Linear-quadratic regulator (LQR) action model. More...

#include <lqr.hpp>

Inheritance diagram for ActionModelLQRTpl< _Scalar >:

Public Types
typedef ActionDataAbstractTpl< Scalar >	ActionDataAbstract

typedef ActionModelAbstractTpl< Scalar >	Base

typedef ActionDataLQRTpl< Scalar >	Data

typedef MathBaseTpl< Scalar >	MathBase

typedef MathBase::MatrixXs	MatrixXs

typedef StateVectorTpl< Scalar >	StateVector

typedef MathBase::VectorXs	VectorXs

Public Types inherited from ActionModelAbstractTpl< _Scalar >
typedef ActionDataAbstractTpl< Scalar >	ActionDataAbstract

typedef MathBaseTpl< Scalar >	MathBase

typedef ScalarSelector< Scalar >::type	ScalarType

typedef StateAbstractTpl< Scalar >	StateAbstract

typedef MathBase::VectorXs	VectorXs

Public Member Functions
	ActionModelLQRTpl (const ActionModelLQRTpl &copy)
	Copy constructor.

	ActionModelLQRTpl (const MatrixXs &A, const MatrixXs &B, const MatrixXs &Q, const MatrixXs &R, const MatrixXs &N)
	Initialize the LQR action model.

	ActionModelLQRTpl (const MatrixXs &A, const MatrixXs &B, const MatrixXs &Q, const MatrixXs &R, const MatrixXs &N, const MatrixXs &G, const MatrixXs &H, const VectorXs &f, const VectorXs &q, const VectorXs &r, const VectorXs &g, const VectorXs &h)
	Initialize the LQR action model.

	ActionModelLQRTpl (const MatrixXs &A, const MatrixXs &B, const MatrixXs &Q, const MatrixXs &R, const MatrixXs &N, const VectorXs &f, const VectorXs &q, const VectorXs &r)
	Initialize the LQR action model.

	ActionModelLQRTpl (const std::size_t nx, const std::size_t nu, const bool drift_free=true)
	Initialize the LQR action model.

virtual void	calc (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) override
	Compute the total cost value for nodes that depends only on the state.

virtual void	calc (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u) override
	Compute the next state and cost value.

virtual void	calcDiff (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) override
	Compute the derivatives of the cost functions with respect to the state only.

virtual void	calcDiff (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u) override
	Compute the derivatives of the dynamics and cost functions.

template<typename NewScalar >
ActionModelLQRTpl< NewScalar >	cast () const
	Cast the LQR model to a different scalar type.

virtual bool	checkData (const std::shared_ptr< ActionDataAbstract > &data) override
	Checks that a specific data belongs to this model.

virtual std::shared_ptr< ActionDataAbstract >	createData () override
	Create the action data.

	DEPRECATED ("Use get_A", const MatrixXs &get_Fx() const { return get_A();}) DEPRECATED("Use get_B"

	DEPRECATED ("Use get_f", const VectorXs &get_f0() const { return get_f();}) DEPRECATED("Use get_q"

	DEPRECATED ("Use get_R", const MatrixXs &get_Lxu() const { return get_R();}) DEPRECATED("Use get_N"

	DEPRECATED ("Use get_r", const VectorXs &get_lu() const { return get_r();}) DEPRECATED("Use get_Q"

	DEPRECATED ("Use set_LQR", void set_f0(const VectorXs &f) { set_LQR(A_, B_, Q_, R_, N_, G_, H_, f, q_, r_, g_, h_);}) DEPRECATED("Use set_LQR"

	DEPRECATED ("Use set_LQR", void set_Fx(const MatrixXs &A) { set_LQR(A, B_, Q_, R_, N_, G_, H_, f_, q_, r_, g_, h_);}) DEPRECATED("Use set_LQR"

	DEPRECATED ("Use set_LQR", void set_lu(const VectorXs &r) { set_LQR(A_, B_, Q_, R_, N_, G_, H_, f_, q_, r, g_, h_);}) DEPRECATED("Use set_LQR"

	DEPRECATED ("Use set_LQR", void set_Luu(const MatrixXs &R) { set_LQR(A_, B_, Q_, R, N_, G_, H_, f_, q_, r_, g_, h_);}) DEPRECATED("Use set_LQR"

const MatrixXs &	get_A () const
	Return the state matrix.

const MatrixXs &	get_B () const
	Return the input matrix.

const VectorXs &	get_f () const
	Return the dynamics drift.

const MatrixXs &	get_Fu () const

const MatrixXs &	get_G () const
	Return the state-input inequality constraint matrix.

const VectorXs &	get_g () const
	Return the state-input inequality constraint bias.

const MatrixXs &	get_H () const
	Return the state-input equality constraint matrix.

const VectorXs &	get_h () const
	Return the state-input equality constraint bias.

const MatrixXs &	get_Luu () const

const VectorXs &	get_lx () const

const MatrixXs &	get_Lxx () const

const MatrixXs &	get_N () const
	Return the state-input weight matrix.

const MatrixXs &	get_Q () const
	Return the state weight matrix.

const VectorXs &	get_q () const
	Return the state weight vector.

const MatrixXs &	get_R () const
	Return the input weight matrix.

const VectorXs &	get_r () const
	Return the input weight vector.

virtual void	print (std::ostream &os) const override
	Print relevant information of the LQR model.

void	set_Fu (const MatrixXs &B)

void	set_LQR (const MatrixXs &A, const MatrixXs &B, const MatrixXs &Q, const MatrixXs &R, const MatrixXs &N, const MatrixXs &G, const MatrixXs &H, const VectorXs &f, const VectorXs &q, const VectorXs &r, const VectorXs &g, const VectorXs &h)
	Modify the LQR action model.

void	set_lx (const VectorXs &q)

void	set_Lxu (const MatrixXs &N)

void	set_Lxx (const MatrixXs &Q)

Public Member Functions inherited from ActionModelAbstractTpl< _Scalar >
	ActionModelAbstractTpl (const ActionModelAbstractTpl< Scalar > &other)
	Copy constructor.

	ActionModelAbstractTpl (std::shared_ptr< StateAbstract > state, const std::size_t nu, const std::size_t nr=0, const std::size_t ng=0, const std::size_t nh=0, const std::size_t ng_T=0, const std::size_t nh_T=0)
	Initialize the action model.

virtual const VectorXs &	get_g_lb () const
	Return the lower bound of the inequality constraints.

virtual const VectorXs &	get_g_ub () const
	Return the upper bound of the inequality constraints.

bool	get_has_control_limits () const
	Indicates if there are defined control limits.

virtual std::size_t	get_ng () const
	Return the number of inequality constraints.

virtual std::size_t	get_ng_T () const
	Return the number of inequality terminal constraints.

virtual std::size_t	get_nh () const
	Return the number of equality constraints.

virtual std::size_t	get_nh_T () const
	Return the number of equality terminal constraints.

std::size_t	get_nr () const
	Return the dimension of the cost-residual vector.

std::size_t	get_nu () const
	Return the dimension of the control input.

const std::shared_ptr< StateAbstract > &	get_state () const
	Return the state.

const VectorXs &	get_u_lb () const
	Return the control lower bound.

const VectorXs &	get_u_ub () const
	Return the control upper bound.

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))
	Computes the quasic static commands.

VectorXs	quasiStatic_x (const std::shared_ptr< ActionDataAbstract > &data, const VectorXs &x, const std::size_t maxiter=100, const Scalar tol=Scalar(1e-9))

void	set_g_lb (const VectorXs &g_lb)
	Modify the lower bound of the inequality constraints.

void	set_g_ub (const VectorXs &g_ub)
	Modify the upper bound of the inequality constraints.

void	set_u_lb (const VectorXs &u_lb)
	Modify the control lower bounds.

void	set_u_ub (const VectorXs &u_ub)
	Modify the control upper bounds.

Static Public Member Functions
static ActionModelLQRTpl	Random (const std::size_t nx, const std::size_t nu, const std::size_t ng=0, const std::size_t nh=0)
	Create a random LQR model.

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Public Attributes inherited from ActionModelAbstractTpl< _Scalar >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Protected Attributes
std::size_t	ng_
	Number of inequality constraints.

std::size_t	nh_
	< Equality constraint dimension

std::size_t	nu_
	< Inequality constraint dimension

std::shared_ptr< StateAbstract >	state_
	< Control dimension

Protected Attributes inherited from ActionModelAbstractTpl< _Scalar >
VectorXs	g_lb_
	Lower bound of the inequality constraints.

