///////////////////////////////////////////////////////////////////////////////

// BSD 3-Clause License

//

// Copyright (C) 2019-2022, LAAS-CNRS, University of Edinburgh, CTU, INRIA,

//                          University of Oxford, Heriot-Watt University

// Copyright note valid unless otherwise stated in individual files.

// All rights reserved.

///////////////////////////////////////////////////////////////////////////////

#ifndef CROCODDYL_MULTIBODY_ACTIONS_CONTACT_FWDDYN_HPP_

#define CROCODDYL_MULTIBODY_ACTIONS_CONTACT_FWDDYN_HPP_

#include <stdexcept>

#include "crocoddyl/core/actuation-base.hpp"

#include "crocoddyl/core/constraints/constraint-manager.hpp"

#include "crocoddyl/core/costs/cost-sum.hpp"

#include "crocoddyl/core/diff-action-base.hpp"

#include "crocoddyl/multibody/contacts/multiple-contacts.hpp"

#include "crocoddyl/multibody/data/contacts.hpp"

#include "crocoddyl/multibody/fwd.hpp"

#include "crocoddyl/multibody/states/multibody.hpp"

namespace crocoddyl {

/**

 * @brief Differential action model for contact forward dynamics in multibody

 * systems.

 *

 * This class implements contact forward dynamics given a stack of

 * rigid-contacts described in `ContactModelMultipleTpl`, i.e., \f[

 * \left[\begin{matrix}\dot{\mathbf{v}}

 * \\ -\boldsymbol{\lambda}\end{matrix}\right] = \left[\begin{matrix}\mathbf{M}

 * & \mathbf{J}^{\top}_c \\ {\mathbf{J}_{c}} & \mathbf{0}

 * \end{matrix}\right]^{-1} \left[\begin{matrix}\boldsymbol{\tau}_b

 * \\ -\mathbf{a}_0 \\\end{matrix}\right], \f] where \f$\mathbf{q}\in Q\f$,

 * \f$\mathbf{v}\in\mathbb{R}^{nv}\f$ are the configuration point and

 * generalized velocity (its tangent vector), respectively;

 * \f$\boldsymbol{\tau}_b=\boldsymbol{\tau} -

 * \mathbf{h}(\mathbf{q},\mathbf{v})\f$ is the bias forces that depends on the

 * torque inputs \f$\boldsymbol{\tau}\f$ and the Coriolis effect and gravity

 * field \f$\mathbf{h}(\mathbf{q},\mathbf{v})\f$;

 * \f$\mathbf{J}_c\in\mathbb{R}^{nc\times nv}\f$ is the contact Jacobian

 * expressed in the local frame; and \f$\mathbf{a}_0\in\mathbb{R}^{nc}\f$ is the

 * desired acceleration in the constraint space. To improve stability in the

 * numerical integration, we define PD gains that are similar in spirit to

 * Baumgarte stabilization: \f[ \mathbf{a}_0 = \mathbf{a}_{\lambda(c)} - \alpha

 * \,^oM^{ref}_{\lambda(c)}\ominus\,^oM_{\lambda(c)}

 * - \beta\mathbf{v}_{\lambda(c)}, \f] where \f$\mathbf{v}_{\lambda(c)}\f$,

 * \f$\mathbf{a}_{\lambda(c)}\f$ are the spatial velocity and acceleration at

 * the parent body of the contact \f$\lambda(c)\f$, respectively; \f$\alpha\f$

 * and \f$\beta\f$ are the stabilization gains;

 * \f$\,^oM^{ref}_{\lambda(c)}\ominus\,^oM_{\lambda(c)}\f$ is the

 * \f$\mathbb{SE}(3)\f$ inverse composition between the reference contact

 * placement and the current one.

 *

 * The derivatives of the system acceleration and contact forces are computed

 * efficiently based on the analytical derivatives of Recursive Newton Euler

 * Algorithm (RNEA) as described in \cite mastalli-icra20. Note that the

 * algorithm for computing the RNEA derivatives is described in \cite

 * carpentier-rss18.

 *

 * The stack of cost and constraint functions are implemented in

 * `CostModelSumTpl` and `ConstraintModelAbstractTpl`, respectively. The

 * computation of the contact dynamics and its derivatives are carrying out

 * inside `calc()` and `calcDiff()` functions, respectively. It is also

 * important to remark that `calcDiff()` computes the derivatives using the

 * latest stored values by `calc()`. Thus, we need to run `calc()` first.

