Template Class ResidualModelContactCoPPositionTpl

Defined in File contact-cop-position.hpp

Inheritance Relationships

Base Type

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

Class Documentation

template<typename _Scalar> class ResidualModelContactCoPPositionTpl : public crocoddyl::ResidualModelAbstractTpl<_Scalar>

Center of pressure residual function.

It builds a residual function that bounds the center of pressure (CoP) for one contact surface to lie inside a certain geometric area defined around the reference contact frame. The residual residual vector is described as \(\mathbf{r}=\mathbf{A}\boldsymbol{\lambda}\geq\mathbf{0}\), where

\[\begin{split} \mathbf{A}= \begin{bmatrix} 0 & 0 & X/2 & 0 & -1 & 0 \\ 0 & 0 & X/2 & 0 & 1 & 0 \\ 0 & 0 & Y/2 & 1 & 0 & 0 \\ 0 & 0 & Y/2 & -1 & 0 & 0 \end{bmatrix} \end{split}\]

is the inequality matrix and \(\boldsymbol{\lambda}\) is the reference spatial contact force in the frame coordinate. The CoP lies inside the convex hull of the foot, see eq.(18-19) of https://hal.archives-ouvertes.fr/hal-02108449/document is we have:

\[\begin{split} \begin{align}\begin{split}\tau^x &\leq Yf^z \\-\tau^x &\leq Yf^z \\\tau^y &\leq Yf^z \\-\tau^y &\leq Yf^z \end{split}\end{align} \end{split}\]

with \(\boldsymbol{\lambda}= \begin{bmatrix}f^x & f^y & f^z & \tau^x & \tau^y & \tau^z \end{bmatrix}^T\).

The residual is computed, from the residual vector \(\mathbf{r}\), through an user defined activation model. Additionally, the contact frame id, the desired support region for the CoP and the inequality matrix are handled within CoPSupportTpl. The force vector \(\boldsymbol{\lambda}\) and its derivatives are computed by DifferentialActionModelContactFwdDynamicsTpl or ActionModelImpulseFwdDynamicTpl. These values are stored in a shared data (i.e., DataCollectorContactTpl or DataCollectorImpulseTpl). Note that this residual function cannot be used with other action models.