With the ROS driver, how can I get the current robot pose (Cartesian and polar coordinates) without using MoveIt (only Universal_Robots_ROS_Driver)?
You probably want to get yourself familiar with ROS built-in tf system.
In particular, you can run
rosrun tf tf_echo [reference_frame] tool0_controller
to get the tool’s pose in the coordinate system of
[reference frame] where
[reference_frame] could be e.g.
base to get the tool’s pose in the robot’s base coordinate system.