A Survey of Optimization Problems Underlying Graph-based Simultaneous Localization and Mapping

In robotics, the problem of Simultaneous Localization and Mapping (SLAM) asks if a mobile robot that is placed at a unknown location in a unknown environment, by making relative observations of the environment, can build a map of the environment and at the same time determine its location within the map. Two decades of active research on the structure of this problem leads to three basic paradigms from which a vast majority of existing solutions are derived: EKF-based, particle filter based, and graph-based methods. Among these, the graphbased methods have recently received tremendous attention from the SLAM community due to the unique advantages they offer over traditional methods, such as computational simplicity and intuitive interpretation. In this report, we will explore the optimization problems underlying graph-based SLAM algorithms, which represent the posterior of the full SLAM problem as a sparse graph of soft constraints, and optimizing the sum of these constraints yields the maximum likelihood map and a corresponding set of robot poses. After formulating the SLAM problem as a least squares optimization problem, we will examine the various nonlinear sparse optimization techniques, such as gradient descent, conjugate descent and Levenberg-Marquardt algorithms in the context of SLAM.