Template Class CostModelResidualTpl

Defined in File residual.hpp

Inheritance Relationships

Base Type

public crocoddyl::CostModelAbstractTpl< _Scalar > (Template Class CostModelAbstractTpl)

Class Documentation

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

Residual-based cost.

This cost function uses a residual model to compute the cost, i.e.,

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

where \(\mathbf{r}(\cdot)\) and \(a(\cdot)\) define the residual and activation functions, respectively.

Note that we only compute the Jacobians of the residual function. Therefore, this cost model computes its Hessians through a Gauss-Newton approximation, e.g., \(\mathbf{l_{xu}} = \mathbf{R_x}^T \mathbf{A_{rr}} \mathbf{R_u} \), where \(\mathbf{R_x}\) and \(\mathbf{R_u}\) are the Jacobians of the residual function, and \(\mathbf{A_{rr}}\) is the Hessian of the activation model.

As described in CostModelAbstractTpl(), the cost value and its derivatives are calculated by calc and calcDiff, respectively.