Template Class IntegratedActionModelRKTpl

Inheritance Relationships

Base Type

Class Documentation

template<typename _Scalar>
class IntegratedActionModelRKTpl : public crocoddyl::IntegratedActionModelAbstractTpl<_Scalar>

Standard RK integrator.

It applies a standard RK integration schemes to a differential (i.e., continuous time) action model. The available integrators are: RK2, RK3, and RK4.

This standard RK scheme introduces also the possibility to parametrize the control trajectory inside an integration step, for instance using polynomials. This requires introducing some notation to clarify the difference between the control inputs of the differential model and the control inputs to the integrated model. We have decided to use \(\mathbf{w}\) to refer to the control inputs of the differential model and \(\mathbf{u}\) for the control inputs of the integrated action model.

See also

IntegratedActionModelAbstractTpl, calc(), calcDiff(), createData()

Public Types

typedef MathBaseTpl<Scalar> MathBase
typedef IntegratedActionModelAbstractTpl<Scalar> Base
typedef IntegratedActionDataRKTpl<Scalar> Data
typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract
typedef DifferentialActionModelAbstractTpl<Scalar> DifferentialActionModelAbstract
typedef DifferentialActionDataAbstractTpl<Scalar> DifferentialActionDataAbstract
typedef ControlParametrizationModelAbstractTpl<Scalar> ControlParametrizationModelAbstract
typedef ControlParametrizationDataAbstractTpl<Scalar> ControlParametrizationDataAbstract
typedef MathBase::VectorXs VectorXs
typedef MathBase::MatrixXs MatrixXs

Public Functions

IntegratedActionModelRKTpl(std::shared_ptr<DifferentialActionModelAbstract> model, std::shared_ptr<ControlParametrizationModelAbstract> control, const RKType rktype, const Scalar time_step = Scalar(1e-3), const bool with_cost_residual = true)

Initialize the RK integrator.

Parameters:

  • model – [in] Differential action model

  • control – [in] Control parametrization

  • rktype – [in] Type of RK integrator

  • time_step – [in] Step time (default 1e-3)

  • with_cost_residual – [in] Compute cost residual (default true)

IntegratedActionModelRKTpl(std::shared_ptr<DifferentialActionModelAbstract> model, const RKType rktype, const Scalar time_step = Scalar(1e-3), const bool with_cost_residual = true)

Initialize the RK integrator.

This initialization uses ControlParametrizationPolyZeroTpl for the control parametrization.

Parameters:

  • model – [in] Differential action model

  • rktype – [in] Type of RK integrator

  • time_step – [in] Step time (default 1e-3)

  • with_cost_residual – [in] Compute cost residual (default true)

virtual ~IntegratedActionModelRKTpl() = default
virtual void calc(const std::shared_ptr<ActionDataAbstract> &data, const Eigen::Ref<const VectorXs> &x, const Eigen::Ref<const VectorXs> &u) override

Integrate the differential action model using RK scheme.

Parameters:

  • data – [in] RK integrator data

  • x – [in] State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)

  • u – [in] Control input \(\mathbf{u}\in\mathbb{R}^{nu}\)

virtual void calc(const std::shared_ptr<ActionDataAbstract> &data, const Eigen::Ref<const VectorXs> &x) override

Integrate the total cost value for nodes that depends only on the state using RK scheme.

It computes the total cost and defines the next state as the current one. This function is used in the terminal nodes of an optimal control problem.

Parameters:

  • data – [in] RK integrator data

  • x – [in] State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)

virtual void calcDiff(const std::shared_ptr<ActionDataAbstract> &data, const Eigen::Ref<const VectorXs> &x, const Eigen::Ref<const VectorXs> &u) override

Compute the partial derivatives of the RK integrator.

Parameters:

  • data – [in] RK integrator data

  • x – [in] State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)

  • u – [in] Control input \(\mathbf{u}\in\mathbb{R}^{nu}\)

virtual void calcDiff(const std::shared_ptr<ActionDataAbstract> &data, const Eigen::Ref<const VectorXs> &x) override

Compute the partial derivatives of the cost.

It updates the derivatives of the cost function with respect to the state only. This function is used in the terminal nodes of an optimal control problem.

Parameters:

  • data – [in] RK integrator data

  • x – [in] State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)

virtual std::shared_ptr<ActionDataAbstract> createData() override

Create the RK integrator data.

Returns:

the RK integrator data

template<typename NewScalar>
IntegratedActionModelRKTpl<NewScalar> cast() const

Cast the RK integrated-action model to a different scalar type.

It is useful for operations requiring different precision or scalar types.

Template Parameters:

NewScalar – The new scalar type to cast to.

Returns:

IntegratedActionModelRKTpl<NewScalar> An action model with the new scalar type.

virtual bool checkData(const std::shared_ptr<ActionDataAbstract> &data) override

Checks that a specific data belongs to this model.

virtual void quasiStatic(const std::shared_ptr<ActionDataAbstract> &data, Eigen::Ref<VectorXs> u, const Eigen::Ref<const VectorXs> &x, const std::size_t maxiter = 100, const Scalar tol = Scalar(1e-9)) override

Computes the quasic static commands.

The quasic static commands are the ones produced for a the reference posture as an equilibrium point, i.e. for \(\mathbf{f^q_x}\delta\mathbf{q}+\mathbf{f_u}\delta\mathbf{u}=\mathbf{0}\)

Parameters:

  • data – [in] RK integrator data

  • u – [out] Quasic static commands

  • x – [in] State point (velocity has to be zero)

  • maxiter – [in] Maximum allowed number of iterations

  • tol – [in] Tolerance

std::size_t get_ni() const

Return the number of nodes of the integrator.

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

Print relevant information of the RK integrator model.

Parameters:

os – [out] Output stream object

Public Members

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar Scalar

Protected Attributes

std::shared_ptr<ControlParametrizationModelAbstract> control_

Model of the control parametrization.

std::shared_ptr<DifferentialActionModelAbstract> differential_

< Control parametrization

std::size_t nu_

< Number of equality constraints

std::shared_ptr<StateAbstract> state_

< Dimension of the control

Scalar time_step2_

< Model of the state

Scalar time_step_

< Square of the time step used for integration

bool with_cost_residual_

< Time step used for integration