Template Class CostModelAbstractTpl

Defined in File cost-base.hpp

Inheritance Relationships

Base Type

public crocoddyl::CostModelBase (Class CostModelBase)

Derived Types

public crocoddyl::CostModelNumDiffTpl< _Scalar > (Template Class CostModelNumDiffTpl)
public crocoddyl::CostModelResidualTpl< _Scalar > (Template Class CostModelResidualTpl)

Class Documentation

template<typename _Scalar> class CostModelAbstractTpl : public crocoddyl::CostModelBase 

Abstract class for cost models.

A cost model is defined by the scalar activation function \(a(\cdot)\) and by the residual function \(\mathbf{r}(\cdot)\) as follows:

\[ \ell(\mathbf{x},\mathbf{u}) = a(\mathbf{r}(\mathbf{x}, \mathbf{u})), \]

where the residual function depends on the state point \(\mathbf{x}\in\mathcal{X}\), which lies in the state manifold described with a nx-tuple, its velocity \(\dot{\mathbf{x}}\in T_{\mathbf{x}}\mathcal{X}\) that belongs to the tangent space with ndx dimension, and the control input \(\mathbf{u}\in\mathbb{R}^{nu}\). The residual vector is defined by \(\mathbf{r}\in\mathbb{R}^{nr}\) where nr describes its dimension in the Euclidean space. On the other hand, the activation function builds a cost value based on the definition of the residual vector. The residual vector has to be specialized in a derived classes.

The main computations are carring out in calc() and calcDiff() routines. calc() computes the cost (and its residual) and calcDiff() computes the derivatives of the cost function (and its residual). Concretely speaking, calcDiff() builds a linear-quadratic approximation of the cost function with the form: \(\mathbf{l_x}\in\mathbb{R}^{ndx}\), \(\mathbf{l_u}\in\mathbb{R}^{nu}\), \(\mathbf{l_{xx}}\in\mathbb{R}^{ndx\times ndx}\), \(\mathbf{l_{xu}}\in\mathbb{R}^{ndx\times nu}\), \(\mathbf{l_{uu}}\in\mathbb{R}^{nu\times nu}\) are the Jacobians and Hessians, respectively. 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().