Interpolate values in 2D space + time (3D interpolation) of multiple objects in concert

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With a given dataset, I have multiple objects that move, in concert, inside a 2D eucledian space. The dataset of one object is given like this:

frame x   y
0     10  22
1     NaN  NaN
2     26  14
...
8999  54  45
9000  59  43

To keep the system fluidity, I want to interpolate all objects in concert with each other. This is necessary, because the objects are body parts, and it wouldn't make any sense if the left ear was placed on the same coordinate as the tail at the identical frame/time.

Any ideas on a solution?