[Warning: this article can be pretty difficult to understand as it refers to higher-dimensional geometry. I would recommend watching some of Miegakure's video about 4D geometry, which explain all this very well.]
The mystery sphere that exists on Antares-4, as it is explained, is an extraterrestrial machine of unknown origin. It has very peculiar behavior, which can sometimes be frustrating to the reader because it appears to have so little link to anything we would consider even remotely possible. I personally found it to be exagerrated, until I realised that if we consider the machine to be a 4-dimensional object, then a lot of it suddenly makes sense.
First, it explains the 'peeling' effect that we see when something or someone is being transported to Antares-4. We would observe such a peeling effect on a 3D object if it were rotated 90 degrees along a 4th dimension. It would then completely disappear if it were to be moved out of the 3D slice their world is in. They could then be moved to the destination through other 3D worlds that constitute other 3D slices of the 4D environment. The purpose of the high-energy beam is unclear however.
Next, it also explains much about the behavior of the mystery sphere. Being really a hypersphere (i.e. 4D-sphere), the 3D sphere that the characters see is only a slice of the entire object. It appears extremely heavy for its size because most of the weight lies in the rest of the object's volume, in the 4th dimension. The fact that the sphere sometime appears smaller or bigger, or even floating in the air, only depends on how the 4D object interescts the 3D plane of their world. It appears to be floating to them, but it is really resting on some ground somehwere else in the 4th dimension.
It also explains how it could copy the group's shuttle so easily: when viewing a 3D object from a 4D-perspective, all the details can be seen at once. Much like nothing can be hidden on 2D-drawing when viewing it from a 3D perspective: everything can be seen at once. So practically, all the machine had to do, so to say, is to take a 'snapshot' of the shuttle and 3D-print it somehow.
The same thing goes for the sphere entering the body of Ashely without touching or damaging anything: a 4D oject can theoretically go through any 3D object simply by moving in the 4th dimension.
Finally, it partly explains the empty space Kim and Alexa find themselves in. If the duplicate shuttle was moved out of their 3D-slice (their world) into another 3D-slice of the 4D-space, then the environment will suddenly be completely different. Here it looks empty and white, just like an empty sheet of paper a 3D being might use as workspace to study a 2D-world. The 'tunnel' that we see that brings them back to their original world might be a path running along the 4th-dimension going back to their world (3D-slice).
Of course all this is purely speculation and is only my suggestion of what Léo might have used as inspiration to model the mystery sphere and its behavior.