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

#include <diff-lqr.hpp>

Inheritance diagram for DifferentialActionModelLQRTpl< _Scalar >:

Public Types
typedef DifferentialActionModelAbstractTpl< Scalar >	Base

typedef DifferentialActionDataLQRTpl< Scalar >	Data

typedef DifferentialActionDataAbstractTpl< Scalar >	DifferentialActionDataAbstract

typedef MathBaseTpl< Scalar >	MathBase

typedef MathBase::MatrixXs	MatrixXs

typedef _Scalar	Scalar

typedef StateVectorTpl< Scalar >	StateVector

typedef MathBase::VectorXs	VectorXs

Public Types inherited from DifferentialActionModelAbstractTpl< _Scalar >
typedef DifferentialActionDataAbstractTpl< Scalar >	DifferentialActionDataAbstract

typedef MathBaseTpl< Scalar >	MathBase

typedef MathBase::MatrixXs	MatrixXs

typedef StateAbstractTpl< Scalar >	StateAbstract

typedef MathBase::VectorXs	VectorXs

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

	DifferentialActionModelLQRTpl (const MatrixXs &Aq, const MatrixXs &Av, const MatrixXs &B, const MatrixXs &Q, const MatrixXs &R, const MatrixXs &N)
	Initialize the LQR action model.

	DifferentialActionModelLQRTpl (const MatrixXs &Aq, const MatrixXs &Av, 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.

	DifferentialActionModelLQRTpl (const MatrixXs &Aq, const MatrixXs &Av, 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.

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

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

virtual void	calc (const std::shared_ptr< DifferentialActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u)
	Compute the system acceleration and cost value.

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

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

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

virtual std::shared_ptr< DifferentialActionDataAbstract >	createData ()
	Create the differential action data.

	DEPRECATED ("Use get_Aq", const MatrixXs &get_Fq() const { return get_Aq();}) DEPRECATED("Use get_Av"

	DEPRECATED ("Use get_B", const MatrixXs &get_Fu() const { return get_B();}) DEPRECATED("Use get_f"

	DEPRECATED ("Use get_Q", const MatrixXs &get_Lxx() const { return get_Q();}) DEPRECATED("Use get_N"

	DEPRECATED ("Use get_q", const VectorXs &get_lx() const { return get_q();}) DEPRECATED("Use get_r"

	DEPRECATED ("Use get_R", const MatrixXs &get_Luu() const { return get_R();}) DEPRECATED("Use set_LQR"

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

	DEPRECATED ("Use set_LQR", void set_Fv(const MatrixXs &Av) { set_LQR(Aq_, Av, 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(Aq_, Av_, B_, Q_, R_, N_, G_, H_, f_, q_, r, g_, h_);}) DEPRECATED("Use set_LQR"

	DEPRECATED ("Use set_LQR", void set_Lxu(const MatrixXs &N) { set_LQR(Aq_, Av_, B_, Q_, R_, N, G_, H_, f_, q_, r_, g_, h_);}) DEPRECATED("Use set_LQR"

const MatrixXs &	get_Aq () const
	Return the position matrix.

const MatrixXs &	get_Av () const
	Return the velocity matrix.

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

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

const VectorXs &	get_f0 () const

const MatrixXs &	get_Fv () 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 VectorXs &	get_lu () const

const MatrixXs &	get_Lxu () 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
	Print relevant information of the LQR model.

void	set_Fq (const MatrixXs &Aq)

void	set_Fu (const MatrixXs &B)

void	set_LQR (const MatrixXs &Aq, const MatrixXs &Av, 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_Luu (const MatrixXs &R)

void	set_lx (const VectorXs &q)

void	set_Lxx (const MatrixXs &Q)

Public Member Functions inherited from DifferentialActionModelAbstractTpl< _Scalar >
	DifferentialActionModelAbstractTpl (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 differential 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< DifferentialActionDataAbstract > &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< DifferentialActionDataAbstract > &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 DifferentialActionModelLQRTpl	Random (const std::size_t nq, const std::size_t nu, const std::size_t ng=0, const std::size_t nh=0)
	Create a random LQR model.

