abstract_time_indexed_problem.cpp

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#include <exotica_core/problems/abstract_time_indexed_problem.h>
#include <exotica_core/setup.h>
 
namespace exotica
{
AbstractTimeIndexedProblem::AbstractTimeIndexedProblem()
{
    flags_ = KIN_FK | KIN_J;
}
 
AbstractTimeIndexedProblem::~AbstractTimeIndexedProblem() = default;
 
Eigen::MatrixXd AbstractTimeIndexedProblem::GetBounds() const
{
    return scene_->GetKinematicTree().GetJointLimits();
}
 
void AbstractTimeIndexedProblem::ReinitializeVariables()
{
    if (debug_) HIGHLIGHT_NAMED("TimeIndexedProblem", "Initialize problem with T=" << T_);
 
    num_tasks = tasks_.size();
    length_Phi = 0;
    length_jacobian = 0;
    TaskSpaceVector y_ref_;
    for (int i = 0; i < num_tasks; ++i)
    {
        AppendVector(y_ref_.map, tasks_[i]->GetLieGroupIndices());
        length_Phi += tasks_[i]->length;
        length_jacobian += tasks_[i]->length_jacobian;
    }
 
    y_ref_.SetZero(length_Phi);
    Phi.assign(T_, y_ref_);
 
    x.assign(T_, Eigen::VectorXd::Zero(N));
    xdiff.assign(T_, Eigen::VectorXd::Zero(N));
    if (flags_ & KIN_J) jacobian.assign(T_, Eigen::MatrixXd(length_jacobian, N));
    if (flags_ & KIN_H)
    {
        Hessian Htmp;
        Htmp.setConstant(length_jacobian, Eigen::MatrixXd::Zero(N, N));
        hessian.assign(T_, Htmp);
    }
 
    // Set initial trajectory
    initial_trajectory_.resize(T_, scene_->GetControlledState());
 
    // Initialize cost and constraints
    cost.ReinitializeVariables(T_, shared_from_this(), cost_Phi);
    inequality.ReinitializeVariables(T_, shared_from_this(), inequality_Phi);
    equality.ReinitializeVariables(T_, shared_from_this(), equality_Phi);
 
    // Initialize joint velocity constraint
    joint_velocity_constraint_dimension_ = N * (T_ - 1);
    joint_velocity_constraint_jacobian_triplets_.clear();
    // The Jacobian is constant so we can allocate the triplets here for the problem:
    typedef Eigen::Triplet<double> T;
    joint_velocity_constraint_jacobian_triplets_.reserve(joint_velocity_constraint_dimension_);
    for (int t = 1; t < T_; ++t)
    {
        for (int n = 0; n < N; ++n)
        {
            // x_t+1 ==> 1
            joint_velocity_constraint_jacobian_triplets_.emplace_back(T((t - 1) * N + n, (t - 1) * N + n, 1.0));
 
            if (t > 1)
            {
                // x_t => -1
                joint_velocity_constraint_jacobian_triplets_.emplace_back(T((t - 1) * N + n, (t - 2) * N + n, -1.0));
            }
        }
    }
 
    // Updates related to tau
    ct = 1.0 / tau_ / T_;
    xdiff_max_ = q_dot_max_ * tau_;
 
    // Pre-update
    PreUpdate();
}
 
int AbstractTimeIndexedProblem::GetT() const
{
    return T_;
}
 
void AbstractTimeIndexedProblem::SetT(const int T_in)
{
    if (T_in <= 2)
    {
        ThrowNamed("Invalid number of timesteps: " << T_in);
    }
    T_ = T_in;
    ReinitializeVariables();
}
 
double AbstractTimeIndexedProblem::GetTau() const
{
    return tau_;
}
 
void AbstractTimeIndexedProblem::SetTau(const double tau_in)
{
    if (tau_in <= 0.) ThrowPretty("tau_ is expected to be greater than 0. (tau_=" << tau_in << ")");
    tau_ = tau_in;
    ReinitializeVariables();
}
 
void AbstractTimeIndexedProblem::PreUpdate()
{
    PlanningProblem::PreUpdate();
    for (int i = 0; i < tasks_.size(); ++i) tasks_[i]->is_used = false;
    cost.UpdateS();
    inequality.UpdateS();
    equality.UpdateS();
 
    // Update list of active equality/inequality constraints:
    active_nonlinear_equality_constraints_dimension_ = 0;
    active_nonlinear_inequality_constraints_dimension_ = 0;
    active_nonlinear_equality_constraints_.clear();
    active_nonlinear_inequality_constraints_.clear();
    for (int t = 1; t < T_; ++t)
    {
        for (const TaskIndexing& task : equality.indexing)
        {
            if (equality.rho[t](task.id) != 0.0)
            {
                active_nonlinear_equality_constraints_.emplace_back(std::make_pair(t, task.id));
                active_nonlinear_equality_constraints_dimension_ += task.length_jacobian;
            }
        }
 
        for (const TaskIndexing& task : inequality.indexing)
        {
            if (inequality.rho[t](task.id) != 0.0)
            {
                active_nonlinear_inequality_constraints_.emplace_back(std::make_pair(t, task.id));
                active_nonlinear_inequality_constraints_dimension_ += task.length_jacobian;
            }
        }
    }
 
    // Create a new set of kinematic solutions with the size of the trajectory
    // based on the lastest KinematicResponse in order to reflect model state
    // updates etc.
    kinematic_solutions_.clear();
    kinematic_solutions_.resize(T_);
    for (int i = 0; i < T_; ++i) kinematic_solutions_[i] = std::make_shared<KinematicResponse>(*scene_->GetKinematicTree().GetKinematicResponse());
}
 
void AbstractTimeIndexedProblem::SetInitialTrajectory(const std::vector<Eigen::VectorXd>& q_init_in)
{
    if (q_init_in.size() != T_)
        ThrowPretty("Expected initial trajectory of length "
                    << T_ << " but got " << q_init_in.size());
    if (q_init_in[0].rows() != N)
        ThrowPretty("Expected states to have " << N << " rows but got "
                                               << q_init_in[0].rows());
 
    initial_trajectory_ = q_init_in;
    SetStartState(q_init_in[0]);
}
 
std::vector<Eigen::VectorXd> AbstractTimeIndexedProblem::GetInitialTrajectory() const
{
    return initial_trajectory_;
}
 
double AbstractTimeIndexedProblem::GetDuration() const
{
    return tau_ * static_cast<double>(T_);
}
 
void AbstractTimeIndexedProblem::Update(Eigen::VectorXdRefConst x_trajectory_in)
{
    if (x_trajectory_in.size() != (T_ - 1) * N)
        ThrowPretty("To update using the trajectory Update method, please use a trajectory of size N x (T-1) (" << N * (T_ - 1) << "), given: " << x_trajectory_in.size());
 
    for (int t = 1; t < T_; ++t)
    {
        Update(x_trajectory_in.segment((t - 1) * N, N), t);
    }
}
 
void AbstractTimeIndexedProblem::Update(Eigen::VectorXdRefConst x_in, int t)
{
    ValidateTimeIndex(t);
 
    x[t] = x_in;
 
    // Set the corresponding KinematicResponse for KinematicTree in order to
    // have Kinematics elements updated based in x_in.
    scene_->GetKinematicTree().SetKinematicResponse(kinematic_solutions_[t]);
 
    // Pass the corresponding number of relevant task kinematics to the TaskMaps
    // via the PlanningProblem::UpdateMultipleTaskKinematics method. For now we
    // support passing _two_ timesteps - this can be easily changed later on.
    std::vector<std::shared_ptr<KinematicResponse>> kinematics_solutions{kinematic_solutions_[t]};
 
    // If the current timestep is 0, pass the 0th timestep's response twice.
    // Otherwise pass the (t-1)th response.
    kinematics_solutions.emplace_back((t == 0) ? kinematic_solutions_[t] : kinematic_solutions_[t - 1]);
 
    // Actually update the tasks' kinematics mappings.
    PlanningProblem::UpdateMultipleTaskKinematics(kinematics_solutions);
 
    scene_->Update(x_in, static_cast<double>(t) * tau_);
    Phi[t].SetZero(length_Phi);
    if (flags_ & KIN_J) jacobian[t].setZero();
    if (flags_ & KIN_H)
        for (int i = 0; i < length_jacobian; ++i) hessian[t](i).setZero();
    for (int i = 0; i < num_tasks; ++i)
    {
        // Only update TaskMap if rho is not 0
        if (tasks_[i]->is_used)
        {
            if (flags_ & KIN_H)
            {
                tasks_[i]->Update(x[t],
                                  Phi[t].data.segment(tasks_[i]->start, tasks_[i]->length),
                                  jacobian[t].middleRows(tasks_[i]->start_jacobian, tasks_[i]->length_jacobian),
                                  hessian[t].segment(tasks_[i]->start_jacobian, tasks_[i]->length_jacobian));
            }
            else if (flags_ & KIN_J)
            {
                tasks_[i]->Update(x[t],
                                  Phi[t].data.segment(tasks_[i]->start, tasks_[i]->length),
                                  Eigen::MatrixXdRef(jacobian[t].middleRows(tasks_[i]->start_jacobian, tasks_[i]->length_jacobian))  // Adding MatrixXdRef(...) is a work-around for issue #737 when using Eigen 3.3.9
                );
            }
            else
            {
                tasks_[i]->Update(x[t], Phi[t].data.segment(tasks_[i]->start, tasks_[i]->length));
            }
        }
    }
    if (flags_ & KIN_H)
    {
        cost.Update(Phi[t], jacobian[t], hessian[t], t);
        inequality.Update(Phi[t], jacobian[t], hessian[t], t);
        equality.Update(Phi[t], jacobian[t], hessian[t], t);
    }
    else if (flags_ & KIN_J)
    {
        cost.Update(Phi[t], jacobian[t], t);
        inequality.Update(Phi[t], jacobian[t], t);
        equality.Update(Phi[t], jacobian[t], t);
    }
    else
    {
        cost.Update(Phi[t], t);
        inequality.Update(Phi[t], t);
        equality.Update(Phi[t], t);
    }
    if (t > 0) xdiff[t] = x[t] - x[t - 1];
    ++number_of_problem_updates_;
}
 
double AbstractTimeIndexedProblem::get_ct() const
{
    return ct;
}
 
double AbstractTimeIndexedProblem::GetCost() const
{
    double cost = 0.0;
    for (int t = 1; t < T_; ++t)
    {
        cost += GetScalarTaskCost(t) + GetScalarTransitionCost(t);
    }
    return cost;
}
 
Eigen::RowVectorXd AbstractTimeIndexedProblem::GetCostJacobian() const
{
    Eigen::RowVectorXd jac = Eigen::RowVectorXd::Zero(N * (T_ - 1));
    for (int t = 1; t < T_; ++t)
    {
        jac.segment((t - 1) * N, N) += GetScalarTaskJacobian(t) + GetScalarTransitionJacobian(t);
        if (t > 1) jac.segment((t - 2) * N, N) -= GetScalarTransitionJacobian(t);
    }
    return jac;
}
 
double AbstractTimeIndexedProblem::GetScalarTaskCost(int t) const
{
    ValidateTimeIndex(t);
    return ct * cost.ydiff[t].transpose() * cost.S[t] * cost.ydiff[t];
}
 
Eigen::RowVectorXd AbstractTimeIndexedProblem::GetScalarTaskJacobian(int t) const
{
    ValidateTimeIndex(t);
    return cost.jacobian[t].transpose() * cost.S[t] * cost.ydiff[t] * 2.0 * ct;
}
 
double AbstractTimeIndexedProblem::GetScalarTransitionCost(int t) const
{
    ValidateTimeIndex(t);
    return ct * xdiff[t].transpose() * W * xdiff[t];
}
 
Eigen::RowVectorXd AbstractTimeIndexedProblem::GetScalarTransitionJacobian(int t) const
{
    ValidateTimeIndex(t);
    return 2.0 * ct * W * xdiff[t];
}
 
int AbstractTimeIndexedProblem::get_active_nonlinear_equality_constraints_dimension() const
{
    return active_nonlinear_equality_constraints_dimension_;
}
 
int AbstractTimeIndexedProblem::get_active_nonlinear_inequality_constraints_dimension() const
{
    return active_nonlinear_inequality_constraints_dimension_;
}
 
Eigen::VectorXd AbstractTimeIndexedProblem::GetEquality() const
{
    Eigen::VectorXd eq = Eigen::VectorXd::Zero(active_nonlinear_equality_constraints_dimension_);
    int start = 0;
    for (const auto& constraint : active_nonlinear_equality_constraints_)
    {
        // First is timestep, second is task id
        const TaskIndexing task = equality.indexing[constraint.second];
        eq.segment(start, task.length_jacobian) = equality.rho[constraint.first](task.id) * equality.ydiff[constraint.first].segment(task.start_jacobian, task.length_jacobian);
        start += task.length_jacobian;
    }
 
    return eq;
}
 
Eigen::SparseMatrix<double> AbstractTimeIndexedProblem::GetEqualityJacobian() const
{
    Eigen::SparseMatrix<double> jac(active_nonlinear_equality_constraints_dimension_, N * (T_ - 1));
    std::vector<Eigen::Triplet<double>> triplet_list = GetEqualityJacobianTriplets();
    jac.setFromTriplets(triplet_list.begin(), triplet_list.end());
    return jac;
}
 
