Template Class ControlParametrizationModelPolyTwoRKTpl

Defined in File poly-two-rk.hpp

Inheritance Relationships

Base Type

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

Class Documentation

template<typename _Scalar> class ControlParametrizationModelPolyTwoRKTpl : public crocoddyl::ControlParametrizationModelAbstractTpl<_Scalar>

A polynomial function of time of degree two, that is a quadratic function.

The size of the parameters \(\mathbf{u}\) is 3 times the size of the control input \(\mathbf{w}\). It defines a polynomial of degree two, customized for the RK4 and RK4 integrators (even though it can be used with whatever integration scheme). The first third of \(\mathbf{u}\) represents the value of \(\mathbf{w}\) at time 0. The second third of \(\mathbf{u}\) represents the value of \(\mathbf{w}\) at time 0.5 or 1/3 for RK4 and RK3 parametrization, respectively. The last third of \(\mathbf{u}\) represents the value of \(\mathbf{w}\) at time 1 or 2/3 for the RK4 and RK3 parametrization, respectively. This parametrization is suitable to be used with the RK-4 or RK-3 integration schemes, because they require the value of \(\mathbf{w}\) exactly at 0, 0.5, 1 (for RK4) or 0, 1/3, 2/3 (for RK3).

The main computations are carried out in calc, multiplyByJacobian and multiplyJacobianTransposeBy, where the former computes control input \(\mathbf{w}\in\mathbb{R}^{nw}\) from a set of control parameters \(\mathbf{u}\in\mathbb{R}^{nu}\) where nw and nu represent the dimension of the control inputs and parameters, respectively, and the latter defines useful operations across the Jacobian of the control-parametrization model. Finally, params allows us to obtain the control parameters from a the control input, i.e., it is the inverse of calc. Note that multiplyByJacobian and multiplyJacobianTransposeBy requires to run calc first.