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/////////////////////////////////////////////////////////////////////////////// |
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// BSD 3-Clause License |
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// |
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// Copyright (C) 2019-2020, LAAS-CNRS, New York University, Max Planck |
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// Gesellschaft, |
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// University of Edinburgh |
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// Copyright note valid unless otherwise stated in individual files. |
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// All rights reserved. |
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/////////////////////////////////////////////////////////////////////////////// |
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#include "crocoddyl/core/solvers/kkt.hpp" |
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namespace crocoddyl { |
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SolverKKT::SolverKKT(std::shared_ptr<ShootingProblem> problem) |
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: SolverAbstract(problem), |
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reg_incfactor_(10.), |
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reg_decfactor_(10.), |
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reg_min_(1e-9), |
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reg_max_(1e9), |
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cost_try_(0.), |
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th_grad_(1e-12), |
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was_feasible_(false) { |
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allocateData(); |
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const std::size_t n_alphas = 10; |
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preg_ = 0.; |
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dreg_ = 0.; |
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alphas_.resize(n_alphas); |
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for (std::size_t n = 0; n < n_alphas; ++n) { |
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alphas_[n] = 1. / pow(2., (double)n); |
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} |
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} |
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SolverKKT::~SolverKKT() {} |
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bool SolverKKT::solve(const std::vector<Eigen::VectorXd>& init_xs, |
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const std::vector<Eigen::VectorXd>& init_us, |
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const std::size_t maxiter, const bool is_feasible, |
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const double) { |
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setCandidate(init_xs, init_us, is_feasible); |
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bool recalc = true; |
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for (iter_ = 0; iter_ < maxiter; ++iter_) { |
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while (true) { |
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try { |
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computeDirection(recalc); |
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} catch (std::exception& e) { |
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recalc = false; |
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if (preg_ == reg_max_) { |
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return false; |
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} else { |
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continue; |
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} |
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} |
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break; |
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} |
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expectedImprovement(); |
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for (std::vector<double>::const_iterator it = alphas_.begin(); |
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it != alphas_.end(); ++it) { |
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steplength_ = *it; |
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try { |
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dV_ = tryStep(steplength_); |
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} catch (std::exception& e) { |
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continue; |
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} |
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dVexp_ = steplength_ * d_[0] + 0.5 * steplength_ * steplength_ * d_[1]; |
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if (d_[0] < th_grad_ || !is_feasible_ || dV_ > th_acceptstep_ * dVexp_) { |
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was_feasible_ = is_feasible_; |
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setCandidate(xs_try_, us_try_, true); |
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cost_ = cost_try_; |
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break; |
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} |
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} |
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stoppingCriteria(); |
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const std::size_t n_callbacks = callbacks_.size(); |
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if (n_callbacks != 0) { |
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for (std::size_t c = 0; c < n_callbacks; ++c) { |
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CallbackAbstract& callback = *callbacks_[c]; |
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callback(*this); |
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} |
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} |
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if (was_feasible_ && stop_ < th_stop_) { |
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return true; |
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} |
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} |
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return false; |
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} |
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void SolverKKT::computeDirection(const bool recalc) { |
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const std::size_t T = problem_->get_T(); |
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if (recalc) { |
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calcDiff(); |
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} |
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computePrimalDual(); |
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const Eigen::VectorBlock<Eigen::VectorXd, Eigen::Dynamic> p_x = |
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primal_.segment(0, ndx_); |
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const Eigen::VectorBlock<Eigen::VectorXd, Eigen::Dynamic> p_u = |
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primal_.segment(ndx_, nu_); |
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std::size_t ix = 0; |
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std::size_t iu = 0; |
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const std::vector<std::shared_ptr<ActionModelAbstract> >& models = |
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problem_->get_runningModels(); |
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for (std::size_t t = 0; t < T; ++t) { |
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const std::size_t ndxi = models[t]->get_state()->get_ndx(); |
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const std::size_t nui = models[t]->get_nu(); |
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dxs_[t] = p_x.segment(ix, ndxi); |