VectorXs	g_ub_
	Lower bound of the inequality constraints.

bool	has_control_limits_

std::size_t	ng_
	Number of inequality constraints.

std::size_t	ng_T_
	Number of inequality terminal constraints.

std::size_t	nh_
	Number of equality constraints.

std::size_t	nh_T_
	Number of equality terminal constraints.

std::size_t	nr_
	Dimension of the cost residual.

std::size_t	nu_
	Control dimension.

std::shared_ptr< StateAbstract >	state_
	Model of the state.

VectorXs	u_lb_
	Lower control limits.

VectorXs	u_ub_
	Upper control limits.

VectorXs	unone_
	Neutral state.

Additional Inherited Members
Protected Member Functions inherited from ActionModelAbstractTpl< _Scalar >
void	update_has_control_limits ()
	Update the status of the control limits (i.e. if there are defined limits)

Detailed Description

template<typename _Scalar>
class crocoddyl::ActionModelLQRTpl< _Scalar >

Linear-quadratic regulator (LQR) action model.

A linear-quadratic regulator (LQR) action has a transition model of the form

\[ \begin{equation} \mathbf{x}^' = \mathbf{A x + B u + f}. \end{equation} \]

Its cost function is quadratic of the form:

\[ \begin{equation} \ell(\mathbf{x},\mathbf{u}) = \begin{bmatrix}1 \\ \mathbf{x} \\ \mathbf{u}\end{bmatrix}^T \begin{bmatrix}0 & \mathbf{q}^T & \mathbf{r}^T \\ \mathbf{q} & \mathbf{Q} & \mathbf{N}^T \\ \mathbf{r} & \mathbf{N} & \mathbf{R}\end{bmatrix} \begin{bmatrix}1 \\ \mathbf{x} \\ \mathbf{u}\end{bmatrix} \end{equation} \]

and the linear equality and inequality constraints has the form:

\[ \begin{aligned} \mathbf{g(x,u)} = \mathbf{G}\begin{bmatrix} \mathbf{x} \\ \mathbf{u} \end{bmatrix} [x,u] + \mathbf{g} \leq \mathbf{0} &\mathbf{h(x,u)} = \mathbf{H}\begin{bmatrix} \mathbf{x} \\ \mathbf{u} \end{bmatrix} [x,u] + \mathbf{h} \end{aligned} \]

Definition at line 45 of file lqr.hpp.

Member Typedef Documentation

◆ ActionDataAbstract

template<typename _Scalar >

typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract

Definition at line 51 of file lqr.hpp.

◆ Base

template<typename _Scalar >

typedef ActionModelAbstractTpl<Scalar> Base

Definition at line 52 of file lqr.hpp.

◆ Data

template<typename _Scalar >

typedef ActionDataLQRTpl<Scalar> Data

Definition at line 53 of file lqr.hpp.

◆ StateVector

template<typename _Scalar >

typedef StateVectorTpl<Scalar> StateVector

Definition at line 54 of file lqr.hpp.

◆ MathBase

template<typename _Scalar >

typedef MathBaseTpl<Scalar> MathBase

Definition at line 55 of file lqr.hpp.

◆ VectorXs

template<typename _Scalar >

typedef MathBase::VectorXs VectorXs

Definition at line 56 of file lqr.hpp.

◆ MatrixXs

template<typename _Scalar >

typedef MathBase::MatrixXs MatrixXs

Definition at line 57 of file lqr.hpp.

Constructor & Destructor Documentation

◆ ActionModelLQRTpl() [1/4]

template<typename _Scalar >

ActionModelLQRTpl	(	const MatrixXs &	A,
		const MatrixXs &	B,
		const MatrixXs &	Q,
		const MatrixXs &	R,
		const MatrixXs &	N
	)

Initialize the LQR action model.

Parameters

[in]	A	State matrix
[in]	B	Input matrix
[in]	Q	State weight matrix
[in]	R	Input weight matrix
[in]	N	State-input weight matrix

◆ ActionModelLQRTpl() [2/4]

template<typename _Scalar >

ActionModelLQRTpl	(	const MatrixXs &	A,
		const MatrixXs &	B,
		const MatrixXs &	Q,
		const MatrixXs &	R,
		const MatrixXs &	N,
		const VectorXs &	f,
		const VectorXs &	q,
		const VectorXs &	r
	)

Initialize the LQR action model.

Parameters

[in]	A	State matrix
[in]	B	Input matrix
[in]	Q	State weight matrix
[in]	R	Input weight matrix
[in]	N	State-input weight matrix
[in]	f	Dynamics drift
[in]	q	State weight vector
[in]	r	Input weight vector

◆ ActionModelLQRTpl() [3/4]

template<typename _Scalar >

ActionModelLQRTpl	(	const MatrixXs &	A,
		const MatrixXs &	B,
		const MatrixXs &	Q,
		const MatrixXs &	R,
		const MatrixXs &	N,
		const MatrixXs &	G,
		const MatrixXs &	H,
		const VectorXs &	f,
		const VectorXs &	q,
		const VectorXs &	r,
		const VectorXs &	g,
		const VectorXs &	h
	)

Initialize the LQR action model.

Parameters

[in]	A	State matrix
[in]	B	Input matrix
[in]	Q	State weight matrix
[in]	R	Input weight matrix
[in]	N	State-input weight matrix
[in]	G	State-input inequality constraint matrix
[in]	H	State-input equality constraint matrix
[in]	f	Dynamics drift
[in]	q	State weight vector
[in]	r	Input weight vector
[in]	g	State-input inequality constraint bias
[in]	h	State-input equality constraint bias

◆ ActionModelLQRTpl() [4/4]

template<typename _Scalar >

ActionModelLQRTpl	(	const std::size_t	nx,
		const std::size_t	nu,
		const bool	drift_free = `true`
	)

Initialize the LQR action model.

Parameters

[in]	nx	Dimension of state vector
[in]	nu	Dimension of control vector
[in]	drif_free	Enable / disable the bias term of the linear dynamics (default true)

Member Function Documentation

◆ calc() [1/2]

template<typename _Scalar >

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

overridevirtual

Compute the next state and cost value.

Parameters

[in]	data	Action data
[in]	x	State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)
[in]	u	Control input \(\mathbf{u}\in\mathbb{R}^{nu}\)

Implements ActionModelAbstractTpl< _Scalar >.

◆ calc() [2/2]

template<typename _Scalar >

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

overridevirtual

Compute the total cost value for nodes that depends only on the state.

It updates the total cost and the next state is not computed as it is not expected to change. This function is used in the terminal nodes of an optimal control problem.

Parameters

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

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [1/2]

template<typename _Scalar >

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

overridevirtual

Compute the derivatives of the dynamics and cost functions.

It computes the partial derivatives of the dynamical system and the cost function. It assumes that calc() has been run first. This function builds a linear-quadratic approximation of the action model (i.e. dynamical system and cost function).

Parameters

[in]	data	Action data
[in]	x	State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)
[in]	u	Control input \(\mathbf{u}\in\mathbb{R}^{nu}\)

Implements ActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [2/2]

template<typename _Scalar >

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

overridevirtual

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

Parameters

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

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ createData()

template<typename _Scalar >

virtual std::shared_ptr< ActionDataAbstract > createData ( )

overridevirtual

Create the action data.

Returns: the action data

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ cast()

template<typename _Scalar >

template<typename NewScalar >

ActionModelLQRTpl< NewScalar > cast ( ) const

Cast the LQR 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: ActionModelLQRTpl<NewScalar> A action model with the new scalar type.

◆ checkData()

template<typename _Scalar >

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

overridevirtual

Checks that a specific data belongs to this model.

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ Random()

template<typename _Scalar >

static ActionModelLQRTpl Random	(	const std::size_t	nx,
		const std::size_t	nu,
		const std::size_t	ng = `0`,
		const std::size_t	nh = `0`
	)

static

Create a random LQR model.

