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// Copyright (c) 2015, Joseph Mirabel |
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// Authors: Joseph Mirabel (joseph.mirabel@laas.fr) |
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// |
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// Redistribution and use in source and binary forms, with or without |
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// modification, are permitted provided that the following conditions are |
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// met: |
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// |
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// 1. Redistributions of source code must retain the above copyright |
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// notice, this list of conditions and the following disclaimer. |
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// |
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// 2. Redistributions in binary form must reproduce the above copyright |
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// notice, this list of conditions and the following disclaimer in the |
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// documentation and/or other materials provided with the distribution. |
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// |
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
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// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH |
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// DAMAGE. |
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#include "hpp/constraints/qp-static-stability.hh" |
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#include <hpp/pinocchio/device.hh> |
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#include <hpp/pinocchio/joint.hh> |
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#include <limits> |
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#include "hpp/constraints/tools.hh" |
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namespace hpp { |
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namespace constraints { |
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namespace { |
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std::size_t forceDatasToNbContacts( |
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const std::vector<ConvexShapeContact::ForceData>& fds) { |
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std::size_t nb = 0; |
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for (std::vector<ConvexShapeContact::ForceData>::const_iterator it = |
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fds.begin(); |
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it != fds.end(); ++it) |
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nb += it->points.size(); |
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return nb; |
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} |
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} // namespace |
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const Eigen::Matrix<value_type, 6, 1> QPStaticStability::Gravity = |
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(Eigen::Matrix<value_type, 6, 1>() << 0, 0, -1, 0, 0, 0).finished(); |
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const Eigen::Matrix<value_type, 6, 1> QPStaticStability::MinusGravity = |
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(Eigen::Matrix<value_type, 6, 1>() << 0, 0, +1, 0, 0, 0).finished(); |
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QPStaticStability::QPStaticStability(const std::string& name, |
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const DevicePtr_t& robot, |
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const Contacts_t& contacts, |
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const CenterOfMassComputationPtr_t& com) |
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: DifferentiableFunction(robot->configSize(), robot->numberDof(), |
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LiegroupSpace::R1(), name), |
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Zeros(new qpOASES::real_t[contacts.size()]), |
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nWSR(40), |
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robot_(robot), |
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nbContacts_(contacts.size()), |
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com_(com), |
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H_(nbContacts_, nbContacts_), |
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G_(nbContacts_), |
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qp_((qpOASES::int_t)nbContacts_, qpOASES::HST_SEMIDEF), |
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phi_(Eigen::Matrix<value_type, 6, Eigen::Dynamic>::Zero(6, nbContacts_), |
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Eigen::Matrix<value_type, 6, Eigen::Dynamic>::Zero( |
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6, nbContacts_ * robot->numberDof())), |
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primal_(vector_t::Zero(nbContacts_)), |
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dual_(vector_t::Zero(nbContacts_)) { |
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VectorMap_t zeros(Zeros, nbContacts_); |
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zeros.setZero(); |
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qpOASES::Options options; |
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qp_.setOptions(options); |
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qp_.setPrintLevel(qpOASES::PL_NONE); |
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phi_.setSize(2, nbContacts_); |
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Traits<PointCom>::Ptr_t OG = PointCom::create(com); |
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for (std::size_t i = 0; i < contacts.size(); ++i) { |
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Traits<PointInJoint>::Ptr_t OP2 = PointInJoint::create( |
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contacts[i].joint, contacts[i].point, robot->numberDof()); |
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Traits<VectorInJoint>::Ptr_t n2 = VectorInJoint::create( |
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contacts[i].joint, contacts[i].normal, robot->numberDof()); |
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phi_(0, i) = n2; |
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phi_(1, i) = (OG - OP2) ^ n2; |
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} |
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} |
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QPStaticStability::QPStaticStability(const std::string& name, |
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const DevicePtr_t& robot, |
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const std::vector<ForceData>& contacts, |
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const CenterOfMassComputationPtr_t& com) |
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: DifferentiableFunction(robot->configSize(), robot->numberDof(), 1, name), |
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Zeros(new qpOASES::real_t[forceDatasToNbContacts(contacts)]), |
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nWSR(40), |
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robot_(robot), |
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nbContacts_(forceDatasToNbContacts(contacts)), |
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com_(com), |
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H_(nbContacts_, nbContacts_), |
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G_(nbContacts_), |
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qp_((qpOASES::int_t)nbContacts_, qpOASES::HST_SEMIDEF), |
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phi_(Eigen::Matrix<value_type, 6, Eigen::Dynamic>::Zero(6, nbContacts_), |
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Eigen::Matrix<value_type, 6, Eigen::Dynamic>::Zero( |
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6, nbContacts_ * robot->numberDof())), |
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primal_(vector_t::Zero(nbContacts_)), |
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dual_(vector_t::Zero(nbContacts_)) { |
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VectorMap_t zeros(Zeros, nbContacts_); |
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zeros.setZero(); |
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qpOASES::Options options; |
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qp_.setOptions(options); |
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qp_.setPrintLevel(qpOASES::PL_NONE); |
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phi_.setSize(2, nbContacts_); |
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Traits<PointCom>::Ptr_t OG = PointCom::create(com); |
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std::size_t col = 0; |
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for (std::size_t i = 0; i < contacts.size(); ++i) { |
