So there’s no maze yet, but I’m getting there.
This is a screenshot of an initial grappling testbed. That’s the Asteroids ship transplanted into a world with gravity, and a rope attached. If the rope’s end touches a box (or any non-static physics object, actually), it will automatically attach, and the player can fly it around. Press the ‘A’ button to release the object. As an initial testbed, it’s working pretty well, I think.
A key point in the implementation here is that the rope changes color, to show you whether or not it has connected to something. Without that, it can sometimes be difficult to tell whether or not it’s managed to grab the object you want it to.