Parameters

[in]	nx	State dimension
[in]	nu	Control dimension
[in]	ng	Inequality constraint dimension (default 0)
[in]	nh	Equality constraint dimension (defaul 0)

◆ set_LQR()

template<typename _Scalar >

void set_LQR	(	const MatrixXs &	A,
		const MatrixXs &	B,
		const MatrixXs &	Q,
		const MatrixXs &	R,
		const MatrixXs &	N,
		const MatrixXs &	G,
		const MatrixXs &	H,
		const VectorXs &	f,
		const VectorXs &	q,
		const VectorXs &	r,
		const VectorXs &	g,
		const VectorXs &	h
	)

Modify the LQR action model.

Parameters

[in]	A	State matrix
[in]	B	Input matrix
[in]	Q	State weight matrix
[in]	R	Input weight matrix
[in]	N	State-input weight matrix
[in]	G	State-input inequality constraint matrix
[in]	H	State-input equality constraint matrix
[in]	f	Dynamics drift
[in]	q	State weight vector
[in]	r	Input weight vector
[in]	g	State-input inequality constraint bias
[in]	h	State-input equality constraint bias

◆ get_Fu()

template<typename _Scalar >

const MatrixXs & get_Fu ( ) const

inline

Definition at line 221 of file lqr.hpp.

◆ get_lx()

template<typename _Scalar >

const VectorXs & get_lx ( ) const

inline

Definition at line 223 of file lqr.hpp.

◆ get_Lxx()

template<typename _Scalar >

const MatrixXs & get_Lxx ( ) const

inline

Definition at line 225 of file lqr.hpp.

◆ get_Luu()

template<typename _Scalar >

const MatrixXs & get_Luu ( ) const

inline

Definition at line 227 of file lqr.hpp.

◆ set_Fu()

template<typename _Scalar >

void set_Fu ( const MatrixXs & B )

inline

Definition at line 233 of file lqr.hpp.

◆ set_lx()

template<typename _Scalar >

void set_lx ( const VectorXs & q )

inline

Definition at line 241 of file lqr.hpp.

◆ set_Lxx()

template<typename _Scalar >

void set_Lxx ( const MatrixXs & Q )

inline

Definition at line 249 of file lqr.hpp.

◆ set_Lxu()

template<typename _Scalar >

void set_Lxu ( const MatrixXs & N )

inline

Definition at line 257 of file lqr.hpp.

◆ print()

template<typename _Scalar >

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

overridevirtual

Print relevant information of the LQR model.

Parameters

[out] os Output stream object

Reimplemented from ActionModelAbstractTpl< _Scalar >.

Member Data Documentation

◆ Scalar

template<typename _Scalar >

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar Scalar

Definition at line 50 of file lqr.hpp.

◆ ng_

template<typename _Scalar >

std::size_t ng_

protected

Number of inequality constraints.

Definition at line 330 of file action-base.hpp.

◆ nh_

template<typename _Scalar >

std::size_t nh_

protected

< Equality constraint dimension

Definition at line 331 of file action-base.hpp.

◆ nu_

template<typename _Scalar >

std::size_t nu_

protected

< Inequality constraint dimension

Definition at line 328 of file action-base.hpp.

◆ state_

template<typename _Scalar >

std::shared_ptr<StateAbstract> state_

protected

< Control dimension

Definition at line 334 of file action-base.hpp.

The documentation for this class was generated from the following file:

/root/robotpkg/optimization/py-crocoddyl/work/crocoddyl-2.1.0/include/crocoddyl/core/actions/lqr.hpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ ActionDataAbstract

◆ Base

◆ Data

◆ StateVector

◆ MathBase

◆ VectorXs

◆ MatrixXs

Constructor & Destructor Documentation

◆ ActionModelLQRTpl() [1/4]

◆ ActionModelLQRTpl() [2/4]

◆ ActionModelLQRTpl() [3/4]

◆ ActionModelLQRTpl() [4/4]

Member Function Documentation

◆ calc() [1/2]

◆ calc() [2/2]

◆ calcDiff() [1/2]

◆ calcDiff() [2/2]

◆ createData()

◆ cast()

◆ checkData()

◆ Random()

◆ set_LQR()

◆ get_Fu()

◆ get_lx()

◆ get_Lxx()

◆ get_Luu()

◆ set_Fu()

◆ set_lx()

◆ set_Lxx()

◆ set_Lxu()

◆ print()

Member Data Documentation

◆ Scalar

◆ ng_

◆ nh_

◆ nu_

◆ state_