Designing a robot, assembling a robot, buying already-made parts + sensor and program a robot, program a mobile robot vs robot arm is all quite different process & require different backgrounds.
Is it the mechanical part? Electrical Engineering part? Mechatronics? Material Science? Design? Control Theory? Motion Planning? Perception? Localization? Autonomous planning? Software? All of em?
As someone who worked in a robotics startup that designed/manufactured the robot and the software, I met a lot of Robotics experts and Engineers with a PhD in relevant area. (Haptics, Mechanics, Industrial Design, Motion planning, Embedded engineering, Computer Vision engineers, Control Engineers, Software Engineers, etc)
But there was rarely any overlapping knowledge past maybe how actuators worked and joints/wheels moved. I could not understand much of the haptics engineers work, but could use his designs through help with the embedded engineers PCB and integration.