Now with minor changes in files out of the way, we can focus on basic_trajectory_action_service.py, the script file that issues commands to move both arm and gripper. I should have renamed it... Ok, next time.
The script includes twi classes, RoboticArmController to control the arm (including gripper) and GraspingController to tell RoboticArmController what exactly to do, depending on state of a gripper.