  Pose graph optimization is a special case of the simultaneous localization
and mapping problem where the only variables to be estimated are pose variables
and the only measurements are inter-pose constraints. The vast majority of pose
graph optimization techniques are vertex based (variables are robot poses), but
recent work has parameterized the pose graph optimization problem in a relative
fashion (variables are the transformations between poses) that utilizes a
minimum cycle basis to maximize the sparsity of the problem. We explore the
construction of a cycle basis in an incremental manner while maximizing the
sparsity. We validate an algorithm that constructs a sparse cycle basis
incrementally and compare its performance with a minimum cycle basis.
Additionally, we present an algorithm to approximate the minimum cycle basis of
two graphs that are sparsely connected as is common in multi-agent scenarios.
Lastly, the relative parameterization of pose graph optimization has been
limited to using rigid body transforms on SE(2) or SE(3) as the constraints
between poses. We introduce a methodology to allow for the use of
lower-degree-of-freedom measurements in the relative pose graph optimization
problem. We provide extensive validation of our algorithms on standard
benchmarks, simulated datasets, and custom hardware.
