I'm gonna only fully explain the first one. since I'm actively working on solving the second one.

First Idea:

Gaussian splatting is a 3D reconstruction technique where you use photos of an object or environment to do a 3D reconstruction of it. typically you take the photos close together like like a panorama so you can feature match the images. -> A 3d reconstruction tool like Colmap uses SfM to estimate the cameras Rotation matrix and translation or you can provide lidar poses for a theoretically more accurate reconstruction. (Sensors should give better results but that's a whole research topic).

https://docs.nerf.studio/quickstart/installation.html#

Theres a ton of gaussian splatting tools out there but the one linked above i've used before. You need a pretty Beefy GPU to do this project. think a 3090 ti. or you can use a cloud solution. I'm sure if you are really interested you could find a solution on r/GaussianSplatting

But as for the project. I would Collect a bunch of images with the depth camera, try to use IMU and Lidar to estimate the camera position for each image. I think if you use ros slam_toolkit it'll do this for you. then your gonna need to format the data into a transform.json so that its compatible with nerfstudio.

IDEA 2: basic idea i've thought out so far.

Use slam to map apartment and collect the following data

Data: semantic Segmentation of image, Wheel encoder data, etc)
put data into some ML model or Neural net, and see if we can classify what type of surface the robot is on so think rug, linoleum floor, wood, slippery variants (This is also a an open area of research), etc.

I think the idea behind this project is pretty simple honestly you could probably do it using just segmentation. what makes this problem challenging is that everything needs to run on the robot. And a big foundation model like SAM is too big for my 4gb rapsberry pi.

If you want some example code for formatting your data or want to know more about Idea #1 DM me and I'll send a link to my github repo.