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 DifferentialActionModelAbstractTpl< _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
Public Attributes inherited from DifferentialActionModelAbstractTpl< _Scalar >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Protected Member Functions inherited from DifferentialActionModelAbstractTpl< _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::DifferentialActionModelLQRTpl< _Scalar >

Linear-quadratic regulator (LQR) differential action model.

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

\[ \begin{equation} \mathbf{\dot{v}} = \mathbf{A_q q + A_v v + B u + f}. \end{equation} \]

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 47 of file diff-lqr.hpp.

Member Typedef Documentation

◆ Scalar

template<typename _Scalar >

typedef _Scalar Scalar

Definition at line 50 of file diff-lqr.hpp.

◆ MathBase

template<typename _Scalar >

typedef MathBaseTpl<Scalar> MathBase

Definition at line 51 of file diff-lqr.hpp.

◆ Base

template<typename _Scalar >

typedef DifferentialActionModelAbstractTpl<Scalar> Base

Definition at line 52 of file diff-lqr.hpp.

◆ Data

template<typename _Scalar >

typedef DifferentialActionDataLQRTpl<Scalar> Data

Definition at line 53 of file diff-lqr.hpp.

◆ StateVector

template<typename _Scalar >

typedef StateVectorTpl<Scalar> StateVector

Definition at line 54 of file diff-lqr.hpp.

◆ DifferentialActionDataAbstract

template<typename _Scalar >

typedef DifferentialActionDataAbstractTpl<Scalar> DifferentialActionDataAbstract

Definition at line 56 of file diff-lqr.hpp.

◆ VectorXs

template<typename _Scalar >

typedef MathBase::VectorXs VectorXs

Definition at line 57 of file diff-lqr.hpp.

◆ MatrixXs

template<typename _Scalar >

typedef MathBase::MatrixXs MatrixXs

Definition at line 58 of file diff-lqr.hpp.

Constructor & Destructor Documentation

◆ DifferentialActionModelLQRTpl() [1/4]

template<typename _Scalar >

DifferentialActionModelLQRTpl	(	const MatrixXs &	Aq,
		const MatrixXs &	Av,
		const MatrixXs &	B,
		const MatrixXs &	Q,
		const MatrixXs &	R,
		const MatrixXs &	N
	)

Initialize the LQR action model.

Parameters

[in]	Aq	Position matrix
[in]	Av	Velocity matrix
[in]	B	Input matrix
[in]	Q	State weight matrix
[in]	R	Input weight matrix
[in]	N	State-input weight matrix

◆ DifferentialActionModelLQRTpl() [2/4]

template<typename _Scalar >

DifferentialActionModelLQRTpl	(	const MatrixXs &	Aq,
		const MatrixXs &	Av,
		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]	Aq	Position matrix
[in]	Av	Velocity 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

◆ DifferentialActionModelLQRTpl() [3/4]

template<typename _Scalar >

DifferentialActionModelLQRTpl	(	const MatrixXs &	Aq,
		const MatrixXs &	Av,
		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]	Aq	Position matrix
[in]	Av	Velocity 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

◆ DifferentialActionModelLQRTpl() [4/4]

template<typename _Scalar >

DifferentialActionModelLQRTpl	(	const std::size_t	nq,
		const std::size_t	nu,
		const bool	drift_free = `true`
	)

Initialize the LQR action model.

Parameters

[in]	nq	Dimension of position 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< DifferentialActionDataAbstract > &	data,
		const Eigen::Ref< const VectorXs > &	x,
		const Eigen::Ref< const VectorXs > &	u
	)

virtual

Compute the system acceleration and cost value.

Parameters

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

Implements DifferentialActionModelAbstractTpl< _Scalar >.

◆ calc() [2/2]

template<typename _Scalar >

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

virtual

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

Parameters

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

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [1/2]

template<typename _Scalar >

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

virtual

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 quadratic approximation of the time-continuous action model (i.e. dynamical system and cost function).

Parameters

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

Implements DifferentialActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [2/2]

template<typename _Scalar >

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

virtual

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

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

◆ createData()

template<typename _Scalar >

virtual std::shared_ptr< DifferentialActionDataAbstract > createData ( )

virtual

Create the differential action data.

