 173 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_DEPRECECATED_DECLARATIONS | ||
| 174 |
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2 | pinocchio::forwardDynamics(model, data, q, v, tau, J, gamma, 0.); |
| 175 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 176 | |||
| 177 |
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2 | data.M.triangularView<Eigen::StrictlyLower>() = |
| 178 |
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4 | data.M.transpose().triangularView<Eigen::StrictlyLower>(); |
| 179 | |||
| 180 |
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2 | Eigen::MatrixXd MJtJ(model.nv + 12, model.nv + 12); |
| 181 |
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2 | MJtJ << data.M, J.transpose(), J, Eigen::MatrixXd::Zero(12, 12); |
| 182 | |||
| 183 |
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2 | Eigen::MatrixXd KKTMatrix_inv(model.nv + 12, model.nv + 12); |
| 184 | |||
| 185 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 186 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_DEPRECECATED_DECLARATIONS | ||
| 187 |
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2 | getKKTContactDynamicMatrixInverse(model, data, J, KKTMatrix_inv); |
| 188 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 189 | |||
| 190 |
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2 | BOOST_CHECK(KKTMatrix_inv.isApprox(MJtJ.inverse())); |
| 191 | |||
| 192 | // Check Impulse Dynamics | ||
| 193 | 2 | const double r_coeff = 1.; | |
| 194 |
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2 | VectorXd v_before = VectorXd::Ones(model.nv); |
| 195 | |||
| 196 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 197 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_DEPRECECATED_DECLARATIONS | ||
| 198 |
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2 | pinocchio::impulseDynamics(model, data, q, v_before, J, r_coeff, 0.); |
| 199 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 200 | |||
| 201 |
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2 | data.M.triangularView<Eigen::StrictlyLower>() = |
| 202 |
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4 | data.M.transpose().triangularView<Eigen::StrictlyLower>(); |
| 203 |
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2 | MJtJ << data.M, J.transpose(), J, Eigen::MatrixXd::Zero(12, 12); |
| 204 | |||
| 205 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 206 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_DEPRECECATED_DECLARATIONS | ||
| 207 |
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2 | getKKTContactDynamicMatrixInverse(model, data, J, KKTMatrix_inv); |
| 208 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 209 | |||
| 210 |
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2 | BOOST_CHECK(KKTMatrix_inv.isApprox(MJtJ.inverse())); |
| 211 | 2 | } | |
| 212 | |||
| 213 |
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4 | BOOST_AUTO_TEST_CASE(test_FD_with_damping) |
| 214 | { | ||
| 215 | using namespace Eigen; | ||
| 216 | using namespace pinocchio; | ||
| 217 | |||
| 218 |
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2 | pinocchio::Model model; |
| 219 |
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2 | pinocchio::buildModels::humanoidRandom(model, true); |
| 220 |
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2 | pinocchio::Data data(model); |
| 221 | |||
| 222 |
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2 | VectorXd q = VectorXd::Ones(model.nq); |
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2 | q.segment<4>(3).normalize(); |
| 224 | |||
| 225 |
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2 | pinocchio::computeJointJacobians(model, data, q); |
| 226 | |||
| 227 |
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2 | VectorXd v = VectorXd::Ones(model.nv); |
| 228 |
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2 | VectorXd tau = VectorXd::Zero(model.nv); |
| 229 | |||
| 230 |
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2 | const std::string RF = "rleg6_joint"; |
| 231 | |||
| 232 |
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2 | Data::Matrix6x J_RF(6, model.nv); |
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2 | J_RF.setZero(); |
| 234 |
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2 | getJointJacobian(model, data, model.getJointId(RF), LOCAL, J_RF); |
| 235 | |||
| 236 |
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2 | Eigen::MatrixXd J(12, model.nv); |
| 237 |
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2 | J.setZero(); |
| 238 |
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2 | J.topRows<6>() = J_RF; |
| 239 |
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2 | J.bottomRows<6>() = J_RF; |
| 240 | |||
| 241 |
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2 | Eigen::VectorXd gamma(VectorXd::Ones(12)); |
| 242 | |||
| 243 | // Forward Dynamics with damping | ||
| 244 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 245 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_DEPRECECATED_DECLARATIONS | ||
| 246 |
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2 | pinocchio::forwardDynamics(model, data, q, v, tau, J, gamma, 1e-12); |
| 247 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 248 | |||
| 249 | // Matrix Definitions | ||
| 250 |
