The Simultaneous Localization and Mapping (SLAM) problem consists of building a map of an unknown environment while simultaneously localizing against this map. The main difficulty of this problem stems from not having any additional external aiding information such as GPS. SLAM has been considered one of the fundamental challenges of robotics. A pose graph optimization problem is one example of a SLAM problem.
The example also illustrates how to use Eigen‘s geometry module with Ceres’ automatic differentiation functionality. To represent the orientation, we will use Eigen‘s quaternion which uses the Hamiltonian convention but has different element ordering as compared with Ceres’s rotation representation. Specifically they differ by whether the scalar component q_w is first or last; the element order for Ceres‘s quaternion is [q_w, q_x, q_y, q_z] where as Eigen’s quaternion is [q_x, q_y, q_z, q_w].
This package defines the necessary Ceres cost functions needed to model the 3-dimensional pose graph optimization problem as well as a binary to build and solve the problem. The cost functions are shown for instruction purposes and can be speed up by using analytical derivatives which take longer to implement.
This package includes an executable pose_graph_3d that will read a problem definition file. This executable can work with any 3D problem definition that uses the g2o format with quaternions used for the orientation representation. It would be relatively straightforward to implement a new reader for a different format such as TORO or others. pose_graph_3d will print the Ceres solver full summary and then output to disk the original and optimized poses (poses_original.txt and poses_optimized.txt, respectively) of the robot in the following format:
pose_id x y z q_x q_y q_z q_w pose_id x y z q_x q_y q_z q_w pose_id x y z q_x q_y q_z q_w ...
where pose_id is the corresponding integer ID from the file definition. Note, the file will be sorted in ascending order for the pose_id.
The executable pose_graph_3d has one flag --input which is the path to the problem definition. To run the executable,
/path/to/bin/pose_graph_3d --input /path/to/dataset/dataset.g2o
A script is provided to visualize the resulting output files. There is also an option to enable equal axes using --axes_equal.
/path/to/repo/examples/slam/pose_graph_3d/plot_results.py --optimized_poses ./poses_optimized.txt --initial_poses ./poses_original.txt