End-effector frame

End-effector frame task map captures the relative transformation between the base frame \(B\) and the tip frame \(A\):

\[\Phi_\text{EffFrame}(\boldsymbol{x}) = \boldsymbol{M}_A^B,\]

where \(\boldsymbol{M}_A^B\in SE(3)\) is computed using the system model using the Scene. We use the task space vector data structure (described later in this section) to handle storage and operations on spatial frames. The Jacobian of this task map is the geometric Jacobian computed by the Scene.