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/////////////////////////////////////////////////////////////////////////////// |
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// BSD 3-Clause License |
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// |
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// Copyright (C) 2019-2025, LAAS-CNRS, University of Edinburgh, CTU, INRIA, |
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// University of Oxford, Heriot-Watt University |
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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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#ifndef CROCODDYL_MULTIBODY_ACTIONS_CONTACT_FWDDYN_HPP_ |
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#define CROCODDYL_MULTIBODY_ACTIONS_CONTACT_FWDDYN_HPP_ |
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#include "crocoddyl/core/actuation-base.hpp" |
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#include "crocoddyl/core/constraints/constraint-manager.hpp" |
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#include "crocoddyl/core/costs/cost-sum.hpp" |
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#include "crocoddyl/core/diff-action-base.hpp" |
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#include "crocoddyl/multibody/contacts/multiple-contacts.hpp" |
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#include "crocoddyl/multibody/data/contacts.hpp" |
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#include "crocoddyl/multibody/fwd.hpp" |
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#include "crocoddyl/multibody/states/multibody.hpp" |
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namespace crocoddyl { |
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/** |
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* @brief Differential action model for contact forward dynamics in multibody |
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* systems. |
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* |
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* This class implements contact forward dynamics given a stack of |
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* rigid-contacts described in `ContactModelMultipleTpl`, i.e., \f[ |
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* \left[\begin{matrix}\dot{\mathbf{v}} |
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* \\ -\boldsymbol{\lambda}\end{matrix}\right] = \left[\begin{matrix}\mathbf{M} |
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* & \mathbf{J}^{\top}_c \\ {\mathbf{J}_{c}} & \mathbf{0} |
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* \end{matrix}\right]^{-1} \left[\begin{matrix}\boldsymbol{\tau}_b |
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* \\ -\mathbf{a}_0 \\\end{matrix}\right], \f] where \f$\mathbf{q}\in Q\f$, |
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* \f$\mathbf{v}\in\mathbb{R}^{nv}\f$ are the configuration point and |
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* generalized velocity (its tangent vector), respectively; |
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* \f$\boldsymbol{\tau}_b=\boldsymbol{\tau} - |
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* \mathbf{h}(\mathbf{q},\mathbf{v})\f$ is the bias forces that depends on the |
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* torque inputs \f$\boldsymbol{\tau}\f$ and the Coriolis effect and gravity |
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* field \f$\mathbf{h}(\mathbf{q},\mathbf{v})\f$; |
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* \f$\mathbf{J}_c\in\mathbb{R}^{nc\times nv}\f$ is the contact Jacobian |
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* expressed in the local frame; and \f$\mathbf{a}_0\in\mathbb{R}^{nc}\f$ is the |
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* desired acceleration in the constraint space. To improve stability in the |
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* numerical integration, we define PD gains that are similar in spirit to |
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* Baumgarte stabilization: \f[ \mathbf{a}_0 = \mathbf{a}_{\lambda(c)} - \alpha |
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* \,^oM^{ref}_{\lambda(c)}\ominus\,^oM_{\lambda(c)} |
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* - \beta\mathbf{v}_{\lambda(c)}, \f] where \f$\mathbf{v}_{\lambda(c)}\f$, |
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* \f$\mathbf{a}_{\lambda(c)}\f$ are the spatial velocity and acceleration at |
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* the parent body of the contact \f$\lambda(c)\f$, respectively; \f$\alpha\f$ |
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* and \f$\beta\f$ are the stabilization gains; |
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* \f$\,^oM^{ref}_{\lambda(c)}\ominus\,^oM_{\lambda(c)}\f$ is the |
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* \f$\mathbb{SE}(3)\f$ inverse composition between the reference contact |
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* placement and the current one. |
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* |
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* The derivatives of the system acceleration and contact forces are computed |
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* efficiently based on the analytical derivatives of Recursive Newton Euler |
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* Algorithm (RNEA) as described in \cite mastalli-icra20. Note that the |
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* algorithm for computing the RNEA derivatives is described in \cite |
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* carpentier-rss18. |
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* |
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* The stack of cost and constraint functions are implemented in |
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* `CostModelSumTpl` and `ConstraintModelAbstractTpl`, respectively. The |
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* computation of the contact dynamics and its derivatives are carrying out |
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* inside `calc()` and `calcDiff()` functions, respectively. It is also |
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* important to remark that `calcDiff()` computes the derivatives using the |
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* latest stored values by `calc()`. Thus, we need to run `calc()` first. |
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* |
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* \sa `DifferentialActionModelAbstractTpl`, `calc()`, `calcDiff()`, |
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* `createData()` |
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*/ |
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template <typename _Scalar> |
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class DifferentialActionModelContactFwdDynamicsTpl |
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: public DifferentialActionModelAbstractTpl<_Scalar> { |
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public: |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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CROCODDYL_DERIVED_CAST(DifferentialActionModelBase, |
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DifferentialActionModelContactFwdDynamicsTpl) |
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typedef _Scalar Scalar; |
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typedef DifferentialActionModelAbstractTpl<Scalar> Base; |
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typedef DifferentialActionDataContactFwdDynamicsTpl<Scalar> Data; |
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typedef MathBaseTpl<Scalar> MathBase; |
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typedef StateMultibodyTpl<Scalar> StateMultibody; |
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typedef CostModelSumTpl<Scalar> CostModelSum; |
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typedef ConstraintModelManagerTpl<Scalar> ConstraintModelManager; |
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typedef ContactModelMultipleTpl<Scalar> ContactModelMultiple; |
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typedef ActuationModelAbstractTpl<Scalar> ActuationModelAbstract; |
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typedef DifferentialActionDataAbstractTpl<Scalar> |
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DifferentialActionDataAbstract; |