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dus_[t] = p_u.segment(iu, nui); |
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lambdas_[t] = dual_.segment(ix, ndxi); |
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ix += ndxi; |
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iu += nui; |
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} |
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const std::size_t ndxi = |
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problem_->get_terminalModel()->get_state()->get_ndx(); |
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dxs_.back() = p_x.segment(ix, ndxi); |
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lambdas_.back() = dual_.segment(ix, ndxi); |
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} |
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double SolverKKT::tryStep(const double steplength) { |
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const std::size_t T = problem_->get_T(); |
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const std::vector<std::shared_ptr<ActionModelAbstract> >& models = |
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problem_->get_runningModels(); |
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for (std::size_t t = 0; t < T; ++t) { |
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const std::shared_ptr<ActionModelAbstract>& m = models[t]; |
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m->get_state()->integrate(xs_[t], steplength * dxs_[t], xs_try_[t]); |
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if (m->get_nu() != 0) { |
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us_try_[t] = us_[t]; |
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us_try_[t] += steplength * dus_[t]; |
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} |
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} |
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const std::shared_ptr<ActionModelAbstract> m = problem_->get_terminalModel(); |
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m->get_state()->integrate(xs_[T], steplength * dxs_[T], xs_try_[T]); |
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cost_try_ = problem_->calc(xs_try_, us_try_); |
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return cost_ - cost_try_; |
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} |
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double SolverKKT::stoppingCriteria() { |
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const std::size_t T = problem_->get_T(); |
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std::size_t ix = 0; |
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std::size_t iu = 0; |
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const std::vector<std::shared_ptr<ActionModelAbstract> >& models = |
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problem_->get_runningModels(); |
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const std::vector<std::shared_ptr<ActionDataAbstract> >& datas = |
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problem_->get_runningDatas(); |
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for (std::size_t t = 0; t < T; ++t) { |
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const std::shared_ptr<ActionDataAbstract>& d = datas[t]; |
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const std::size_t ndxi = models[t]->get_state()->get_ndx(); |
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const std::size_t nui = models[t]->get_nu(); |
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dF.segment(ix, ndxi) = lambdas_[t]; |
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dF.segment(ix, ndxi).noalias() -= d->Fx.transpose() * lambdas_[t + 1]; |
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dF.segment(ndx_ + iu, nui).noalias() = -lambdas_[t + 1].transpose() * d->Fu; |
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ix += ndxi; |
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iu += nui; |
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} |
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const std::size_t ndxi = |
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problem_->get_terminalModel()->get_state()->get_ndx(); |
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dF.segment(ix, ndxi) = lambdas_.back(); |
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stop_ = (kktref_.segment(0, ndx_ + nu_) + dF).squaredNorm() + |
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kktref_.segment(ndx_ + nu_, ndx_).squaredNorm(); |
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return stop_; |
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} |
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const Eigen::Vector2d& SolverKKT::expectedImprovement() { |
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d_ = Eigen::Vector2d::Zero(); |
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// -grad^T.primal |
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d_(0) = -kktref_.segment(0, ndx_ + nu_).dot(primal_); |
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// -(hessian.primal)^T.primal |
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kkt_primal_.noalias() = kkt_.block(0, 0, ndx_ + nu_, ndx_ + nu_) * primal_; |
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d_(1) = -kkt_primal_.dot(primal_); |
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return d_; |
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} |
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const Eigen::MatrixXd& SolverKKT::get_kkt() const { return kkt_; } |
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const Eigen::VectorXd& SolverKKT::get_kktref() const { return kktref_; } |
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const Eigen::VectorXd& SolverKKT::get_primaldual() const { return primaldual_; } |
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const std::vector<Eigen::VectorXd>& SolverKKT::get_dxs() const { return dxs_; } |
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const std::vector<Eigen::VectorXd>& SolverKKT::get_dus() const { return dus_; } |
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const std::vector<Eigen::VectorXd>& SolverKKT::get_lambdas() const { |
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return lambdas_; |
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} |
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std::size_t SolverKKT::get_nx() const { return nx_; } |
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std::size_t SolverKKT::get_ndx() const { return ndx_; } |
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std::size_t SolverKKT::get_nu() const { return nu_; } |
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double SolverKKT::calcDiff() { |
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cost_ = problem_->calc(xs_, us_); |
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cost_ = problem_->calcDiff(xs_, us_); |
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// offset on constraint xnext = f(x,u) due to x0 = ref. |
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const std::size_t cx0 = |
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problem_->get_runningModels()[0]->get_state()->get_ndx(); |
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std::size_t ix = 0; |
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std::size_t iu = 0; |
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const std::size_t T = problem_->get_T(); |
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kkt_.block(ndx_ + nu_, 0, ndx_, ndx_).setIdentity(); |
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for (std::size_t t = 0; t < T; ++t) { |
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const std::shared_ptr<ActionModelAbstract>& m = |
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problem_->get_runningModels()[t]; |
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const std::shared_ptr<ActionDataAbstract>& d = |