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2 | Eigen::MatrixXd H(J.transpose()); |
| 251 |
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2 | data.M.triangularView<Eigen::StrictlyLower>() = |
| 252 |
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4 | data.M.transpose().triangularView<Eigen::StrictlyLower>(); |
| 253 | |||
| 254 |
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2 | MatrixXd Minv(data.M.inverse()); |
| 255 |
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2 | MatrixXd JMinvJt(J * Minv * J.transpose()); |
| 256 | |||
| 257 | // Check that JMinvJt is correctly formed | ||
| 258 |
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2 | Eigen::MatrixXd G_ref(J.transpose()); |
| 259 |
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2 | cholesky::Uiv(model, data, G_ref); |
| 260 |
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66 | for (int k = 0; k < model.nv; ++k) |
| 261 |
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64 | G_ref.row(k) /= sqrt(data.D[k]); |
| 262 |
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2 | Eigen::MatrixXd H_ref(G_ref.transpose() * G_ref); |
| 263 |
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2 | BOOST_CHECK(H_ref.isApprox(JMinvJt, 1e-12)); |
| 264 | |||
| 265 | // Actual Residuals | ||
| 266 |
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2 | Eigen::VectorXd constraint_residual(J * data.ddq + gamma); |
| 267 | Eigen::VectorXd dynamics_residual( | ||
| 268 |
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2 | data.M * data.ddq + data.nle - tau - J.transpose() * data.lambda_c); |
| 269 |
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2 | BOOST_CHECK(constraint_residual.norm() <= 1e-9); |
| 270 |
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2 | BOOST_CHECK(dynamics_residual.norm() <= 1e-12); |
| 271 | 2 | } | |
| 272 | |||
| 273 |
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4 | BOOST_AUTO_TEST_CASE(test_ID) |
| 274 | { | ||
| 275 | using namespace Eigen; | ||
| 276 | using namespace pinocchio; | ||
| 277 | |||
| 278 |
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2 | pinocchio::Model model; |
| 279 |
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2 | pinocchio::buildModels::humanoidRandom(model, true); |
| 280 |
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2 | pinocchio::Data data(model); |
| 281 | |||
| 282 |
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2 | VectorXd q = VectorXd::Ones(model.nq); |
| 283 |
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2 | q.segment<4>(3).normalize(); |
| 284 | |||
| 285 |
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2 | pinocchio::computeJointJacobians(model, data, q); |
| 286 | |||
| 287 |
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2 | VectorXd v_before = VectorXd::Ones(model.nv); |
| 288 | |||
| 289 |
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2 | const std::string RF = "rleg6_joint"; |
| 290 |
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2 | const std::string LF = "lleg6_joint"; |
| 291 | |||
| 292 |
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2 | Data::Matrix6x J_RF(6, model.nv); |
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2 | J_RF.setZero(); |
| 294 |
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2 | getJointJacobian(model, data, model.getJointId(RF), LOCAL, J_RF); |
| 295 |
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2 | Data::Matrix6x J_LF(6, model.nv); |
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2 | J_LF.setZero(); |
| 297 |
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2 | getJointJacobian(model, data, model.getJointId(LF), LOCAL, J_LF); |
| 298 | |||
| 299 |
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2 | Eigen::MatrixXd J(12, model.nv); |
| 300 |
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2 | J.setZero(); |
| 301 |
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2 | J.topRows<6>() = J_RF; |
| 302 |
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2 | J.bottomRows<6>() = J_LF; |
| 303 | |||
| 304 | 2 | const double r_coeff = 1.; | |
| 305 | |||
| 306 |
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2 | Eigen::MatrixXd H(J.transpose()); |
| 307 | |||
| 308 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 309 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_DEPRECECATED_DECLARATIONS | ||
| 310 |
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2 | pinocchio::impulseDynamics(model, data, q, v_before, J, r_coeff, 0.); |
| 311 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 312 | |||
| 313 |
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2 | data.M.triangularView<Eigen::StrictlyLower>() = |
| 314 |
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4 | data.M.transpose().triangularView<Eigen::StrictlyLower>(); |
| 315 | |||
| 316 |
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2 | MatrixXd Minv(data.M.inverse()); |
| 317 |
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2 | MatrixXd JMinvJt(J * Minv * J.transpose()); |
| 318 | |||
| 319 |
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2 | Eigen::MatrixXd G_ref(J.transpose()); |
| 320 |
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2 | cholesky::Uiv(model, data, G_ref); |
| 321 |
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66 | for (int k = 0; k < model.nv; ++k) |
