This class computes the numerical differentiation of a differential action model. More...
#include <crocoddyl/core/numdiff/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 |
Public Member Functions | |
DifferentialActionModelNumDiffTpl (boost::shared_ptr< Base > model, const bool with_gauss_approx=false) | |
Initialize the numdiff differential action model. More... | |
virtual void | calc (const boost::shared_ptr< DifferentialActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) |
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) |
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 dynamics and cost functions. More... | |
virtual boost::shared_ptr< DifferentialActionDataAbstract > | createData () |
Create the differential action data. More... | |
const Scalar | get_disturbance () const |
Return the disturbance used in the numerical differentiation routine. | |
const boost::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. | |
void | set_disturbance (const Scalar disturbance) |
Modify the disturbance used in the numerical differentiation routine. | |
Public Attributes | |
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar | Scalar |
Protected Attributes | |
bool | has_control_limits_ |
Indicates whether any of the control limits is finite. | |
std::size_t | nr_ |
< Indicates whether any of the control limits | |
std::size_t | nu_ |
< Dimension of the cost residual | |
boost::shared_ptr< StateAbstract > | state_ |
< Control dimension | |
VectorXs | u_lb_ |
< Model of the state | |
VectorXs | u_ub_ |
< Lower control limits | |
VectorXs | unone_ |
< Upper control limits | |
This class computes the numerical differentiation of a differential action model.
It computes 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()
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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 \(\mathbf{u}\in\mathbb{R}^{nu}\) |
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virtual |
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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 \(\mathbf{u}\in\mathbb{R}^{nu}\) |
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virtual |
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virtual |
Create the differential action data.