Abstract class for differential action model. More...

#include <diff-action-base.hpp>

Inheritance diagram for DifferentialActionModelAbstractTpl< _Scalar >:

Public Types
typedef DifferentialActionDataAbstractTpl< Scalar >	DifferentialActionDataAbstract

typedef MathBaseTpl< Scalar >	MathBase

typedef MathBase::MatrixXs	MatrixXs

typedef StateAbstractTpl< Scalar >	StateAbstract

typedef MathBase::VectorXs	VectorXs

Public Member Functions
	DifferentialActionModelAbstractTpl (boost::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)
	Initialize the differential action model. More...

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

virtual void	calc (const boost::shared_ptr< DifferentialActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u)=0
	Compute the system acceleration and cost value. More...

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

virtual void	calcDiff (const boost::shared_ptr< DifferentialActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u)=0
	Compute the derivatives of the dynamics and cost functions. More...

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

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

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_nh () const
	Return the number of equality 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 boost::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	print (std::ostream &os) const
	Print relevant information of the differential action model. More...

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))
	Computes the quasic static commands. More...

VectorXs	quasiStatic_x (const boost::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.

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Protected Member Functions
void	update_has_control_limits ()
	Update the status of the control limits (i.e. if there are defined limits)

Protected Attributes
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	nh_
	Number of equality constraints.

std::size_t	nr_
	Dimension of the cost residual.

std::size_t	nu_
	Control dimension.

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

VectorXs	u_lb_
	Lower control limits.

VectorXs	u_ub_
	Upper control limits.

VectorXs	unone_
	Neutral state.

Friends
template<class Scalar >
class	ConstraintModelManagerTpl

template<class Scalar >
class	IntegratedActionModelAbstractTpl

template<class Scalar >
std::ostream &	operator<< (std::ostream &os, const DifferentialActionModelAbstractTpl< Scalar > &model)
	Print information on the differential action model.

Detailed Description

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

Abstract class for differential action model.

A differential action model combines dynamics, cost and constraints models. We can use it in each node of our optimal control problem thanks to dedicated integration rules (e.g., IntegratedActionModelEulerTpl or IntegratedActionModelRK4Tpl). These integrated action models produce action models (ActionModelAbstractTpl). Thus, every time that we want to describe a problem, we need to provide ways of computing the dynamics, cost, constraints functions and their derivatives. All these are described inside the differential action model.

Concretely speaking, the differential action model is the time-continuous version of an action model, i.e.,

\[ \begin{aligned} &\dot{\mathbf{v}} = \mathbf{f}(\mathbf{q}, \mathbf{v}, \mathbf{u}), &\textrm{(dynamics)}\\ &\ell(\mathbf{q}, \mathbf{v},\mathbf{u}) = \int_0^{\delta t} a(\mathbf{r}(\mathbf{q}, \mathbf{v},\mathbf{u}))\,dt, &\textrm{(cost)}\\ &\mathbf{g}(\mathbf{q}, \mathbf{v},\mathbf{u})<\mathbf{0}, &\textrm{(inequality constraint)}\\ &\mathbf{h}(\mathbf{q}, \mathbf{v},\mathbf{u})=\mathbf{0}, &\textrm{(equality constraint)} \end{aligned} \]

where

the configuration \(\mathbf{q}\in\mathcal{Q}\) lies in the configuration manifold described with a nq-tuple,
the velocity \(\mathbf{v}\in T_{\mathbf{q}}\mathcal{Q}\) is the tangent vector to the configuration manifold with nv dimension,
the control input \(\mathbf{u}\in\mathbb{R}^{nu}\) is an Euclidean vector,
\(\mathbf{r}(\cdot)\) and \(a(\cdot)\) are the residual and activation functions (see ResidualModelAbstractTpl and ActivationModelAbstractTpl, respectively),
\(\mathbf{g}(\cdot)\in\mathbb{R}^{ng}\) and \(\mathbf{h}(\cdot)\in\mathbb{R}^{nh}\) are the inequality and equality vector functions, respectively.

Both configuration and velocity describe the system space \(\mathbf{x}=(\mathbf{q}, \mathbf{v})\in\mathcal{X}\) which lies in the state manifold. Note that the acceleration \(\dot{\mathbf{v}}\in T_{\mathbf{q}}\mathcal{Q}\) lies also in the tangent space of the configuration manifold. The computation of these equations are carried out inside calc() function. In short, this function computes the system acceleration, cost and constraints values (also called constraints violations). This procedure is equivalent to running a forward pass of the action model.