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problem_->get_runningDatas()[t]; |
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const std::size_t ndxi = m->get_state()->get_ndx(); |
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const std::size_t nui = m->get_nu(); |
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// Computing the gap at the initial state |
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if (t == 0) { |
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m->get_state()->diff(problem_->get_x0(), xs_[0], |
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kktref_.segment(ndx_ + nu_, ndxi)); |
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} |
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// Filling KKT matrix |
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kkt_.block(ix, ix, ndxi, ndxi) = d->Lxx; |
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kkt_.block(ix, ndx_ + iu, ndxi, nui) = d->Lxu; |
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kkt_.block(ndx_ + iu, ix, nui, ndxi) = d->Lxu.transpose(); |
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kkt_.block(ndx_ + iu, ndx_ + iu, nui, nui) = d->Luu; |
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kkt_.block(ndx_ + nu_ + cx0 + ix, ix, ndxi, ndxi) = -d->Fx; |
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kkt_.block(ndx_ + nu_ + cx0 + ix, ndx_ + iu, ndxi, nui) = -d->Fu; |
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// Filling KKT vector |
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kktref_.segment(ix, ndxi) = d->Lx; |
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kktref_.segment(ndx_ + iu, nui) = d->Lu; |
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m->get_state()->diff(d->xnext, xs_[t + 1], |
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kktref_.segment(ndx_ + nu_ + cx0 + ix, ndxi)); |
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ix += ndxi; |
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iu += nui; |
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} |
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const std::shared_ptr<ActionDataAbstract>& df = problem_->get_terminalData(); |
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const std::size_t ndxf = |
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problem_->get_terminalModel()->get_state()->get_ndx(); |
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kkt_.block(ix, ix, ndxf, ndxf) = df->Lxx; |
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kktref_.segment(ix, ndxf) = df->Lx; |
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kkt_.block(0, ndx_ + nu_, ndx_ + nu_, ndx_) = |
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kkt_.block(ndx_ + nu_, 0, ndx_, ndx_ + nu_).transpose(); |
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return cost_; |
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} |
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✗ |
void SolverKKT::computePrimalDual() { |
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primaldual_ = kkt_.lu().solve(-kktref_); |
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primal_ = primaldual_.segment(0, ndx_ + nu_); |
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dual_ = primaldual_.segment(ndx_ + nu_, ndx_); |
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} |
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void SolverKKT::increaseRegularization() { |
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preg_ *= reg_incfactor_; |
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if (preg_ > reg_max_) { |
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preg_ = reg_max_; |
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} |
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dreg_ = preg_; |
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} |
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void SolverKKT::decreaseRegularization() { |
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preg_ /= reg_decfactor_; |
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if (preg_ < reg_min_) { |
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preg_ = reg_min_; |
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} |
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dreg_ = preg_; |
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} |
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void SolverKKT::allocateData() { |
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const std::size_t T = problem_->get_T(); |
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dxs_.resize(T + 1); |
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dus_.resize(T); |
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lambdas_.resize(T + 1); |
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xs_try_.resize(T + 1); |
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us_try_.resize(T); |
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nx_ = 0; |
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ndx_ = 0; |
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nu_ = 0; |
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const std::size_t nx = problem_->get_nx(); |
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const std::size_t ndx = problem_->get_ndx(); |
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const std::vector<std::shared_ptr<ActionModelAbstract> >& models = |
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problem_->get_runningModels(); |
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for (std::size_t t = 0; t < T; ++t) { |
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const std::shared_ptr<ActionModelAbstract>& model = models[t]; |
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if (t == 0) { |
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xs_try_[t] = problem_->get_x0(); |
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} else { |
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xs_try_[t] = Eigen::VectorXd::Constant(nx, NAN); |
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} |
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const std::size_t nu = model->get_nu(); |
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us_try_[t] = Eigen::VectorXd::Constant(nu, NAN); |
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dxs_[t] = Eigen::VectorXd::Zero(ndx); |
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dus_[t] = Eigen::VectorXd::Zero(nu); |
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lambdas_[t] = Eigen::VectorXd::Zero(ndx); |
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nx_ += nx; |
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ndx_ += ndx; |
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nu_ += nu; |
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} |
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nx_ += nx; |
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ndx_ += ndx; |
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xs_try_.back() = problem_->get_terminalModel()->get_state()->zero(); |
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dxs_.back() = Eigen::VectorXd::Zero(ndx); |
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lambdas_.back() = Eigen::VectorXd::Zero(ndx); |
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// Set dimensions for kkt matrix and kkt_ref vector |
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kkt_.resize(2 * ndx_ + nu_, 2 * ndx_ + nu_); |
| 309 |
|
✗ |
kkt_.setZero(); |
| 310 |
|
✗ |
kktref_.resize(2 * ndx_ + nu_); |
| 311 |
|
✗ |
kktref_.setZero(); |
| 312 |
|
✗ |
primaldual_.resize(2 * ndx_ + nu_); |
| 313 |
|
✗ |
primaldual_.setZero(); |
| 314 |
|
✗ |
primal_.resize(ndx_ + nu_); |
| 315 |
|
✗ |
primal_.setZero(); |
| 316 |
|
✗ |
kkt_primal_.resize(ndx_ + nu_); |
| 317 |
|
✗ |
kkt_primal_.setZero(); |
| 318 |
|
✗ |
dual_.resize(ndx_); |
| 319 |
|
✗ |
dual_.setZero(); |
| 320 |
|
✗ |
dF.resize(ndx_ + nu_); |
| 321 |
|
✗ |
dF.setZero(); |
| 322 |
|
|
} |
| 323 |
|
|
|
| 324 |
|
|
} // namespace crocoddyl |
| 325 |
|
|
|