Differential action model for contact forward dynamics in multibody systems. More...

#include <contact-fwddyn.hpp>

Inheritance diagram for DifferentialActionModelContactFwdDynamicsTpl< _Scalar >:

Public Types
typedef ActuationModelAbstractTpl< Scalar >	ActuationModelAbstract

typedef DifferentialActionModelAbstractTpl< Scalar >	Base

typedef ConstraintModelManagerTpl< Scalar >	ConstraintModelManager

typedef ContactModelMultipleTpl< Scalar >	ContactModelMultiple

typedef CostModelSumTpl< Scalar >	CostModelSum

typedef DifferentialActionDataContactFwdDynamicsTpl< Scalar >	Data

typedef DifferentialActionDataAbstractTpl< Scalar >	DifferentialActionDataAbstract

typedef MathBaseTpl< Scalar >	MathBase

typedef MathBase::MatrixXs	MatrixXs

typedef StateMultibodyTpl< Scalar >	StateMultibody

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
	DifferentialActionModelContactFwdDynamicsTpl (boost::shared_ptr< StateMultibody > state, boost::shared_ptr< ActuationModelAbstract > actuation, boost::shared_ptr< ContactModelMultiple > contacts, boost::shared_ptr< CostModelSum > costs, boost::shared_ptr< ConstraintModelManager > constraints, const Scalar JMinvJt_damping=Scalar(0.), const bool enable_force=false)
	Initialize the contact forward-dynamics action model. More...

	DifferentialActionModelContactFwdDynamicsTpl (boost::shared_ptr< StateMultibody > state, boost::shared_ptr< ActuationModelAbstract > actuation, boost::shared_ptr< ContactModelMultiple > contacts, boost::shared_ptr< CostModelSum > costs, const Scalar JMinvJt_damping=Scalar(0.), const bool enable_force=false)
	Initialize the contact forward-dynamics 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)
	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)
	Compute the derivatives of the contact dynamics, and cost function. More...

virtual bool	checkData (const boost::shared_ptr< DifferentialActionDataAbstract > &data)
	Check that the given data belongs to the contact forward-dynamics data.

virtual boost::shared_ptr< DifferentialActionDataAbstract >	createData ()
	Create the contact forward-dynamics data. More...

const boost::shared_ptr< ActuationModelAbstract > &	get_actuation () const
	Return the actuation model.

const VectorXs &	get_armature () const
	Return the armature vector.

const boost::shared_ptr< ConstraintModelManager > &	get_constraints () const
	Return the constraint model manager.

const boost::shared_ptr< ContactModelMultiple > &	get_contacts () const
	Return the contact model.

const boost::shared_ptr< CostModelSum > &	get_costs () const
	Return the cost model.

const Scalar	get_damping_factor () const
	Return the damping factor used in operational space inertia matrix.

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.

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.

pinocchio::ModelTpl< Scalar > &	get_pinocchio () const
	Return the Pinocchio model.

virtual void	print (std::ostream &os) const
	Print relevant information of the contact forward-dynamics 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...

void	set_armature (const VectorXs &armature)
	Modify the armature vector.

void	set_damping_factor (const Scalar damping)
	Modify the damping factor used in operational space inertia matrix.

Public Member Functions inherited from DifferentialActionModelAbstractTpl< _Scalar >
	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...

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

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.

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

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

Protected Attributes
VectorXs	g_lb_
	Lower bound of the inequality constraints.

VectorXs	g_ub_
	< Lower bound of the inequality constraints

std::size_t	nu_
	< Upper bound of the inequality constraints

boost::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	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.

Additional Inherited Members
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::DifferentialActionModelContactFwdDynamicsTpl< _Scalar >

Differential action model for contact forward dynamics in multibody systems.

This class implements contact forward dynamics given a stack of rigid-contacts described in ContactModelMultipleTpl, i.e.,

\[ \left[\begin{matrix}\dot{\mathbf{v}} \\ -\boldsymbol{\lambda}\end{matrix}\right] = \left[\begin{matrix}\mathbf{M} & \mathbf{J}^{\top}_c \\ {\mathbf{J}_{c}} & \mathbf{0} \end{matrix}\right]^{-1} \left[\begin{matrix}\boldsymbol{\tau}_b \\ -\mathbf{a}_0 \\\end{matrix}\right], \]

where \(\mathbf{q}\in Q\), \(\mathbf{v}\in\mathbb{R}^{nv}\) are the configuration point and generalized velocity (its tangent vector), respectively; \(\boldsymbol{\tau}_b=\boldsymbol{\tau} - \mathbf{h}(\mathbf{q},\mathbf{v})\) is the bias forces that depends on the torque inputs \(\boldsymbol{\tau}\) and the Coriolis effect and gravity field \(\mathbf{h}(\mathbf{q},\mathbf{v})\); \(\mathbf{J}_c\in\mathbb{R}^{nc\times nv}\) is the contact Jacobian expressed in the local frame; and \(\mathbf{a}_0\in\mathbb{R}^{nc}\) is the desired acceleration in the constraint space. To improve stability in the numerical integration, we define PD gains that are similar in spirit to Baumgarte stabilization:

\[ \mathbf{a}_0 = \mathbf{a}_{\lambda(c)} - \alpha \,^oM^{ref}_{\lambda(c)}\ominus\,^oM_{\lambda(c)} - \beta\mathbf{v}_{\lambda(c)}, \]

where \(\mathbf{v}_{\lambda(c)}\), \(\mathbf{a}_{\lambda(c)}\) are the spatial velocity and acceleration at the parent body of the contact \(\lambda(c)\), respectively; \(\alpha\) and \(\beta\) are the stabilization gains; \(\,^oM^{ref}_{\lambda(c)}\ominus\,^oM_{\lambda(c)}\) is the \(\mathbb{SE}(3)\) inverse composition between the reference contact placement and the current one.

