This class computes the numerical differentiation of a differential action model. More...
#include <diff-action.hpp>
Public Types | |
typedef DifferentialActionModelAbstractTpl< Scalar > | Base |
typedef DifferentialActionDataNumDiffTpl< Scalar > | Data |
typedef DifferentialActionDataAbstractTpl< Scalar > | DifferentialActionDataAbstract |
typedef MathBaseTpl< Scalar > | MathBase |
typedef MathBase::MatrixXs | MatrixXs |
typedef MathBase::VectorXs | VectorXs |
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typedef DifferentialActionDataAbstractTpl< Scalar > | DifferentialActionDataAbstract |
typedef MathBaseTpl< Scalar > | MathBase |
typedef MathBase::MatrixXs | MatrixXs |
typedef StateAbstractTpl< Scalar > | StateAbstract |
typedef MathBase::VectorXs | VectorXs |
Public Member Functions | |
DifferentialActionModelNumDiffTpl (std::shared_ptr< Base > model, const bool with_gauss_approx=false) | |
Initialize the numdiff differential action model. | |
virtual void | calc (const std::shared_ptr< DifferentialActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) |
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) |
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 std::shared_ptr< DifferentialActionDataAbstract > | createData () |
Create the differential action data. | |
const Scalar | get_disturbance () const |
Return the disturbance constant used in the numerical differentiation routine. | |
const std::shared_ptr< Base > & | get_model () const |
Return the differential acton model that we use to numerical differentiate. | |
bool | get_with_gauss_approx () |
Identify if the Gauss approximation is going to be used or not. | |
virtual void | print (std::ostream &os) const |
Print relevant information of the action numdiff model. | |
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. | |
void | set_disturbance (const Scalar disturbance) |
Modify the disturbance constant used in the numerical differentiation routine. | |
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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 bool | checkData (const std::shared_ptr< DifferentialActionDataAbstract > &data) |
Checks that a specific data belongs to this 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. | |
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. | |
Public Attributes | |
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar | Scalar |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar | Scalar |
Protected Attributes | |
bool | has_control_limits_ |
std::size_t | nr_ |
std::size_t | nu_ |
< Dimension of the cost residual | |
std::shared_ptr< StateAbstract > | state_ |
< Control dimension | |
VectorXs | u_lb_ |
< Model of the state | |
VectorXs | u_ub_ |
< Lower control limits | |
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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 | |
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void | update_has_control_limits () |
Update the status of the control limits (i.e. if there are defined limits) | |
This class computes the numerical differentiation of a differential action model.
It computes the Jacobian of the cost, its residual and dynamics via numerical differentiation. It considers that the action model owns a cost residual and the cost is the square of this residual, i.e., \(\ell(\mathbf{x},\mathbf{u})=\frac{1}{2}\|\mathbf{r}(\mathbf{x},\mathbf{u})\|^2\), where \(\mathbf{r}(\mathbf{x},\mathbf{u})\) is the residual vector. The Hessian is computed only through the Gauss-Newton approximation, i.e.,
\begin{eqnarray*} \mathbf{\ell}_\mathbf{xx} &=& \mathbf{R_x}^T\mathbf{R_x} \\ \mathbf{\ell}_\mathbf{uu} &=& \mathbf{R_u}^T\mathbf{R_u} \\ \mathbf{\ell}_\mathbf{xu} &=& \mathbf{R_x}^T\mathbf{R_u} \end{eqnarray*}
where the Jacobians of the cost residuals are denoted by \(\mathbf{R_x}\) and \(\mathbf{R_u}\). Note that this approximation ignores the tensor products (e.g., \(\mathbf{R_{xx}}\mathbf{r}\)).
Finally, in the case that the cost does not have a residual, we set the Hessian to zero, i.e., \(\mathbf{L_{xx}} = \mathbf{L_{xu}} = \mathbf{L_{uu}} = \mathbf{0}\).
DifferentialActionModelAbstractTpl()
, calcDiff()
Definition at line 47 of file diff-action.hpp.
typedef MathBaseTpl<Scalar> MathBase |
Definition at line 53 of file diff-action.hpp.
typedef DifferentialActionModelAbstractTpl<Scalar> Base |
Definition at line 54 of file diff-action.hpp.
typedef DifferentialActionDataNumDiffTpl<Scalar> Data |
Definition at line 55 of file diff-action.hpp.
typedef DifferentialActionDataAbstractTpl<Scalar> DifferentialActionDataAbstract |
Definition at line 57 of file diff-action.hpp.
typedef MathBase::VectorXs VectorXs |
Definition at line 58 of file diff-action.hpp.
typedef MathBase::MatrixXs MatrixXs |
Definition at line 59 of file diff-action.hpp.
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explicit |
Initialize the numdiff differential action model.
[in] | model | Differential action model that we want to apply the numerical differentiation |
[in] | with_gauss_approx | True if we want to use the Gauss approximation for computing the Hessians |
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virtual |
Compute the system acceleration and cost value.
[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 >.
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virtual |
Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.
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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).
[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 >.
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virtual |
Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.
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virtual |
Create the differential action data.
Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.
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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 \(\mathbf{f}(\mathbf{q},\mathbf{v}=\mathbf{0},\mathbf{u})=\mathbf{0}\)
[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 >.
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virtual |
Print relevant information of the action numdiff model.
[out] | os | Output stream object |
Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar Scalar |
Definition at line 52 of file diff-action.hpp.
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protected |
Indicates whether any of the control limits is finite
Definition at line 369 of file diff-action-base.hpp.
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protected |
< Indicates whether any of the control limits
Definition at line 358 of file diff-action-base.hpp.
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protected |
< Dimension of the cost residual
Definition at line 357 of file diff-action-base.hpp.
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protected |
< Control dimension
Definition at line 363 of file diff-action-base.hpp.
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protected |
< Model of the state
Definition at line 367 of file diff-action-base.hpp.
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protected |
< Lower control limits
Definition at line 368 of file diff-action-base.hpp.