std::vector<Eigen::Triplet<double>> AbstractTimeIndexedProblem::GetEqualityJacobianTriplets() const
{
    typedef Eigen::Triplet<double> T;
    std::vector<T> triplet_list;
    triplet_list.reserve(active_nonlinear_equality_constraints_dimension_ * N);
    int start = 0;
    for (const auto& constraint : active_nonlinear_equality_constraints_)
    {
        // First is timestep, second is task id
        const TaskIndexing task = equality.indexing[constraint.second];
 
        const int row_start = start;
        const int row_length = task.length_jacobian;
        const int column_start = (constraint.first - 1) * N;  // (t - 1) * N
        const int column_length = N;
 
        const Eigen::MatrixXd jacobian = equality.rho[constraint.first](task.id) * equality.jacobian[constraint.first].middleRows(task.start_jacobian, task.length_jacobian);
        int row_idx = 0;
        for (int row = row_start; row < row_start + row_length; ++row)
        {
            int column_idx = 0;
            for (int column = column_start; column < column_start + column_length; ++column)
            {
                triplet_list.emplace_back(Eigen::Triplet<double>(row, column, jacobian(row_idx, column_idx)));
                ++column_idx;
            }
            ++row_idx;
        }
 
        start += task.length_jacobian;
    }
    return triplet_list;
}
 
Eigen::VectorXd AbstractTimeIndexedProblem::GetEquality(int t) const
{
    ValidateTimeIndex(t);
    return equality.S[t] * equality.ydiff[t];
}
 
Eigen::MatrixXd AbstractTimeIndexedProblem::GetEqualityJacobian(int t) const
{
    ValidateTimeIndex(t);
    return equality.S[t] * equality.jacobian[t];
}
 
Eigen::VectorXd AbstractTimeIndexedProblem::GetInequality() const
{
    Eigen::VectorXd neq = Eigen::VectorXd::Zero(active_nonlinear_inequality_constraints_dimension_);
    int start = 0;
    for (const auto& constraint : active_nonlinear_inequality_constraints_)
    {
        // First is timestep, second is task id
        const TaskIndexing task = inequality.indexing[constraint.second];
        neq.segment(start, task.length_jacobian) = inequality.rho[constraint.first](task.id) * inequality.ydiff[constraint.first].segment(task.start_jacobian, task.length_jacobian);
        start += task.length_jacobian;
    }
 
    return neq;
}
 
Eigen::SparseMatrix<double> AbstractTimeIndexedProblem::GetInequalityJacobian() const
{
    Eigen::SparseMatrix<double> jac(active_nonlinear_inequality_constraints_dimension_, N * (T_ - 1));
    std::vector<Eigen::Triplet<double>> triplet_list = GetInequalityJacobianTriplets();
    jac.setFromTriplets(triplet_list.begin(), triplet_list.end());
    return jac;
}
 
std::vector<Eigen::Triplet<double>> AbstractTimeIndexedProblem::GetInequalityJacobianTriplets() const
{
    typedef Eigen::Triplet<double> T;
    std::vector<T> triplet_list;
    triplet_list.reserve(active_nonlinear_inequality_constraints_dimension_ * N);
    int start = 0;
    for (const auto& constraint : active_nonlinear_inequality_constraints_)
    {
        // First is timestep, second is task id
        const TaskIndexing task = inequality.indexing[constraint.second];
 
        const int row_start = start;
        const int row_length = task.length_jacobian;
        const int column_start = (constraint.first - 1) * N;  // (t - 1) * N
        const int column_length = N;
 
        const Eigen::MatrixXd jacobian = inequality.rho[constraint.first](task.id) * inequality.jacobian[constraint.first].middleRows(task.start_jacobian, task.length_jacobian);
        int row_idx = 0;
        for (int row = row_start; row < row_start + row_length; ++row)
        {
            int column_idx = 0;
            for (int column = column_start; column < column_start + column_length; ++column)
            {
                triplet_list.emplace_back(Eigen::Triplet<double>(row, column, jacobian(row_idx, column_idx)));
                ++column_idx;
            }
            ++row_idx;
        }
 
        start += task.length_jacobian;
    }
    return triplet_list;
}
 
Eigen::VectorXd AbstractTimeIndexedProblem::GetInequality(int t) const
{
    ValidateTimeIndex(t);
    return inequality.S[t] * inequality.ydiff[t];
}
 
Eigen::MatrixXd AbstractTimeIndexedProblem::GetInequalityJacobian(int t) const
{
    ValidateTimeIndex(t);
    return inequality.S[t] * inequality.jacobian[t];
}
 
int AbstractTimeIndexedProblem::get_joint_velocity_constraint_dimension() const
{
    return joint_velocity_constraint_dimension_;
}
 