Returns: the differential action data

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

◆ checkData()

template<typename _Scalar >

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

virtual

Checks that a specific data belongs to this model.

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

◆ Random()

template<typename _Scalar >

static DifferentialActionModelLQRTpl Random	(	const std::size_t	nq,
		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]	nq	Position dimension
[in]	nu	Control dimension
[in]	ng	Inequality constraint dimension (default 0)
[in]	nh	Equality constraint dimension (default 0)

◆ set_LQR()

template<typename _Scalar >

void set_LQR	(	const MatrixXs &	Aq,
		const MatrixXs &	Av,
		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]	Aq	Position matrix
[in]	Av	Velocity 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_Fv()

template<typename _Scalar >

const MatrixXs & get_Fv ( ) const

inline

Definition at line 225 of file diff-lqr.hpp.

◆ get_f0()

template<typename _Scalar >

const VectorXs & get_f0 ( ) const

inline

Definition at line 227 of file diff-lqr.hpp.

◆ get_lu()

template<typename _Scalar >

const VectorXs & get_lu ( ) const

inline

Definition at line 229 of file diff-lqr.hpp.

◆ get_Lxu()

template<typename _Scalar >

const MatrixXs & get_Lxu ( ) const

inline

Definition at line 231 of file diff-lqr.hpp.

◆ set_Fq()

template<typename _Scalar >

void set_Fq ( const MatrixXs & Aq )

inline

Definition at line 234 of file diff-lqr.hpp.

◆ set_Fu()

template<typename _Scalar >

void set_Fu ( const MatrixXs & B )

inline

Definition at line 242 of file diff-lqr.hpp.

◆ set_lx()

template<typename _Scalar >

void set_lx ( const VectorXs & q )

inline

Definition at line 250 of file diff-lqr.hpp.

◆ set_Lxx()

template<typename _Scalar >

void set_Lxx ( const MatrixXs & Q )

inline

Definition at line 258 of file diff-lqr.hpp.

◆ set_Luu()

template<typename _Scalar >

void set_Luu ( const MatrixXs & R )

inline

Definition at line 266 of file diff-lqr.hpp.

◆ print()

template<typename _Scalar >

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

virtual

Print relevant information of the LQR model.

Parameters

[out] os Output stream object

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

Member Data Documentation

◆ ng_

template<typename _Scalar >

std::size_t ng_

protected

Number of inequality constraints.

Definition at line 359 of file diff-action-base.hpp.

◆ nh_

template<typename _Scalar >

std::size_t nh_

protected

< Equality constraint dimension

Definition at line 360 of file diff-action-base.hpp.

◆ nu_

template<typename _Scalar >

std::size_t nu_

protected

< Inequality constraint dimension

Definition at line 357 of file diff-action-base.hpp.

◆ state_

template<typename _Scalar >

std::shared_ptr<StateAbstract> state_

protected

< Control dimension

Definition at line 363 of file diff-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/diff-lqr.hpp

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Scalar

◆ MathBase

◆ Base

◆ Data

◆ StateVector

◆ DifferentialActionDataAbstract

◆ VectorXs

◆ MatrixXs

Constructor & Destructor Documentation

◆ DifferentialActionModelLQRTpl() [1/4]

◆ DifferentialActionModelLQRTpl() [2/4]

◆ DifferentialActionModelLQRTpl() [3/4]

◆ DifferentialActionModelLQRTpl() [4/4]

Member Function Documentation

◆ calc() [1/2]

◆ calc() [2/2]

◆ calcDiff() [1/2]

◆ calcDiff() [2/2]

◆ createData()

◆ checkData()

◆ Random()

◆ set_LQR()

◆ get_Fv()

◆ get_f0()

◆ get_lu()

◆ get_Lxu()

◆ set_Fq()

◆ set_Fu()

◆ set_lx()

◆ set_Lxx()

◆ set_Luu()

◆ print()

Member Data Documentation

◆ ng_

◆ nh_

◆ nu_

◆ state_