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// Copyright (c) 2014, LAAS-CNRS |
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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/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 <hpp/pinocchio/liegroup-element.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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using hpp::pinocchio::LiegroupElement; |
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const value_type StaticStability::G = 9.81; |
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const Eigen::Matrix<value_type, 6, 1> StaticStability::Gravity = |
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(Eigen::Matrix<value_type, 6, 1>() << 0, 0, -1, 0, 0, 0).finished(); |
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StaticStability::StaticStability(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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contacts.size() + 6, name), |
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robot_(robot), |
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contacts_(contacts), |
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com_(com), |
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phi_(Eigen::Matrix<value_type, 6, Eigen::Dynamic>::Zero(6, |
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contacts.size()), |
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Eigen::Matrix<value_type, 6, Eigen::Dynamic>::Zero( |
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6, contacts.size() * robot->numberDof())), |
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u_(contacts.size()), |
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uMinus_(contacts.size()), |
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v_(contacts.size()), |
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uDot_(contacts.size(), robot->numberDof()), |
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uMinusDot_(contacts.size(), robot->numberDof()), |
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vDot_(contacts.size(), robot->numberDof()), |
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lambdaDot_(robot->numberDof()) { |
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phi_.setSize(2, contacts.size()); |
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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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StaticStabilityPtr_t StaticStability::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 StaticStabilityPtr_t(new StaticStability(name, robot, contacts, com)); |
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} |
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StaticStabilityPtr_t StaticStability::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("StaticStability", robot, contacts, com); |
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} |
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void StaticStability::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_.computeSVD(argument); |
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const Eigen::Matrix<value_type, 6, 1> G = -1 * Gravity; |
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u_.noalias() = phi_.svd().solve(G); |
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if (computeUminusAndV(u_, uMinus_, v_)) { |
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// value_type lambda, unused_lMax; size_type iMax, iMin; |
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// findBoundIndex (u_, v_, lambda, &iMin, unused_lMax, &iMax); |
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value_type lambda = 1; |
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result.vector().segment(0, contacts_.size()) = u_ + lambda * v_; |
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} else { |
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result.vector().segment(0, contacts_.size()) = u_; |
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} |
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result.vector().segment<6>(contacts_.size()) = Gravity + phi_.value() * u_; |
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} |
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void StaticStability::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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phi_.computePseudoInverse(argument); |
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const Eigen::Matrix<value_type, 6, 1> G = -1 * Gravity; |
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u_.noalias() = phi_.svd().solve(G); |
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phi_.computePseudoInverseJacobian(argument, G); |
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uDot_.noalias() = phi_.pinvJacobian(); |
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jacobian.block(0, 0, contacts_.size(), robot_->numberDof()).noalias() = uDot_; |
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if (computeUminusAndV(u_, uMinus_, v_)) { |
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matrix_t S = -matrix_t::Identity(u_.size(), u_.size()); |
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S.diagonal() = 1 * (u_.array() >= 0).select(0, -vector_t::Ones(u_.size())); |
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// value_type lambda, unused_lMax; size_type iMax, iMin; |
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// findBoundIndex (u_, v_, lambda, &iMin, unused_lMax, &iMax); |
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// if (lambda < Eigen::NumTraits <value_type>::dummy_precision()) |
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// return; |
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value_type lambda = 1; |
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computeVDot(argument, uMinus_, S.diagonal(), uDot_, uMinusDot_, vDot_); |
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// computeLambdaDot (u_, v_, iMin, uDot_, vDot_, lambdaDot_); |
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// jacobian.block (0, 0, contacts_.size(), robot_->numberDof()).noalias () |
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// += lambda * vDot_ + v_ * lambdaDot_.transpose (); |
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jacobian.block(0, 0, contacts_.size(), robot_->numberDof()).noalias() += |
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lambda * vDot_; |
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} |
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phi_.jacobianTimes( |
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argument, u_, |
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jacobian.block(contacts_.size(), 0, 6, robot_->numberDof())); |
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phi_.computePseudoInverseJacobian(argument, Gravity); |
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jacobian.block(contacts_.size(), 0, 6, robot_->numberDof()) += |
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-phi_.value() * phi_.pinvJacobian(); |
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} |
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void StaticStability::findBoundIndex(vectorIn_t u, vectorIn_t v, |
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value_type& lambdaMin, size_type* iMin, |
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value_type& lambdaMax, size_type* iMax) { |
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// Be carefull when v has small values. |
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// Consider them as 0 |
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const value_type eps = Eigen::NumTraits<value_type>::dummy_precision(); |
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vector_t lambdas = |
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(v.array().cwiseAbs() < eps).select(0, -u.cwiseQuotient(v)); |
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lambdaMin = (v.array() > eps).select(lambdas, 0).maxCoeff(iMin); |
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lambdaMax = (v.array() < eps).select(lambdas, 0).minCoeff(iMax); |
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} |
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bool StaticStability::computeUminusAndV(vectorIn_t u, vectorOut_t uMinus, |
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vectorOut_t v) const { |
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using namespace hpp::pinocchio; |
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uMinus.noalias() = (u.array() >= 0).select(0, -u); |
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if (uMinus.isZero()) return false; |
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size_type rank = phi_.svd().rank(); |
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v.noalias() = getV2<MoE_t::SVD_t>(phi_.svd(), rank) * |
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(getV2<MoE_t::SVD_t>(phi_.svd(), rank).adjoint() * uMinus); |
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// v.noalias() = uMinus; |
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// v.noalias() -= getV1 <MoE_t::SVD_t> (phi_.svd()) * |
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// ( getV1 <MoE_t::SVD_t> (phi_.svd()).adjoint() * uMinus ); |
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return true; |
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} |
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void StaticStability::computeVDot(const ConfigurationIn_t arg, |
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vectorIn_t uMinus, vectorIn_t S, |
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matrixIn_t uDot, matrixOut_t uMinusDot, |
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matrixOut_t vDot) const { |
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using namespace hpp::pinocchio; |
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size_type rank = phi_.svd().rank(); |
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uMinusDot.noalias() = S.asDiagonal() * uDot; |
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vDot.noalias() = uMinusDot; |
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vDot.noalias() -= |
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getV1<MoE_t::SVD_t>(phi_.svd(), rank) * |
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(getV1<MoE_t::SVD_t>(phi_.svd(), rank).adjoint() * uMinusDot); |
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// TODO: preallocate this matrix |
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Eigen::Matrix<value_type, 6, Eigen::Dynamic> JphiTimesUMinus( |
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6, robot_->numberDof()); |
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phi_.jacobianTimes(arg, uMinus, JphiTimesUMinus); |
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vDot.noalias() -= phi_.pinv() * JphiTimesUMinus; |
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phi_.computePseudoInverseJacobian(arg, phi_.value() * uMinus); |
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vDot.noalias() -= phi_.pinvJacobian(); |
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} |
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void StaticStability::computeLambdaDot(vectorIn_t u, vectorIn_t v, |
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const std::size_t i0, matrixIn_t uDot, |
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matrixIn_t vDot, |
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vectorOut_t lambdaDot) const { |
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if (std::abs(v(i0)) < Eigen::NumTraits<value_type>::dummy_precision()) |
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lambdaDot.setZero(); |
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else { |
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lambdaDot.noalias() = -uDot.row(i0) / v(i0); |
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lambdaDot.noalias() += (u(i0) / (v(i0) * v(i0))) * vDot.row(i0); |
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} |
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} |
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} // namespace constraints |
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} // namespace hpp |
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