  Navigation in complex 3D scenarios requires appropriate environment
representation for efficient scene understanding and trajectory generation. We
propose a highly efficient and extensible global navigation framework based on
a tomographic understanding of the environment to navigate ground robots in
multi-layer structures. Our approach generates tomogram slices using the point
cloud map to encode the geometric structure as ground and ceiling elevations.
Then it evaluates the scene traversability considering the robot's motion
capabilities. Both the tomogram construction and the scene evaluation are
accelerated through parallel computation. Our approach further alleviates the
trajectory generation complexity compared with planning in 3D spaces directly.
It generates 3D trajectories by searching through multiple tomogram slices and
separately adjusts the robot height to avoid overhangs. We evaluate our
framework in various simulation scenarios and further test it in the real world
on a quadrupedal robot. Our approach reduces the scene evaluation time by 3
orders of magnitude and improves the path planning speed by 3 times compared
with existing approaches, demonstrating highly efficient global navigation in
various complex 3D environments. The code is available at:
https://github.com/byangw/PCT_planner.
