def jacobe(self, q=None, T=None):
r"""
Jacobian in base frame
:param q: joint coordinates
:type q: array_like
:param T: ETS value as an SE(3) matrix if known
:type T: ndarray(4,4)
:return: Jacobian matrix
:rtype: ndarray(6,n)
``jacobe(q)`` is the manipulator Jacobian matrix which maps joint
velocity to end-effector spatial velocity.
End-effector spatial velocity :math:`\nu = (v_x, v_y, v_z, \omega_x, \omega_y, \omega_z)^T`
is related to joint velocity by :math:`{}^{e}\nu = {}^{e}\mathbf{J}_0(q) \dot{q}`.
If ``ets.eval(q)`` is already computed it can be passed in as ``T`` to
reduce computation time.
:seealso: :func:`jacob`, :func:`hessian0`
""" # noqa
if T is None:
T = self.eval(q)
return tr2jac(T.A) @ self.jacob0(q, T)
def jacob(self):
"""
Velocity transform for SE(3)
:return: Jacobian matrix
:rtype: numpy.ndarray, shape=(6,6)
``SE3.jacob()`` is the 6x6 Jacobian that maps spatial velocity or
differential motion from frame {B} to frame {A} where the pose of {B}
relative to {A} is represented by the homogeneous transform T =
:math:`{}^A {\bf T}_B`.
.. note::
- To map from frame {A} to frame {B} use the transpose of this matrix.
- Use this method to map velocities between the robot end-effector frame
and the base frames.
.. warning:: Do not use this method to map velocities between two frames
on the same rigid-body.
:seealso: SE3.Ad, Twist.ad, :func:`~spatialmath.base.tr2jac`
:Reference: Robotics, Vision & Control: Second Edition, P. Corke, Springer 2016; p65.
:SymPy: supported
"""
return base.tr2jac(self.A)