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typedef typename MathBase::VectorXs VectorXs; |
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typedef typename MathBase::MatrixXs MatrixXs; |
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/** |
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* @brief Initialize the contact forward-dynamics action model |
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* |
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* It describes the dynamics evolution of a multibody system under |
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* rigid-contact constraints defined by `ContactModelMultipleTpl`. It computes |
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* the cost described in `CostModelSumTpl`. |
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* |
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* @param[in] state State of the multibody system |
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* @param[in] actuation Actuation model |
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* @param[in] contacts Stack of rigid contact |
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* @param[in] costs Stack of cost functions |
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* @param[in] JMinvJt_damping Damping term used in operational space inertia |
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* matrix (default 0.) |
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* @param[in] enable_force Enable the computation of the contact force |
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* derivatives (default false) |
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*/ |
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DifferentialActionModelContactFwdDynamicsTpl( |
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std::shared_ptr<StateMultibody> state, |
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std::shared_ptr<ActuationModelAbstract> actuation, |
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std::shared_ptr<ContactModelMultiple> contacts, |
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std::shared_ptr<CostModelSum> costs, |
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const Scalar JMinvJt_damping = Scalar(0.), |
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const bool enable_force = false); |
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/** |
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* @brief Initialize the contact forward-dynamics action model |
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* |
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* It describes the dynamics evolution of a multibody system under |
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* rigid-contact constraints defined by `ContactModelMultipleTpl`. It computes |
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* the cost described in `CostModelSumTpl`. |
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* |
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* @param[in] state State of the multibody system |
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* @param[in] actuation Actuation model |
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* @param[in] contacts Stack of rigid contact |
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* @param[in] costs Stack of cost functions |
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* @param[in] constraints Stack of constraints |
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* @param[in] JMinvJt_damping Damping term used in operational space inertia |
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* matrix (default 0.) |
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* @param[in] enable_force Enable the computation of the contact force |
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* derivatives (default false) |
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*/ |
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DifferentialActionModelContactFwdDynamicsTpl( |
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std::shared_ptr<StateMultibody> state, |
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std::shared_ptr<ActuationModelAbstract> actuation, |
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std::shared_ptr<ContactModelMultiple> contacts, |
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std::shared_ptr<CostModelSum> costs, |
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std::shared_ptr<ConstraintModelManager> constraints, |
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const Scalar JMinvJt_damping = Scalar(0.), |
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const bool enable_force = false); |
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virtual ~DifferentialActionModelContactFwdDynamicsTpl() = default; |
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/** |
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* @brief Compute the system acceleration, and cost value |
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* |
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* It computes the system acceleration using the contact dynamics. |
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* |
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* @param[in] data Contact forward-dynamics data |
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* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
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* @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ |
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*/ |
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virtual void calc(const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& u) override; |
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/** |
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* @brief Compute the total cost value for nodes that depends only on the |
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* state |
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* |
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* It updates the total cost and the system acceleration is not updated as it |
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* is expected to be zero. Additionally, it does not update the contact |
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* forces. This function is used in the terminal nodes of an optimal control |
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* problem. |
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* |
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* @param[in] data Contact forward-dynamics data |
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* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
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*/ |
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virtual void calc(const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x) override; |
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/** |
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* @brief Compute the derivatives of the contact dynamics, and cost function |
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* |
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* @param[in] data Contact forward-dynamics data |
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* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
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* @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ |
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*/ |
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virtual void calcDiff( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& u) override; |
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/** |
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* @brief Compute the derivatives of the cost functions with respect to the |
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* state only |
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* |
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* It updates the derivatives of the cost function with respect to the state |
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* only. Additionally, it does not update the contact forces derivatives. This |
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* function is used in the terminal nodes of an optimal control problem. |
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* |
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* @param[in] data Contact forward-dynamics data |