However, during numerical optimization, we also need to run backward passes of the differential action model. These calculations are performed by calcDiff(). In short, this function builds a linear-quadratic approximation of the differential action model, i.e.,

\[ \begin{aligned} &\delta\dot{\mathbf{v}} = \mathbf{f_{q}}\delta\mathbf{q}+\mathbf{f_{v}}\delta\mathbf{v}+\mathbf{f_{u}}\delta\mathbf{u}, &\textrm{(dynamics)}\\ &\ell(\delta\mathbf{q},\delta\mathbf{v},\delta\mathbf{u}) = \begin{bmatrix}1 \\ \delta\mathbf{q} \\ \delta\mathbf{v} \\ \delta\mathbf{u}\end{bmatrix}^T \begin{bmatrix}0 & \mathbf{\ell_q}^T & \mathbf{\ell_v}^T & \mathbf{\ell_u}^T \\ \mathbf{\ell_q} & \mathbf{\ell_{qq}} & \mathbf{\ell_{qv}} & \mathbf{\ell_{uq}}^T \\ \mathbf{\ell_v} & \mathbf{\ell_{vq}} & \mathbf{\ell_{vv}} & \mathbf{\ell_{uv}}^T \\ \mathbf{\ell_u} & \mathbf{\ell_{uq}} & \mathbf{\ell_{uv}} & \mathbf{\ell_{uu}}\end{bmatrix} \begin{bmatrix}1 \\ \delta\mathbf{q} \\ \delta\mathbf{v} \\ \delta\mathbf{u}\end{bmatrix}, &\textrm{(cost)}\\ &\mathbf{g_q}\delta\mathbf{q}+\mathbf{g_v}\delta\mathbf{v}+\mathbf{g_u}\delta\mathbf{u}\leq\mathbf{0}, &\textrm{(inequality constraints)}\\ &\mathbf{h_q}\delta\mathbf{q}+\mathbf{h_v}\delta\mathbf{v}+\mathbf{h_u}\delta\mathbf{u}=\mathbf{0}, &\textrm{(equality constraints)} \end{aligned} \]

where

\(\mathbf{f_x}=(\mathbf{f_q};\,\, \mathbf{f_v})\in\mathbb{R}^{nv\times ndx}\) and \(\mathbf{f_u}\in\mathbb{R}^{nv\times nu}\) are the Jacobians of the dynamics,
\(\mathbf{\ell_x}=(\mathbf{\ell_q};\,\, \mathbf{\ell_v})\in\mathbb{R}^{ndx}\) and \(\mathbf{\ell_u}\in\mathbb{R}^{nu}\) are the Jacobians of the cost function,
\(\mathbf{\ell_{xx}}=(\mathbf{\ell_{qq}}\,\, \mathbf{\ell_{qv}};\,\, \mathbf{\ell_{vq}}\, \mathbf{\ell_{vv}})\in\mathbb{R}^{ndx\times ndx}\), \(\mathbf{\ell_{xu}}=(\mathbf{\ell_q};\,\, \mathbf{\ell_v})\in\mathbb{R}^{ndx\times nu}\) and \(\mathbf{\ell_{uu}}\in\mathbb{R}^{nu\times nu}\) are the Hessians of the cost function,
\(\mathbf{g_x}=(\mathbf{g_q};\,\, \mathbf{g_v})\in\mathbb{R}^{ng\times ndx}\) and \(\mathbf{g_u}\in\mathbb{R}^{ng\times nu}\) are the Jacobians of the inequality constraints, and
\(\mathbf{h_x}=(\mathbf{h_q};\,\, \mathbf{h_v})\in\mathbb{R}^{nh\times ndx}\) and \(\mathbf{h_u}\in\mathbb{R}^{nh\times nu}\) are the Jacobians of the equality constraints.

Additionally, it is important to note that calcDiff() computes the derivatives using the latest stored values by calc(). Thus, we need to first run calc().

See also: ActionModelAbstractTpl, calc(), calcDiff(), createData()

Definition at line 119 of file diff-action-base.hpp.

Constructor & Destructor Documentation

◆ DifferentialActionModelAbstractTpl()

DifferentialActionModelAbstractTpl	(	boost::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`
	)

Initialize the differential action model.

Parameters

[in]	state	State description
[in]	nu	Dimension of control vector
[in]	nr	Dimension of cost-residual vector
[in]	ng	Number of inequality constraints
[in]	nh	Number of equality constraints

Member Function Documentation

◆ calc() [1/2]

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

pure 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 \(\mathbf{u}\in\mathbb{R}^{nu}\)

Implemented in DifferentialActionModelFreeInvDynamicsTpl< _Scalar >, DifferentialActionModelFreeFwdDynamicsTpl< _Scalar >, DifferentialActionModelContactInvDynamicsTpl< _Scalar >, DifferentialActionModelContactFwdDynamicsTpl< _Scalar >, DifferentialActionModelNumDiffTpl< _Scalar >, and DifferentialActionModelLQRTpl< _Scalar >.

