[andrewallbright]

Full disclosure: I'm just a hobbyist game dev with experience with arduino, and volunteering at my local robotics competition.

I would recommend getting into arduino. It's fun to buy little components, build little circuits, and see how your ability to program can have a physical manifestation.

As for programming concepts -- yes kinematics and inverse kinematics will allow you to move robotic limbs to certain points in real space.

And you'll find yourself wanting a larger conceptual framework to put those technical bits. That's where things like finite state machines, hierarchical finite state machines, behavior trees, and/or goal oriented action planners may come in handy. This grouping of concepts is often called "ai programming" but whatever you decide to call it, they're algorithms to decide what to do at any given slice of time.

Obviously follow your own path in this subject; follow the bits that resonate with you.