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* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
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*/ |
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virtual void calcDiff( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x) override; |
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/** |
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* @brief Create the contact forward-dynamics data |
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* |
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* @return contact forward-dynamics data |
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*/ |
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virtual std::shared_ptr<DifferentialActionDataAbstract> createData() override; |
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/** |
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* @brief Cast the contact-fwddyn model to a different scalar type. |
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* |
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* It is useful for operations requiring different precision or scalar types. |
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* |
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* @tparam NewScalar The new scalar type to cast to. |
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* @return DifferentialActionModelContactFwdDynamicsTpl<NewScalar> A |
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* differential-action model with the new scalar type. |
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*/ |
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template <typename NewScalar> |
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DifferentialActionModelContactFwdDynamicsTpl<NewScalar> cast() const; |
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/** |
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* @brief Check that the given data belongs to the contact forward-dynamics |
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* data |
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*/ |
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virtual bool checkData( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data) override; |
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/** |
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* @brief @copydoc Base::quasiStatic() |
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*/ |
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virtual void quasiStatic( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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Eigen::Ref<VectorXs> u, const Eigen::Ref<const VectorXs>& x, |
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const std::size_t maxiter = 100, |
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const Scalar tol = Scalar(1e-9)) override; |
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/** |
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* @brief Return the number of inequality constraints |
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*/ |
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virtual std::size_t get_ng() const override; |
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/** |
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* @brief Return the number of equality constraints |
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*/ |
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virtual std::size_t get_nh() const override; |
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/** |
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* @brief Return the number of equality terminal constraints |
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*/ |
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virtual std::size_t get_ng_T() const override; |
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/** |
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* @brief Return the number of equality terminal constraints |
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*/ |
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virtual std::size_t get_nh_T() const override; |
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/** |
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* @brief Return the lower bound of the inequality constraints |
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*/ |
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virtual const VectorXs& get_g_lb() const override; |
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/** |
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* @brief Return the upper bound of the inequality constraints |
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*/ |
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virtual const VectorXs& get_g_ub() const override; |
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/** |
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* @brief Return the actuation model |
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*/ |
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const std::shared_ptr<ActuationModelAbstract>& get_actuation() const; |
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/** |
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* @brief Return the contact model |
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*/ |
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const std::shared_ptr<ContactModelMultiple>& get_contacts() const; |
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/** |
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* @brief Return the cost model |
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*/ |
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const std::shared_ptr<CostModelSum>& get_costs() const; |
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/** |
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* @brief Return the constraint model manager |
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*/ |
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const std::shared_ptr<ConstraintModelManager>& get_constraints() const; |
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/** |
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* @brief Return the Pinocchio model |
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*/ |
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pinocchio::ModelTpl<Scalar>& get_pinocchio() const; |
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/** |
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* @brief Return the armature vector |
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*/ |
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const VectorXs& get_armature() const; |
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/** |
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* @brief Return the damping factor used in operational space inertia matrix |
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*/ |
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const Scalar get_damping_factor() const; |
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/** |
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* @brief Modify the armature vector |
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*/ |
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void set_armature(const VectorXs& armature); |
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/** |
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* @brief Modify the damping factor used in operational space inertia matrix |
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*/ |
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void set_damping_factor(const Scalar damping); |
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/** |
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* @brief Print relevant information of the contact forward-dynamics model |
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* |
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* @param[out] os Output stream object |
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*/ |
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virtual void print(std::ostream& os) const override; |
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protected: |
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using Base::g_lb_; //!< Lower bound of the inequality constraints |
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using Base::g_ub_; //!< Upper bound of the inequality constraints |
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using Base::nu_; //!< Control dimension |