| 322 |
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64 | G_ref.row(k) /= sqrt(data.D[k]); |
| 323 |
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2 | Eigen::MatrixXd H_ref(G_ref.transpose() * G_ref); |
| 324 |
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2 | BOOST_CHECK(H_ref.isApprox(JMinvJt, 1e-12)); |
| 325 | |||
| 326 |
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2 | VectorXd lambda_ref = JMinvJt.inverse() * (-r_coeff * J * v_before - J * v_before); |
| 327 |
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2 | BOOST_CHECK(data.impulse_c.isApprox(lambda_ref, 1e-12)); |
| 328 | |||
| 329 |
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2 | VectorXd v_after_ref = Minv * (data.M * v_before + J.transpose() * lambda_ref); |
| 330 | |||
| 331 |
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2 | Eigen::VectorXd constraint_residual(J * data.dq_after + r_coeff * J * v_before); |
| 332 |
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2 | BOOST_CHECK(constraint_residual.norm() <= 1e-12); |
| 333 | |||
| 334 | Eigen::VectorXd dynamics_residual( | ||
| 335 |
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2 | data.M * data.dq_after - data.M * v_before - J.transpose() * data.impulse_c); |
| 336 |
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2 | BOOST_CHECK(dynamics_residual.norm() <= 1e-12); |
| 337 | 2 | } | |
| 338 | |||
| 339 |
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|
4 | BOOST_AUTO_TEST_CASE(timings_fd_llt) |
| 340 | { | ||
| 341 | using namespace Eigen; | ||
| 342 | using namespace pinocchio; | ||
| 343 | |||
| 344 |
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2 | pinocchio::Model model; |
| 345 |
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2 | pinocchio::buildModels::humanoidRandom(model, true); |
| 346 |
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2 | pinocchio::Data data(model); |
| 347 | |||
| 348 | #ifdef NDEBUG | ||
| 349 | #ifdef _INTENSE_TESTING_ | ||
| 350 | const size_t NBT = 1000 * 1000; | ||
| 351 | #else | ||
| 352 | const size_t NBT = 100; | ||
| 353 | #endif | ||
| 354 | |||
| 355 | #else | ||
| 356 | 2 | const size_t NBT = 1; | |
| 357 |
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2 | std::cout << "(the time score in debug mode is not relevant) "; |
| 358 | #endif // ifndef NDEBUG | ||
| 359 | |||
| 360 |
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2 | VectorXd q = VectorXd::Ones(model.nq); |
| 361 |
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2 | q.segment<4>(3).normalize(); |
| 362 | |||
| 363 |
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2 | pinocchio::computeJointJacobians(model, data, q); |
| 364 | |||
| 365 |
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2 | VectorXd v = VectorXd::Ones(model.nv); |
| 366 |
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2 | VectorXd tau = VectorXd::Zero(model.nv); |
| 367 | |||
| 368 |
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2 | const std::string RF = "rleg6_joint"; |
| 369 |
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2 | const std::string LF = "lleg6_joint"; |
| 370 | |||
| 371 |
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2 | Data::Matrix6x J_RF(6, model.nv); |
| 372 |
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2 | J_RF.setZero(); |
| 373 |
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2 | getJointJacobian(model, data, model.getJointId(RF), LOCAL, J_RF); |
| 374 |
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2 | Data::Matrix6x J_LF(6, model.nv); |
| 375 |
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2 | J_LF.setZero(); |
| 376 |
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2 | getJointJacobian(model, data, model.getJointId(LF), LOCAL, J_LF); |
| 377 | |||
| 378 |
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2 | Eigen::MatrixXd J(12, model.nv); |
| 379 |
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2 | J.topRows<6>() = J_RF; |
| 380 |
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2 | J.bottomRows<6>() = J_LF; |
| 381 | |||
| 382 |
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2 | Eigen::VectorXd gamma(VectorXd::Ones(12)); |
| 383 | |||
| 384 |
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2 | model.lowerPositionLimit.head<7>().fill(-1.); |
| 385 |
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2 | model.upperPositionLimit.head<7>().fill(1.); |
| 386 | |||
| 387 |
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2 | q = pinocchio::randomConfiguration(model); |
| 388 | |||
| 389 |
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2 | PinocchioTicToc timer(PinocchioTicToc::US); |
| 390 |
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2 | timer.tic(); |
| 391 |
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4 | SMOOTH(NBT) |
| 392 | { | ||
| 393 | PINOCCHIO_COMPILER_DIAGNOSTIC_PUSH | ||
| 394 | PINOCCHIO_COMPILER_DIAGNOSTIC_IGNORED_DEPRECECATED_DECLARATIONS | ||
| 395 |
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2 | pinocchio::forwardDynamics(model, data, q, v, tau, J, gamma, 0.); |
| 396 | PINOCCHIO_COMPILER_DIAGNOSTIC_POP | ||
| 397 | } | ||
| 398 |
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2 | timer.toc(std::cout, NBT); |
| 399 | 2 | } | |
| 400 | |||
| 401 | BOOST_AUTO_TEST_SUITE_END() | ||
| 402 |