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 \(M_1(A, B) = A B\) and \(m_1 = \log_6(M_1) \). Then, we have the following partial (right) Jacobians:

\( \frac{\partial m_1}{\partial A} = Jlog_6(M_1) Ad_B^{-1} \),
\( \frac{\partial m_1}{\partial B} = Jlog_6(M_1) \).

Let \(A \in SE(3)\), \(M_2(A) = A^{-1}\) and \(m_2 = \log_6(M_2)\). Then, we have the following partial (right) Jacobian:

\( \frac{\partial m_2}{\partial A} = - Jlog_6(M_2) Ad_A \).

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)

\( \frac{\partial\ominus}{\partial q_1} {}^1X_0 = - \frac{\partial\ominus}{\partial q_0} \)