 *

 * \sa `DifferentialActionModelAbstractTpl`, `calc()`, `calcDiff()`,

 * `createData()`

 */

template <typename _Scalar>

class DifferentialActionModelContactFwdDynamicsTpl

    : public DifferentialActionModelAbstractTpl<_Scalar> {

 public:

  typedef _Scalar Scalar;

  typedef DifferentialActionModelAbstractTpl<Scalar> Base;

  typedef DifferentialActionDataContactFwdDynamicsTpl<Scalar> Data;

  typedef MathBaseTpl<Scalar> MathBase;

  typedef StateMultibodyTpl<Scalar> StateMultibody;

  typedef CostModelSumTpl<Scalar> CostModelSum;

  typedef ConstraintModelManagerTpl<Scalar> ConstraintModelManager;

  typedef ContactModelMultipleTpl<Scalar> ContactModelMultiple;

  typedef ActuationModelAbstractTpl<Scalar> ActuationModelAbstract;

  typedef DifferentialActionDataAbstractTpl<Scalar>

      DifferentialActionDataAbstract;

  typedef typename MathBase::VectorXs VectorXs;

  typedef typename MathBase::MatrixXs MatrixXs;

  /**

   * @brief Initialize the contact forward-dynamics action model

   *

   * It describes the dynamics evolution of a multibody system under

   * rigid-contact constraints defined by `ContactModelMultipleTpl`. It computes

   * the cost described in `CostModelSumTpl`.

   *

   * @param[in] state            State of the multibody system

   * @param[in] actuation        Actuation model

   * @param[in] contacts         Stack of rigid contact

   * @param[in] costs            Stack of cost functions

   * @param[in] JMinvJt_damping  Damping term used in operational space inertia

   * matrix (default 0.)

   * @param[in] enable_force     Enable the computation of the contact force

   * derivatives (default false)

   */

  DifferentialActionModelContactFwdDynamicsTpl(

      boost::shared_ptr<StateMultibody> state,

      boost::shared_ptr<ActuationModelAbstract> actuation,

      boost::shared_ptr<ContactModelMultiple> contacts,

      boost::shared_ptr<CostModelSum> costs,

      const Scalar JMinvJt_damping = Scalar(0.),

      const bool enable_force = false);

  /**

   * @brief Initialize the contact forward-dynamics action model

   *

   * It describes the dynamics evolution of a multibody system under

   * rigid-contact constraints defined by `ContactModelMultipleTpl`. It computes

   * the cost described in `CostModelSumTpl`.

   *

   * @param[in] state            State of the multibody system

   * @param[in] actuation        Actuation model

   * @param[in] contacts         Stack of rigid contact

   * @param[in] costs            Stack of cost functions

   * @param[in] constraints      Stack of constraints

   * @param[in] JMinvJt_damping  Damping term used in operational space inertia

   * matrix (default 0.)

   * @param[in] enable_force     Enable the computation of the contact force

   * derivatives (default false)

   */

  DifferentialActionModelContactFwdDynamicsTpl(

      boost::shared_ptr<StateMultibody> state,

      boost::shared_ptr<ActuationModelAbstract> actuation,

      boost::shared_ptr<ContactModelMultiple> contacts,

      boost::shared_ptr<CostModelSum> costs,

      boost::shared_ptr<ConstraintModelManager> constraints,

      const Scalar JMinvJt_damping = Scalar(0.),

      const bool enable_force = false);

  virtual ~DifferentialActionModelContactFwdDynamicsTpl();

  /**

   * @brief Compute the system acceleration, and cost value

   *

   * It computes the system acceleration using the contact dynamics.

   *

   * @param[in] data  Contact forward-dynamics data

   * @param[in] x     State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$

   * @param[in] u     Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$

   */

  virtual void calc(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data,

      const Eigen::Ref<const VectorXs>& x, const Eigen::Ref<const VectorXs>& u);

  /**

   * @brief Compute the total cost value for nodes that depends only on the

   * state

   *

   * It updates the total cost and the system acceleration is not updated as it

   * is expected to be zero. Additionally, it does not update the contact

   * forces. This function is used in the terminal nodes of an optimal control

   * problem.

   *

   * @param[in] data  Contact forward-dynamics data

   * @param[in] x     State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$

   */

  virtual void calc(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data,

      const Eigen::Ref<const VectorXs>& x);

  /**

   * @brief Compute the derivatives of the contact dynamics, and cost function

   *

   * @param[in] data  Contact forward-dynamics data

   * @param[in] x     State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$

   * @param[in] u     Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$

   */

  virtual void calcDiff(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data,

      const Eigen::Ref<const VectorXs>& x, const Eigen::Ref<const VectorXs>& u);

  /**

   * @brief Compute the derivatives of the cost functions with respect to the

   * state only

   *

   * It updates the derivatives of the cost function with respect to the state

   * only. Additionally, it does not update the contact forces derivatives. This

   * function is used in the terminal nodes of an optimal control problem.

