Crocoddyl
DifferentialActionModelAbstractTpl< _Scalar > Class Template Referenceabstract

Abstract class for differential action model. More...

#include <diff-action-base.hpp>

Inheritance diagram for DifferentialActionModelAbstractTpl< _Scalar >:
DifferentialActionModelContactFwdDynamicsTpl< _Scalar > DifferentialActionModelContactInvDynamicsTpl< _Scalar > DifferentialActionModelFreeFwdDynamicsTpl< _Scalar > DifferentialActionModelFreeInvDynamicsTpl< _Scalar > DifferentialActionModelLQRTpl< _Scalar > DifferentialActionModelNumDiffTpl< _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< DifferentialActionDataAbstractcreateData ()
 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< StateAbstractstate_
 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]stateState description
[in]nuDimension of control vector
[in]nrDimension of cost-residual vector
[in]ngNumber of inequality constraints
[in]nhNumber 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]dataDifferential action data
[in]xState point \(\mathbf{x}\in\mathbb{R}^{ndx}\)
[in]uControl 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]dataDifferential action data
[in]xState 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]dataDifferential action data
[in]xState point \(\mathbf{x}\in\mathbb{R}^{ndx}\)
[in]uControl 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]dataDifferential action data
[in]xState point \(\mathbf{x}\in\mathbb{R}^{ndx}\)

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

◆ createData()

◆ 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]dataDifferential action data
[out]uQuasic static commands
[in]xState point (velocity has to be zero)
[in]maxiterMaximum allowed number of iterations
[in]tolTolerance

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]dataDifferential action data
[in]xState point (velocity has to be zero)
[in]maxiterMaximum allowed number of iterations
[in]tolTolerance
Returns
Quasic static commands

◆ print()

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: