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// Copyright (c) 2022 INRIA |
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#ifndef __pinocchio_algorithm_pgs_solver_hxx__ |
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#define __pinocchio_algorithm_pgs_solver_hxx__ |
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#include <limits> |
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#include "pinocchio/algorithm/constraints/coulomb-friction-cone.hpp" |
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namespace pinocchio |
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{ |
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template<typename _Scalar> |
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template< |
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typename MatrixLike, |
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typename VectorLike, |
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typename ConstraintAllocator, |
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typename VectorLikeOut> |
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bool PGSContactSolverTpl<_Scalar>::solve( |
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const MatrixLike & G, |
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const Eigen::MatrixBase<VectorLike> & g, |
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const std::vector<CoulombFrictionConeTpl<Scalar>, ConstraintAllocator> & cones, |
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const Eigen::DenseBase<VectorLikeOut> & x_sol, |
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const Scalar over_relax) |
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{ |
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typedef CoulombFrictionConeTpl<Scalar> CoulombFrictionCone; |
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typedef Eigen::Matrix<Scalar, 2, 1> Vector2; |
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typedef Eigen::Matrix<Scalar, 3, 1> Vector3; |
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// typedef Eigen::Matrix<Scalar,6,1> Vector6; |
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PINOCCHIO_CHECK_INPUT_ARGUMENT( |
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over_relax < Scalar(2) && over_relax > Scalar(0), "over_relax should lie in ]0,2[.") |
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PINOCCHIO_CHECK_ARGUMENT_SIZE(g.size(), this->getProblemSize()); |
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PINOCCHIO_CHECK_ARGUMENT_SIZE(G.rows(), this->getProblemSize()); |
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PINOCCHIO_CHECK_ARGUMENT_SIZE(G.cols(), this->getProblemSize()); |
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PINOCCHIO_CHECK_ARGUMENT_SIZE(x_sol.size(), this->getProblemSize()); |
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const size_t nc = cones.size(); // num constraints |
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int it = 0; |
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PINOCCHIO_EIGEN_MALLOC_NOT_ALLOWED(); |
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#ifdef PINOCCHIO_WITH_HPP_FCL |
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timer.start(); |
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#endif // PINOCCHIO_WITH_HPP_FCL |
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Scalar complementarity, proximal_metric, dual_feasibility; |
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bool abs_prec_reached = false, rel_prec_reached = false; |
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x = x_sol; |
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Scalar x_previous_norm_inf = x.template lpNorm<Eigen::Infinity>(); |
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for (; it < this->max_it; ++it) |
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{ |
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x_previous = x; |
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complementarity = Scalar(0); |
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dual_feasibility = Scalar(0); |
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for (size_t cone_id = 0; cone_id < nc; ++cone_id) |
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{ |
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Vector3 velocity; // tmp variable |
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const Eigen::DenseIndex row_id = 3 * cone_id; |
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const CoulombFrictionCone & cone = cones[cone_id]; |
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const auto G_block = G.template block<3, 3>(row_id, row_id, 3, 3); |
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auto x_segment = x.template segment<3>(row_id); |
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velocity.noalias() = G.template middleRows<3>(row_id) * x + g.template segment<3>(row_id); |
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// Normal update |
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Scalar & fz = x_segment.coeffRef(2); |
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const Scalar fz_previous = fz; |
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fz -= Scalar(over_relax / G_block.coeff(2, 2)) * velocity[2]; |
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fz = math::max(Scalar(0), fz); |
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// Account for the fz updated value |
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velocity += G_block.col(2) * (fz - fz_previous); |
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// Tangential update |
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const Scalar min_D_tangent = math::min(G_block.coeff(0, 0), G_block.coeff(1, 1)); |
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auto f_tangent = x_segment.template head<2>(); |
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const Vector2 f_tangent_previous = f_tangent; |
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assert(min_D_tangent > 0 && "min_D_tangent is zero"); |
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f_tangent -= over_relax / min_D_tangent * velocity.template head<2>(); |
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const Scalar f_tangent_norm = f_tangent.norm(); |
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const Scalar mu_fz = cone.mu * fz; |
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if (f_tangent_norm > mu_fz) // Project in the circle of radius mu_fz |
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f_tangent *= mu_fz / f_tangent_norm; |
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// Account for the f_tangent updated value |
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velocity.noalias() = G_block.template leftCols<2>() * (f_tangent - f_tangent_previous); |
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// Compute problem feasibility |
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Scalar contact_complementarity = cone.computeContactComplementarity(velocity, x_segment); |
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assert( |
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contact_complementarity >= Scalar(0) && "contact_complementarity should be positive"); |
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complementarity = math::max(complementarity, contact_complementarity); |
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velocity += cone.computeNormalCorrection(velocity); |
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const Vector3 velocity_proj = cone.dual().project(velocity) - velocity; |
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Scalar contact_dual_feasibility = velocity_proj.norm(); |
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dual_feasibility = math::max(dual_feasibility, contact_dual_feasibility); |
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} |
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// Checking stopping residual |
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if ( |
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check_expression_if_real<Scalar, false>(complementarity <= this->absolute_precision) |
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&& check_expression_if_real<Scalar, false>(dual_feasibility <= this->absolute_precision)) |
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abs_prec_reached = true; |
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else |
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abs_prec_reached = false; |
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proximal_metric = (x - x_previous).template lpNorm<Eigen::Infinity>(); |
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const Scalar x_norm_inf = x.template lpNorm<Eigen::Infinity>(); |
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if (check_expression_if_real<Scalar, false>( |
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proximal_metric |
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<= this->relative_precision * math::max(x_norm_inf, x_previous_norm_inf))) |
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rel_prec_reached = true; |
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else |
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rel_prec_reached = false; |
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if (abs_prec_reached || rel_prec_reached) |
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break; |
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x_previous_norm_inf = x_norm_inf; |
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} |
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#ifdef PINOCCHIO_WITH_HPP_FCL |
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timer.stop(); |
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#endif // PINOCCHIO_WITH_HPP_FCL |
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PINOCCHIO_EIGEN_MALLOC_ALLOWED(); |
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this->absolute_residual = math::max(complementarity, dual_feasibility); |
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this->relative_residual = proximal_metric; |
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this->it = it; |
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x_sol.const_cast_derived() = x; |
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if (abs_prec_reached || rel_prec_reached) |
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return true; |
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return false; |
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} |
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} // namespace pinocchio |
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#endif // ifndef __pinocchio_algorithm_pgs_solver_hxx__ |
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