Eigen::VectorXd AbstractTimeIndexedProblem::GetJointVelocityLimits() const
{
    return q_dot_max_;
}
 
void AbstractTimeIndexedProblem::SetJointVelocityLimits(const Eigen::VectorXd& qdot_max_in)
{
    if (qdot_max_in.size() == N)
    {
        q_dot_max_ = qdot_max_in;
    }
    else if (qdot_max_in.size() == 1)
    {
        q_dot_max_ = qdot_max_in(0) * Eigen::VectorXd::Ones(N);
    }
    else
    {
        ThrowPretty("Received size " << qdot_max_in.size() << " but expected 1 or " << N);
    }
    xdiff_max_ = q_dot_max_ * tau_;
}
 
Eigen::VectorXd AbstractTimeIndexedProblem::GetJointVelocityConstraint() const
{
    Eigen::VectorXd g(joint_velocity_constraint_dimension_);
    for (int t = 1; t < T_; ++t)
    {
        g.segment((t - 1) * N, N) = xdiff[t];
    }
    return g;
}
 
Eigen::MatrixXd AbstractTimeIndexedProblem::GetJointVelocityConstraintBounds() const
{
    Eigen::MatrixXd b(joint_velocity_constraint_dimension_, 2);
    for (int t = 1; t < T_; ++t)
    {
        // As we are not including the T=0 in the optimization problem, we cannot
        // define a transition (xdiff) constraint for the 0th-to-1st timestep
        // directly - we need to include the constant x_{t=0} values in the ``b``
        //  element of the linear constraint, i.e., as an additional offset in bounds.
        if (t == 1)
        {
            b.block((t - 1) * N, 0, N, 1) = -xdiff_max_ + initial_trajectory_[0];
            b.block((t - 1) * N, 1, N, 1) = xdiff_max_ + initial_trajectory_[0];
        }
        else
        {
            b.block((t - 1) * N, 0, N, 1) = -xdiff_max_;
            b.block((t - 1) * N, 1, N, 1) = xdiff_max_;
        }
    }
    return b;
}
 
std::vector<Eigen::Triplet<double>> AbstractTimeIndexedProblem::GetJointVelocityConstraintJacobianTriplets() const
{
    // The Jacobian is constant - and thus cached (in ReinitializeVariables)
    return joint_velocity_constraint_jacobian_triplets_;
}
 
void AbstractTimeIndexedProblem::SetGoal(const std::string& task_name, Eigen::VectorXdRefConst goal, int t)
{
    cost.SetGoal(task_name, goal, t);
}
 
void AbstractTimeIndexedProblem::SetRho(const std::string& task_name, const double rho, int t)
{
    cost.SetRho(task_name, rho, t);
    PreUpdate();
}
 
Eigen::VectorXd AbstractTimeIndexedProblem::GetGoal(const std::string& task_name, int t)
{
    return cost.GetGoal(task_name, t);
}
 
double AbstractTimeIndexedProblem::GetRho(const std::string& task_name, int t)
{
    return cost.GetRho(task_name, t);
}
 
void AbstractTimeIndexedProblem::SetGoalEQ(const std::string& task_name, Eigen::VectorXdRefConst goal, int t)
{
    equality.SetGoal(task_name, goal, t);
}
 
void AbstractTimeIndexedProblem::SetRhoEQ(const std::string& task_name, const double rho, int t)
{
    equality.SetRho(task_name, rho, t);
    PreUpdate();
}
 
Eigen::VectorXd AbstractTimeIndexedProblem::GetGoalEQ(const std::string& task_name, int t)
{
    return equality.GetGoal(task_name, t);
}
 
double AbstractTimeIndexedProblem::GetRhoEQ(const std::string& task_name, int t)
{
    return equality.GetRho(task_name, t);
}
 
void AbstractTimeIndexedProblem::SetGoalNEQ(const std::string& task_name, Eigen::VectorXdRefConst goal, int t)
{
    inequality.SetGoal(task_name, goal, t);
}
 
void AbstractTimeIndexedProblem::SetRhoNEQ(const std::string& task_name, const double rho, int t)
{
    inequality.SetRho(task_name, rho, t);
    PreUpdate();
}
 
Eigen::VectorXd AbstractTimeIndexedProblem::GetGoalNEQ(const std::string& task_name, int t)
{
    return inequality.GetGoal(task_name, t);
}
 
double AbstractTimeIndexedProblem::GetRhoNEQ(const std::string& task_name, int t)
{
    return inequality.GetRho(task_name, t);
}
}  // namespace exotica