pinocchio
2.6.3
A fast and flexible implementation of Rigid Body Dynamics algorithms and their analytical derivatives
Cheat sheet
Member
LieGroupBase< Derived >::dDifference
(const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Eigen::MatrixBase< JacobianOut_t > &J) const
\( \frac{\partial\ominus}{\partial q_1} \frac{\partial\oplus}{\partial v} = I \)
Member
LieGroupBase< Derived >::difference
(const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Eigen::MatrixBase< Tangent_t > &v) const
\( q_1 \ominus q_0 = - \left( q_0 \ominus q_1 \right) \)
Member
LieGroupBase< Derived >::isSameConfiguration
(const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Scalar &prec=Eigen::NumTraits< Scalar >::dummy_precision()) const
\( q_1 \equiv q_0 \oplus \left( q_1 \ominus q_0 \right) \) ( \(\equiv\) means equivalent, not equal).
Member
pinocchio::Jlog6
(const
SE3Tpl< Scalar, Options >
&M, const Eigen::MatrixBase< Matrix6Like > &Jlog)
For \((A,B) \in SE(3)^2\), let \(m_1 = log_6(A B) \) and \( m_2 = log_6(A^{-1}) \). Then, we have:
\( \frac{\partial m_1}{\partial A} = Jlog_6(M_1) Ad_B^{-1} \),
\( \frac{\partial m_1}{\partial B} = Jlog_6(M_1) \),
\( \frac{\partial m_2}{\partial A} = - Jlog_6(M_2) Ad_A \).
Class
SE3Base< Derived >
\( {}^aM_c = {}^aM_b {}^bM_c \)
Member
SE3Base< Derived >::toActionMatrix
() const
\( {}^a\nu_c = {}^aX_b {}^b\nu_c \)
Member
SpecialEuclideanOperationTpl< 3, _Scalar, _Options >::dDifference_impl
(const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Eigen::MatrixBase< JacobianOut_t > &J) const
\( \frac{\partial\ominus}{\partial q_1} {}^1X_0 = - \frac{\partial\ominus}{\partial q_0} \)
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