Pose Graph 3D

----------------

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.

Running

-----------

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` expects the first argument to be the path to the

problem definition. To run the executable,

```

/path/to/bin/pose_graph_3d /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

```