Template Class ActionModelImpulseFwdDynamicsTpl

Defined in File impulse-fwddyn.hpp

Inheritance Relationships

Base Type

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

Class Documentation

template<typename _Scalar> class ActionModelImpulseFwdDynamicsTpl : public crocoddyl::ActionModelAbstractTpl<_Scalar>

Action model for impulse forward dynamics in multibody systems.

This class implements impulse forward dynamics given a stack of rigid-impulses described in ImpulseModelMultipleTpl, i.e.,

\[\begin{split} \left[\begin{matrix}\mathbf{v}^+ \\ -\boldsymbol{\Lambda}\end{matrix}\right] = \left[\begin{matrix}\mathbf{M} & \mathbf{J}^{\top}_c \\ {\mathbf{J}_{c}} & \mathbf{0} \end{matrix}\right]^{-1} \left[\begin{matrix}\mathbf{M}\mathbf{v}^- \\ -e\mathbf{J}_c\mathbf{v}^- \\\end{matrix}\right], \end{split}\]

where \(\mathbf{q}\in Q\), \(\mathbf{v}\in\mathbb{R}^{nv}\) are the configuration point and generalized velocity (its tangent vector), respectively; \(\mathbf{v}^+\), \(\mathbf{v}^-\) are the discontinuous changes in the generalized velocity (i.e., velocity before and after impact, respectively); \(\mathbf{J}_c\in\mathbb{R}^{nc\times nv}\) is the contact Jacobian expressed in the local frame; and \(\boldsymbol{\Lambda}\in\mathbb{R}^{nc}\) is the impulse vector.

The derivatives of the next state and contact impulses are computed efficiently based on the analytical derivatives of Recursive Newton Euler Algorithm (RNEA) as described in mastalli-icra20. Note that the algorithm for computing the RNEA derivatives is described in carpentier-rss18.

The stack of cost and constraint functions are implemented in CostModelSumTpl and ConstraintModelAbstractTpl, respectively. The computation of the impulse dynamics and its derivatives are carrying out inside calc() and calcDiff() functions, respectively. It is also important to remark that calcDiff() computes the derivatives using the latest stored values by calc(). Thus, we need to run calc() first.