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Traits<VectorInJoint>::Ptr_t n = VectorInJoint::create( |
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contacts[i].joint, contacts[i].normal, robot->numberDof()); |
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for (std::size_t j = 0; j < contacts[i].points.size(); ++j) { |
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Traits<PointInJoint>::Ptr_t OP = PointInJoint::create( |
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contacts[i].joint, contacts[i].points[j], robot->numberDof()); |
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phi_(0, col) = n; |
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phi_(1, col) = (OG - OP) ^ n; |
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col++; |
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} |
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} |
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} |
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QPStaticStabilityPtr_t QPStaticStability::create( |
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const std::string& name, const DevicePtr_t& robot, |
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const Contacts_t& contacts, const CenterOfMassComputationPtr_t& com) { |
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return QPStaticStabilityPtr_t( |
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new QPStaticStability(name, robot, contacts, com)); |
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} |
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QPStaticStabilityPtr_t QPStaticStability::create( |
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const std::string& name, const DevicePtr_t& robot, |
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const std::vector<ForceData>& contacts, |
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const CenterOfMassComputationPtr_t& com) { |
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return QPStaticStabilityPtr_t( |
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new QPStaticStability(name, robot, contacts, com)); |
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} |
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QPStaticStabilityPtr_t QPStaticStability::create( |
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const DevicePtr_t& robot, const Contacts_t& contacts, |
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const CenterOfMassComputationPtr_t& com) { |
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return create("QPStaticStability", robot, contacts, com); |
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} |
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void QPStaticStability::impl_compute(LiegroupElementRef result, |
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ConfigurationIn_t argument) const { |
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robot_->currentConfiguration(argument); |
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robot_->computeForwardKinematics(pinocchio::JOINT_POSITION); |
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phi_.invalidate(); |
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phi_.computeValue(argument); |
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// phi_.computeSVD (argument); |
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qpOASES::returnValue ret = solveQP(result.vector()); |
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if (ret != qpOASES::SUCCESSFUL_RETURN) { |
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hppDout(error, "QP could not be solved. Error is " << ret); |
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} |
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if (!checkQPSol()) { |
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hppDout(error, "QP solution does not satisfies the constraints"); |
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} |
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} |
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void QPStaticStability::impl_jacobian(matrixOut_t jacobian, |
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ConfigurationIn_t argument) const { |
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robot_->currentConfiguration(argument); |
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robot_->computeForwardKinematics(pinocchio::JOINT_POSITION | |
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pinocchio::JACOBIAN); |
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phi_.invalidate(); |
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// phi_.computeSVD (argument); |
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phi_.computeJacobian(argument); |
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vector_t res(1); |
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qpOASES::returnValue ret = solveQP(res); |
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if (ret != qpOASES::SUCCESSFUL_RETURN) { |
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hppDout(error, "QP could not be solved. Error is " << ret); |
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} |
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if (!checkQPSol()) { |
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hppDout(error, "QP solution does not satisfies the constraints"); |
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} |
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if (!checkStrictComplementarity()) { |
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hppDout(error, |
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"Strict complementary slackness does not hold. " |
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"Jacobian WILL be wrong."); |
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} |
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// TODO preallocate this. |
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matrix_t JT_phi_F(nbContacts_, robot_->numberDof()); |
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matrix_t J_F(6, robot_->numberDof()); |
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phi_.jacobianTransposeTimes(argument, phi_.value() * primal_, JT_phi_F); |
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phi_.jacobianTimes(argument, primal_, J_F); |
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jacobian = 0.5 * primal_.transpose() * JT_phi_F + |
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(0.5 * phi_.value() * primal_ + Gravity).transpose() * J_F; |
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} |
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inline qpOASES::returnValue QPStaticStability::solveQP( |
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vectorOut_t result) const { |
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// TODO: Use the SVD to solve a smaller quadratic problem |
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// Try to find a positive solution |
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using qpOASES::SUCCESSFUL_RETURN; |
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H_ = phi_.value().transpose() * phi_.value(); |
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G_ = phi_.value().transpose() * Gravity; |
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qpOASES::int_t nwsr = nWSR; |
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qp_.reset(); |
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qp_.setHessianType(qpOASES::HST_SEMIDEF); |
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qpOASES::returnValue ret; |
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ret = qp_.init(H_.data(), G_.data(), Zeros, 0, nwsr, 0); |
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qp_.getPrimalSolution(primal_.data()); |
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qp_.getDualSolution(dual_.data()); |
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result[0] = 2 * qp_.getObjVal() + MinusGravity.squaredNorm(); |
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return ret; |
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} |
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bool QPStaticStability::checkQPSol() const { |
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return (primal_.array() >= -1e-8).all(); |
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} |
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bool QPStaticStability::checkStrictComplementarity() const { |
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qpOASES::real_t eps = qp_.getOptions().boundTolerance; |
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return ((primal_.array() > eps && dual_.cwiseAbs().array() <= eps) || |
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(dual_.array() > eps && primal_.cwiseAbs().array() <= eps)) |
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.all(); |
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} |
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} // namespace constraints |
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} // namespace hpp |
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