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What is the best way to model the SLAM problem (offline) for a wheeled robot moving on a flat floor in 3D space (the pose has only 3 degrees of freedom)?

In terms of sensor data, we have the wheel odometry and 3D measurements of landmarks (coming from a Kinect v2).

The bit that I'm confused about is that this is a very standard setting, yet all the examples I've seen for 2D SLAM use 2D features and don't mention anything about what to do with 3D sensor measurements, and vice-versa, I haven't seen a 3D SLAM solution where we could easily incorporate known constraints on the robot pose (has to lie on a plane). It would be great to know what is common practice in this setting. An explanation or a link to an example implemented in some SLAM framework would be of much help.

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Since you are using Kinect my advise is to use Octomap ROS package to build a 3D map. You can extract the 2D occupancy grid map of the ground floor from the Octomap for path planning and navigation.

One disadvantage of using Octomap is, it doesn't have a pose correction method. It just build the map based on the poses provided by the odometry.

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