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using Base::state_; //!< Model of the state |
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private: |
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void init(); |
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std::shared_ptr<ActuationModelAbstract> actuation_; //!< Actuation model |
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std::shared_ptr<ContactModelMultiple> contacts_; //!< Contact model |
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std::shared_ptr<CostModelSum> costs_; //!< Cost model |
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std::shared_ptr<ConstraintModelManager> constraints_; //!< Constraint model |
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pinocchio::ModelTpl<Scalar>* pinocchio_; //!< Pinocchio model |
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bool with_armature_; //!< Indicate if we have defined an armature |
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VectorXs armature_; //!< Armature vector |
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Scalar JMinvJt_damping_; //!< Damping factor used in operational space |
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//!< inertia matrix |
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bool enable_force_; //!< Indicate if we have enabled the computation of the |
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//!< contact-forces derivatives |
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}; |
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template <typename _Scalar> |
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struct DifferentialActionDataContactFwdDynamicsTpl |
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: public DifferentialActionDataAbstractTpl<_Scalar> { |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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typedef _Scalar Scalar; |
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typedef MathBaseTpl<Scalar> MathBase; |
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typedef DifferentialActionDataAbstractTpl<Scalar> Base; |
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typedef JointDataAbstractTpl<Scalar> JointDataAbstract; |
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typedef DataCollectorJointActMultibodyInContactTpl<Scalar> |
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DataCollectorJointActMultibodyInContact; |
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typedef typename MathBase::VectorXs VectorXs; |
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typedef typename MathBase::MatrixXs MatrixXs; |
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template <template <typename Scalar> class Model> |
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explicit DifferentialActionDataContactFwdDynamicsTpl( |
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Model<Scalar>* const model) |
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: Base(model), |
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pinocchio(pinocchio::DataTpl<Scalar>(model->get_pinocchio())), |
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multibody( |
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&pinocchio, model->get_actuation()->createData(), |
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std::make_shared<JointDataAbstract>( |
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model->get_state(), model->get_actuation(), model->get_nu()), |
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model->get_contacts()->createData(&pinocchio)), |
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costs(model->get_costs()->createData(&multibody)), |
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Kinv(model->get_state()->get_nv() + |
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model->get_contacts()->get_nc_total(), |
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model->get_state()->get_nv() + |
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model->get_contacts()->get_nc_total()), |
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df_dx(model->get_contacts()->get_nc_total(), |
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model->get_state()->get_ndx()), |
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df_du(model->get_contacts()->get_nc_total(), model->get_nu()), |
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tmp_xstatic(model->get_state()->get_nx()), |
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tmp_Jstatic(model->get_state()->get_nv(), |
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model->get_nu() + model->get_contacts()->get_nc_total()) { |
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multibody.joint->dtau_du.diagonal().setOnes(); |
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costs->shareMemory(this); |
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if (model->get_constraints() != nullptr) { |
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constraints = model->get_constraints()->createData(&multibody); |
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constraints->shareMemory(this); |
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} |
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Kinv.setZero(); |
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df_dx.setZero(); |
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df_du.setZero(); |
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tmp_xstatic.setZero(); |
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tmp_Jstatic.setZero(); |
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pinocchio.lambda_c.resize(model->get_contacts()->get_nc_total()); |
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pinocchio.lambda_c.setZero(); |
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} |
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virtual ~DifferentialActionDataContactFwdDynamicsTpl() = default; |
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pinocchio::DataTpl<Scalar> pinocchio; |
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DataCollectorJointActMultibodyInContact multibody; |
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std::shared_ptr<CostDataSumTpl<Scalar> > costs; |
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std::shared_ptr<ConstraintDataManagerTpl<Scalar> > constraints; |
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MatrixXs Kinv; |
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MatrixXs df_dx; |
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MatrixXs df_du; |
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VectorXs tmp_xstatic; |
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MatrixXs tmp_Jstatic; |
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using Base::cost; |
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using Base::Fu; |
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using Base::Fx; |
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using Base::Lu; |
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using Base::Luu; |
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using Base::Lx; |
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using Base::Lxu; |
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using Base::Lxx; |
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using Base::r; |
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using Base::xout; |
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}; |
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} // namespace crocoddyl |
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/* --- Details -------------------------------------------------------------- */ |
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/* --- Details -------------------------------------------------------------- */ |
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/* --- Details -------------------------------------------------------------- */ |
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#include <crocoddyl/multibody/actions/contact-fwddyn.hxx> |
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CROCODDYL_DECLARE_EXTERN_TEMPLATE_CLASS( |
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crocoddyl::DifferentialActionModelContactFwdDynamicsTpl) |
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CROCODDYL_DECLARE_EXTERN_TEMPLATE_STRUCT( |
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crocoddyl::DifferentialActionDataContactFwdDynamicsTpl) |
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#endif // CROCODDYL_MULTIBODY_ACTIONS_CONTACT_FWDDYN_HPP_ |
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