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 PGO
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