◆ calc() [2/2]

virtual void calc	(	const boost::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 in DifferentialActionModelFreeInvDynamicsTpl< _Scalar >, DifferentialActionModelFreeFwdDynamicsTpl< _Scalar >, DifferentialActionModelContactInvDynamicsTpl< _Scalar >, DifferentialActionModelContactFwdDynamicsTpl< _Scalar >, DifferentialActionModelNumDiffTpl< _Scalar >, and DifferentialActionModelLQRTpl< _Scalar >.

◆ calcDiff() [1/2]

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

pure 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 \(\mathbf{u}\in\mathbb{R}^{nu}\)

Implemented in DifferentialActionModelFreeInvDynamicsTpl< _Scalar >, DifferentialActionModelFreeFwdDynamicsTpl< _Scalar >, DifferentialActionModelContactInvDynamicsTpl< _Scalar >, DifferentialActionModelContactFwdDynamicsTpl< _Scalar >, DifferentialActionModelNumDiffTpl< _Scalar >, and DifferentialActionModelLQRTpl< _Scalar >.

◆ calcDiff() [2/2]

virtual void calcDiff	(	const boost::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 in DifferentialActionModelFreeInvDynamicsTpl< _Scalar >, DifferentialActionModelFreeFwdDynamicsTpl< _Scalar >, DifferentialActionModelContactInvDynamicsTpl< _Scalar >, DifferentialActionModelContactFwdDynamicsTpl< _Scalar >, DifferentialActionModelNumDiffTpl< _Scalar >, and DifferentialActionModelLQRTpl< _Scalar >.

◆ createData()

virtual boost::shared_ptr<DifferentialActionDataAbstract> createData ( )

virtual

Create the differential action data.

Returns: the differential action data

Reimplemented in DifferentialActionModelFreeInvDynamicsTpl< _Scalar >, DifferentialActionModelFreeFwdDynamicsTpl< _Scalar >, DifferentialActionModelContactInvDynamicsTpl< _Scalar >, DifferentialActionModelContactFwdDynamicsTpl< _Scalar >, DifferentialActionModelNumDiffTpl< _Scalar >, and DifferentialActionModelLQRTpl< _Scalar >.

◆ 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)`
	)

virtual

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 \(\mathbf{f}(\mathbf{q},\mathbf{v}=\mathbf{0},\mathbf{u})=\mathbf{0}\)

Parameters

[in]	data	Differential action data
[out]	u	Quasic static commands
[in]	x	State point (velocity has to be zero)
[in]	maxiter	Maximum allowed number of iterations
[in]	tol	Tolerance

Reimplemented in DifferentialActionModelFreeInvDynamicsTpl< _Scalar >, DifferentialActionModelFreeFwdDynamicsTpl< _Scalar >, DifferentialActionModelContactInvDynamicsTpl< _Scalar >, DifferentialActionModelContactFwdDynamicsTpl< _Scalar >, and DifferentialActionModelNumDiffTpl< _Scalar >.

◆ quasiStatic_x()

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

Parameters

[in]	data	Differential action data
[in]	x	State point (velocity has to be zero)
[in]	maxiter	Maximum allowed number of iterations
[in]	tol	Tolerance

Returns: Quasic static commands

◆ print()

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

virtual

Print relevant information of the differential action model.

Parameters

[out] os Output stream object

Reimplemented in DifferentialActionModelFreeInvDynamicsTpl< _Scalar >, DifferentialActionModelFreeFwdDynamicsTpl< _Scalar >, DifferentialActionModelContactInvDynamicsTpl< _Scalar >, DifferentialActionModelContactFwdDynamicsTpl< _Scalar >, DifferentialActionModelNumDiffTpl< _Scalar >, and DifferentialActionModelLQRTpl< _Scalar >.

Member Data Documentation

◆ has_control_limits_

bool has_control_limits_

protected

Indicates whether any of the control limits is finite

Definition at line 355 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/diff-action-base.hpp

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Friends

Detailed Description

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

Constructor & Destructor Documentation

◆ DifferentialActionModelAbstractTpl()

Member Function Documentation

◆ calc() [1/2]

◆ calc() [2/2]

◆ calcDiff() [1/2]

◆ calcDiff() [2/2]

◆ createData()

◆ quasiStatic()

◆ quasiStatic_x()

◆ print()

Member Data Documentation

◆ has_control_limits_

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