What is the core of Robotics as a discipline?

You could argue that robotics is an engineering discipline, because we work on the design, building and use of robots.

You could also argue that robotics ought to be more a science than an engineering discipline alone, since we provide new kinds of tools and models for other disciplines in much the same way mathematics does (with the admittedly large difference that our tools exist as physical objects).

Or you could argue that mathematics and robotics lie on either side of engineering, with mathematics providing the inputs to engineering and science and robotics coming out the other end as the ultimate synthesis of engineering and scientific fields.

Or you could even argue that robotics sits to the side of traditional classifications – roboticists tend to have significant experience in a wide range of fields not limited to engineering.  Those fields can include electrical engineering, mechanical engineering and computer science, as well as some degree of familiarity with the fields in which their robots were supposed to be operating, with deep expertise in individual pockets of each of those fields dependent on the details of the robots and the problems in question.  When a roboticist moves from problem to problem within robotics, they can view all the breadth of their expertise as potential opportunities to develop new pockets of deep expertise in some new area within that breadth, rather than something outside their expertise to be hired out to someone else.

An individual might start working on a project requiring their expertise in visual sensors for ground robots in urban environments, and then discover a need to apply that skill to working on visual sensors in aerial environments.  Their next project might involve machine learning to support improved perception, which could in turn lead to work on machine learning for decision making.  As part of that work, this individual might move to the design or improvement of specific behaviors the robot is deciding between, from there to low level control of some actuator on the system to improve a specific behavior, and finally to a mechanical redesign of the arm, leg or propeller.

That individual will have worked through electrical engineering to computer science to a different branch of electrical engineering to mechanical engineering, but in context, the path is instead a seamless trajectory through robotics.

And every element of that path is more fundamentally part of robotics than part of the discipline in which it is currently based, because every element of that path is rooted in the core of robotics as a field:  how active machines interact with the world.  Robotics is not just about designing the robot; it is about understanding the environment in which the robot is expected to operate.  It is not just about building the robot, it is about ensuring it is capable of the desired range of behaviors.  It is not just about using the robot, it is about understanding and improving the relationship between the robot and the user.

We worry about signal processing not as an abstract tool in the electrical engineering toolbox that can be used to clean up signals for human consumption, but because it enables the robot to obtain better information about its environment.

We worry about machine learning because the world is a large and unpredictable place, and we can’t always constrain the environments our robots need to operate in to the environments we can fully model and understand (and we can’t fully model and understand any but the simplest environments right now).

We worry about the individual behaviors because we build robots to do things, and they should be able to do those things well.

We worry about low level control because that determines how effectively it can act in its environment, and we design new tools and legs because we want it to be capable of doing new things.

Every step in that path is about the robot performing a task, in a complex and potentially unknown environment.  That is the core of robotics.