Template Function pinocchio::getJointJacobian

Function Documentation

template<typename Scalar, int Options, template<typename, int> class JointCollectionTpl, typename Matrix6Like>
inline void pinocchio::getJointJacobian(const ModelTpl<Scalar, Options, JointCollectionTpl> &model, const DataTpl<Scalar, Options, JointCollectionTpl> &data, const typename ModelTpl<Scalar, Options, JointCollectionTpl>::JointIndex jointId, const ReferenceFrame rf, const Eigen::MatrixBase<Matrix6Like> &J)

Computes the Jacobian of a specific joint frame expressed in one of the pinocchio::ReferenceFrame options.

For the LOCAL reference frame, the Jacobian \({}^j J_{0j}\) from the joint frame \(j\) to the world frame \(0\) is such that \({}^j v_{0j} = {}^j J_{0j} \dot{q}\), where \({}^j v_{0j}\) is the velocity of the origin of the moving joint frame relative to the fixed world frame, projected into the basis of the joint frame. LOCAL_WORLD_ALIGNED is the same velocity but projected into the world frame basis.

For the WORLD reference frame, the Jacobian \({}^0 J_{0j}\) from the joint frame \(j\) to the world frame \(0\) is such that \({}^0 v_{0j} = {}^0 J_{0j} \dot{q}\), where \({}^0 v_{0j}\) is the spatial velocity of the joint frame. The linear component of this spatial velocity is the velocity of a (possibly imaginary) point attached to the moving joint frame j which is traveling through the origin of the world frame at that instant. The angular component is the instantaneous angular velocity of the joint frame as viewed in the world frame.

When serialized to a 6D vector, the order of coordinates is: three linear followed by three angular.

For further details regarding the different velocities or the Jacobian see Chapters 2 and 3 respectively in A Mathematical Introduction to Robotic Manipulation by Murray, Li and Sastry.

Note

This jacobian is extracted from data.J. You have to run pinocchio::computeJointJacobians before calling it.

Template Parameters:

  • JointCollection – Collection of Joint types.

  • Matrix6xLike – Type of the matrix containing the joint Jacobian.

Parameters:

  • localFrame – [in] Expressed the Jacobian in the local frame or world frame coordinates system.

  • model – [in] The model structure of the rigid body system.

  • data – [in] The data structure of the rigid body system.

  • jointId – [in] The id of the joint.

  • J – [out] A reference to the Jacobian matrix where the results will be stored (dim 6 x model.nv). You must fill J with zero elements, e.g. J.fill(0.).