SLAM possibilities,where does it end ?

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Depending on what you do it might even be enough to localize and navigate, this can be done to some degree from a floorplan map and scanmatching (LIDAR) in AMCL. Nice Video and Software link for creating pgm and yaml map from "pictures"/plans. Slam might not be needed in your case.

https://www.youtube.com/watch?v=ySlU5CIXUKE

Regarding the stair problem. To be safe you need additional sensors because light based sensors have problems with reflective surfaces and transparency. Depending on the floor they might get problems. But if that isnt the issus. RTABMAP (from depth image) has nice features, like obstacle-map, clear-space-map etc. Doesnt have testet negative height obstacles yet, but for sure that should be possible. RTABMAP also provides visual odometry and SLAM. Needs some computation power though.

I would agree with what @stevemacenski states. Start with an RPlidar or similar an get gmapping to work. This should be fairly easy as this has been done countless times before.

Typically the stairs/hole problem is solved differently and depends on your robot (is it holonomic, i.e. can it generate a velocity in any direction or is it differential drive?). You can decide to put a second lidar on the robot on an angle and manually detect any sudden terrain changes, or similarly using a depth sensor to do the same.

These things you learn by experience. I would recommend you to go ahead and get started as opposed to spending countless hours researching what to do. A lot of problems will become clear just by trying something. Happy tinkering!

So, i may be late in answering, but can you add to what you said?

able to do SLAM without falling down the stairs

do you want to skip the stairs and move around or detect the stairs and go up/down? if its the detection and moving away scenario, you can do something like this.

1. feed the point cloud from camera to octomap server
2. evaluate the octomap's ground layer or a layer below that. you can use a leaf iterator and check nodes with z coordinate 0 or -1 for occupancy.
3. if you find any unoccupied cells, then that means there is a hole in the ground. probably stairs :D
4. finally, you can generate a cost map layer with that details or add it directly to the cost map you are using. add the detected region as a obstacle and the robot will navigate around it.

hope this is helpful.

if you can get your hands on a Kinect, then its IR depth camera would enable you to capture indoors easily, without any light issues. outdoors might cause issues due to sun. computational requirements are not that high for a static environment i would say. Ran Octomap server on a RPi perfectly (but cannot use rviz on RPi of course).