calculate_rigid_joint_constraint.hpp

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#pragma once
 
#include <KokkosBatched_Copy_Decl.hpp>
#include <Kokkos_Core.hpp>
 
#include "math/matrix_operations.hpp"
#include "math/quaternion_operations.hpp"
#include "math/vector_operations.hpp"
 
namespace kynema::constraints {
 
template <typename DeviceType>
struct CalculateRigidJointConstraint {
    template <typename ValueType>
    using View = Kokkos::View<ValueType, DeviceType>;
    template <typename ValueType>
    using ConstView = typename View<ValueType>::const_type;
 
    KOKKOS_FUNCTION static void invoke(
        const ConstView<double[3]>& X0, const ConstView<double[7]>& base_node_u,
        const ConstView<double[7]>& target_node_u, const View<double[6]>& residual_terms,
        const View<double[6][6]>& base_gradient_terms,
        const View<double[6][6]>& target_gradient_terms
    ) {
        using Kokkos::Array;
        using Kokkos::make_pair;
        using Kokkos::subview;
        using CopyMatrixTranspose = KokkosBatched::SerialCopy<KokkosBatched::Trans::Transpose>;
        using CopyMatrix = KokkosBatched::SerialCopy<>;
 
        const auto u1_data = Array<double, 3>{base_node_u(0), base_node_u(1), base_node_u(2)};
        const auto R1_data =
            Array<double, 4>{base_node_u(3), base_node_u(4), base_node_u(5), base_node_u(6)};
        const auto u2_data = Array<double, 3>{target_node_u(0), target_node_u(1), target_node_u(2)};
        const auto R2_data =
            Array<double, 4>{target_node_u(3), target_node_u(4), target_node_u(5), target_node_u(6)};
        auto R1_X0_data = Array<double, 3>{};
        auto C_data = Array<double, 9>{};
        auto R1t_data = Array<double, 4>{};
        auto R2_R1t_data = Array<double, 4>{};
        auto V3_data = Array<double, 3>{};
        auto A_data = Array<double, 9>{};
 
        const auto u1 = ConstView<double[3]>{u1_data.data()};
        const auto R1 = ConstView<double[4]>{R1_data.data()};
        const auto u2 = ConstView<double[3]>{u2_data.data()};
        const auto R2 = ConstView<double[4]>{R2_data.data()};
        const auto R1_X0 = View<double[3]>{R1_X0_data.data()};
        const auto C = View<double[3][3]>{C_data.data()};
        const auto R1t = View<double[4]>{R1t_data.data()};
        const auto R2_R1t = View<double[4]>{R2_R1t_data.data()};
        const auto V3 = View<double[3]>{V3_data.data()};
        const auto A = View<double[3][3]>{A_data.data()};
 
        //----------------------------------------------------------------------
        // Residual Vector
        //----------------------------------------------------------------------
 
        // Phi(0:3) = u2 + X0 - u1 - R1*X0
        math::QuaternionInverse(R1, R1t);
        math::RotateVectorByQuaternion(R1, X0, R1_X0);
        for (auto component = 0; component < 3; ++component) {
            residual_terms(component) =
                u2(component) + X0(component) - u1(component) - R1_X0(component);
        }
 
        // Phi(3:6) = axial(R2*inv(RC)*inv(R1))
        math::QuaternionCompose(R2, R1t, R2_R1t);
        math::QuaternionToRotationMatrix(R2_R1t, C);
        math::AxialVectorOfMatrix(C, V3);
        for (auto component = 0; component < 3; ++component) {
            residual_terms(component + 3) = V3(component);
        }
 
        //----------------------------------------------------------------------
        // Constraint Gradient Matrix
        //----------------------------------------------------------------------
 
        // Target Node gradients
        // B(0:3,0:3) = I
        for (auto component = 0; component < 3; ++component) {
            target_gradient_terms(component, component) = 1.;
        }
 
        // B(3:6,3:6) = AX(R1*RC*inv(R2)) = transpose(AX(R2*inv(RC)*inv(R1)))
        math::AX_Matrix(C, A);
        CopyMatrixTranspose::invoke(
            A, subview(target_gradient_terms, make_pair(3, 6), make_pair(3, 6))
        );
 
        // Base Node gradients
        // B(0:3,0:3) = -I
        for (auto component = 0; component < 3; ++component) {
            base_gradient_terms(component, component) = -1.;
        }
 
        // B(0:3,3:6) = tilde(R1*X0)
        math::VecTilde(R1_X0, A);
        CopyMatrix::invoke(A, subview(base_gradient_terms, make_pair(0, 3), make_pair(3, 6)));
 
        // B(3:6,3:6) = -AX(R2*inv(RC)*inv(R1))
        math::AX_Matrix(C, A);
        for (auto component_1 = 0; component_1 < 3; ++component_1) {
            for (auto component_2 = 0; component_2 < 3; ++component_2) {
                base_gradient_terms(component_1 + 3, component_2 + 3) = -A(component_1, component_2);
            }
        }
    }
};
}  // namespace kynema::constraints