The derivatives of the system acceleration and contact forces are computed efficiently based on the analytical derivatives of Recursive Newton Euler Algorithm (RNEA) as described in [mastalli-icra20]. Note that the algorithm for computing the RNEA derivatives is described in [carpentier-rss18].

The stack of cost and constraint functions are implemented in CostModelSumTpl and ConstraintModelAbstractTpl, respectively. The computation of the contact dynamics and its derivatives are carrying out inside calc() and calcDiff() functions, respectively. It is also important to remark that calcDiff() computes the derivatives using the latest stored values by calc(). Thus, we need to run calc() first.

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

Definition at line 74 of file contact-fwddyn.hpp.

Constructor & Destructor Documentation

◆ DifferentialActionModelContactFwdDynamicsTpl() [1/2]

DifferentialActionModelContactFwdDynamicsTpl	(	boost::shared_ptr< StateMultibody >	state,
		boost::shared_ptr< ActuationModelAbstract >	actuation,
		boost::shared_ptr< ContactModelMultiple >	contacts,
		boost::shared_ptr< CostModelSum >	costs,
		const Scalar	JMinvJt_damping = `Scalar(0.)`,
		const bool	enable_force = `false`
	)

Initialize the contact forward-dynamics action model.

It describes the dynamics evolution of a multibody system under rigid-contact constraints defined by ContactModelMultipleTpl. It computes the cost described in CostModelSumTpl.

Parameters

[in]	state	State of the multibody system
[in]	actuation	Actuation model
[in]	contacts	Stack of rigid contact
[in]	costs	Stack of cost functions
[in]	JMinvJt_damping	Damping term used in operational space inertia matrix (default 0.)
[in]	enable_force	Enable the computation of the contact force derivatives (default false)

◆ DifferentialActionModelContactFwdDynamicsTpl() [2/2]

DifferentialActionModelContactFwdDynamicsTpl	(	boost::shared_ptr< StateMultibody >	state,
		boost::shared_ptr< ActuationModelAbstract >	actuation,
		boost::shared_ptr< ContactModelMultiple >	contacts,
		boost::shared_ptr< CostModelSum >	costs,
		boost::shared_ptr< ConstraintModelManager >	constraints,
		const Scalar	JMinvJt_damping = `Scalar(0.)`,
		const bool	enable_force = `false`
	)

Initialize the contact forward-dynamics action model.

It describes the dynamics evolution of a multibody system under rigid-contact constraints defined by ContactModelMultipleTpl. It computes the cost described in CostModelSumTpl.

Parameters

[in]	state	State of the multibody system
[in]	actuation	Actuation model
[in]	contacts	Stack of rigid contact
[in]	costs	Stack of cost functions
[in]	constraints	Stack of constraints
[in]	JMinvJt_damping	Damping term used in operational space inertia matrix (default 0.)
[in]	enable_force	Enable the computation of the contact force derivatives (default false)

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
	)

virtual

Compute the system acceleration, and cost value.

It computes the system acceleration using the contact dynamics.

Parameters

[in]	data	Contact forward-dynamics 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]

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 it is expected to be zero. Additionally, it does not update the contact forces. This function is used in the terminal nodes of an optimal control problem.

Parameters

[in]	data	Contact forward-dynamics data
[in]	x	State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)

Reimplemented from DifferentialActionModelAbstractTpl< _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
	)

virtual

Compute the derivatives of the contact dynamics, and cost function.

Parameters

[in]	data	Contact forward-dynamics 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]

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. Additionally, it does not update the contact forces derivatives. This function is used in the terminal nodes of an optimal control problem.

Parameters

[in]	data	Contact forward-dynamics data
[in]	x	State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

◆ createData()

virtual boost::shared_ptr<DifferentialActionDataAbstract> createData ( )

virtual

Create the contact forward-dynamics data.

Returns: contact forward-dynamics data

Reimplemented from DifferentialActionModelAbstractTpl< _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 from DifferentialActionModelAbstractTpl< _Scalar >.

◆ print()

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

virtual

Print relevant information of the contact forward-dynamics model.

Parameters

[out] os Output stream object

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

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

/root/robotpkg/optimization/py-crocoddyl/work/crocoddyl-2.0.2/include/crocoddyl/multibody/actions/contact-fwddyn.hpp

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ DifferentialActionModelContactFwdDynamicsTpl() [1/2]

◆ DifferentialActionModelContactFwdDynamicsTpl() [2/2]

Member Function Documentation

◆ calc() [1/2]

◆ calc() [2/2]

◆ calcDiff() [1/2]

◆ calcDiff() [2/2]

◆ createData()

◆ quasiStatic()

◆ print()

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