   *

   * @param[in] data  Contact forward-dynamics data

   * @param[in] x     State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$

   */

  virtual void calcDiff(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data,

      const Eigen::Ref<const VectorXs>& x);

  /**

   * @brief Create the contact forward-dynamics data

   *

   * @return contact forward-dynamics data

   */

  virtual boost::shared_ptr<DifferentialActionDataAbstract> createData();

  /**

   * @brief Check that the given data belongs to the contact forward-dynamics

   * data

   */

  virtual bool checkData(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data);

  /**

   * @brief @copydoc Base::quasiStatic()

   */

  virtual void quasiStatic(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data,

      Eigen::Ref<VectorXs> u, const Eigen::Ref<const VectorXs>& x,

      const std::size_t maxiter = 100, const Scalar tol = Scalar(1e-9));

  /**

   * @brief Return the number of inequality constraints

   */

  virtual std::size_t get_ng() const;

  /**

   * @brief Return the number of equality constraints

   */

  virtual std::size_t get_nh() const;

  /**

   * @brief Return the lower bound of the inequality constraints

   */

  virtual const VectorXs& get_g_lb() const;

  /**

   * @brief Return the upper bound of the inequality constraints

   */

  virtual const VectorXs& get_g_ub() const;

  /**

   * @brief Return the actuation model

   */

  const boost::shared_ptr<ActuationModelAbstract>& get_actuation() const;

  /**

   * @brief Return the contact model

   */

  const boost::shared_ptr<ContactModelMultiple>& get_contacts() const;

  /**

   * @brief Return the cost model

   */

  const boost::shared_ptr<CostModelSum>& get_costs() const;

  /**

   * @brief Return the constraint model manager

   */

  const boost::shared_ptr<ConstraintModelManager>& get_constraints() const;

  /**

   * @brief Return the Pinocchio model

   */

  pinocchio::ModelTpl<Scalar>& get_pinocchio() const;

  /**

   * @brief Return the armature vector

   */

  const VectorXs& get_armature() const;

  /**

   * @brief Return the damping factor used in operational space inertia matrix

   */

  const Scalar get_damping_factor() const;

  /**

   * @brief Modify the armature vector

   */

  void set_armature(const VectorXs& armature);

  /**

   * @brief Modify the damping factor used in operational space inertia matrix

   */

  void set_damping_factor(const Scalar damping);

  /**

   * @brief Print relevant information of the contact forward-dynamics model

   *

   * @param[out] os  Output stream object

   */

  virtual void print(std::ostream& os) const;

 protected:

  using Base::g_lb_;   //!< Lower bound of the inequality constraints

  using Base::g_ub_;   //!< Upper bound of the inequality constraints

  using Base::nu_;     //!< Control dimension

  using Base::state_;  //!< Model of the state

 private:

  void init();

  boost::shared_ptr<ActuationModelAbstract> actuation_;    //!< Actuation model

  boost::shared_ptr<ContactModelMultiple> contacts_;       //!< Contact model

  boost::shared_ptr<CostModelSum> costs_;                  //!< Cost model

  boost::shared_ptr<ConstraintModelManager> constraints_;  //!< Constraint model

  pinocchio::ModelTpl<Scalar>& pinocchio_;                 //!< Pinocchio model

  bool with_armature_;      //!< Indicate if we have defined an armature

  VectorXs armature_;       //!< Armature vector

  Scalar JMinvJt_damping_;  //!< Damping factor used in operational space

                            //!< inertia matrix

  bool enable_force_;  //!< Indicate if we have enabled the computation of the

                       //!< contact-forces derivatives

};

template <typename _Scalar>

struct DifferentialActionDataContactFwdDynamicsTpl

    : public DifferentialActionDataAbstractTpl<_Scalar> {

  typedef _Scalar Scalar;

  typedef MathBaseTpl<Scalar> MathBase;

  typedef DifferentialActionDataAbstractTpl<Scalar> Base;

  typedef JointDataAbstractTpl<Scalar> JointDataAbstract;

  typedef DataCollectorJointActMultibodyInContactTpl<Scalar>

      DataCollectorJointActMultibodyInContact;

  typedef typename MathBase::VectorXs VectorXs;

  typedef typename MathBase::MatrixXs MatrixXs;

  template <template <typename Scalar> class Model>

      Model<Scalar>* const model)

      : Base(model),

        multibody(

                model->get_state(), model->get_actuation(), model->get_nu()),

    }

  pinocchio::DataTpl<Scalar> pinocchio;

  DataCollectorJointActMultibodyInContact multibody;

  boost::shared_ptr<CostDataSumTpl<Scalar> > costs;

  boost::shared_ptr<ConstraintDataManagerTpl<Scalar> > constraints;

  MatrixXs Kinv;

  MatrixXs df_dx;

  MatrixXs df_du;

  VectorXs tmp_xstatic;

  MatrixXs tmp_Jstatic;

  using Base::cost;

  using Base::Fu;

  using Base::Fx;

  using Base::Lu;

  using Base::Luu;

  using Base::Lx;

  using Base::Lxu;

  using Base::Lxx;

  using Base::r;

  using Base::xout;

};

}  // namespace crocoddyl

/* --- Details -------------------------------------------------------------- */

/* --- Details -------------------------------------------------------------- */

/* --- Details -------------------------------------------------------------- */

#include <crocoddyl/multibody/actions/contact-fwddyn.hxx>

#endif  // CROCODDYL_MULTIBODY_ACTIONS_CONTACT_FWDDYN_HPP_