How does Hector_mapping and Gmapping do if the robot is on the slope?

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Actually, I don't see the problem, yet. There are transforms for the robot base relative to its horizontally oriented projection over ground and to the map, transforms for the laser relative to the robot base etc. Shouldn't hector_mapping be able to make use of these transforms?

Yes, if the robot is setup like that. However, if you drive up a slope and the environment completely changes at a certain height it becomes problematic.

Thank you very much for answering,dornhege. I set in the launch file. I plan to set odom_frame equals to base_footprint ,and base_footprint equals to base_stablized,and use the hector_imu_attitude_to_tf to add the transform from base_stablized to base_link.

are there any problems with the tf setting?And would you please give me some advice about how to calculate the height between base_footprint and base_stablized ?

Why are you going to calculate the height between base_footprint and base_stabilized? Isn't that something that a sensor of some kind should measure?

I think that depends on the definition of what base_footprint should be. Is that at zero height relative to the robot or at zero height in the world. SLAM with 6-dof pose estimation would probably include the height offset in the map->odom transform.