How to use 2D LiDAR with a constant near object?

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You can filter out the points which are the robot itself. In your case you can define the minimum and maximum azimuth angle that the LIDAR can see and remove anything outside of that range. You can use the existing Angle Bounds laser filter for this.

I'm not sure but it's possible that they were doing something similar in the hetor_slam demo you showed. They were using a Hokuyo LIDAR with a 270 degree FOV so most of the use was probably obscured anyway.

Hope this helps.