A Comparison of Graph Optimization Approaches for Pose Estimation in SLAM An ¯ dela Juri´ c *,1 , Filip Kendeš * , Ivan Markovi´ c * , Ivan Petrovi´ c * * University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, Croatia {andela.juric, filip.kendes, ivan.markovic, ivan.petrovic}@fer.hr INTEL MIT M3500 M3500a M3500b M3500c Sphere-a Torus Cube Garage Cubicle Rim Fig. 1: Two-dimensional (first row) and three-dimensional (second row) pose graphs used in the benchmarking process. Abstract—Simultaneous localization and mapping (SLAM) is an important tool that enables autonomous navigation of mobile robots through unknown environments. As the name SLAM suggests, it is important to obtain a correct representation of the environment and estimate a correct trajectory of the robot poses in the map. Dominant state-of-the-art approaches solve the pose estimation problem using graph optimization techniques based on the least squares minimization method. Among the most popular approaches are libraries such as g 2 o, Ceres, GTSAM and SE-Sync. The aim of this paper is to describe these approaches in a unified manner and to evaluate them on an array of publicly available synthetic and real-world pose graph datasets. In the evaluation experiments, the computation time and the value of the objective function of the four optimization libraries are analyzed. Index Terms—pose-graph, optimization, trajectory esti- mation, SLAM, g 2 o, GTSAM, Ceres, SE-Sync I. I NTRODUCTION After years of dominance in the SLAM scene, filter-based methods are more and more replaced by optimization-based approaches. Pose graph optimization (PGO) was first introduced in [1], but was not very popular due to computational inefficiency. Today, with the increase of the computational power, PGO methods have become the state-of-the-art and are able to solve SLAM optimization and estimation problems quickly and accurately. Optimization-based SLAM methods generally consist of two parts. The first part identifies the constraints 1 This work has been supported by the Croatian National Science Foundation under the grant no. DOK-2018-01-9392. between new observations and the map using correspon- dences based on sensor data. The second part computes the robot poses and the map given the constraints. It can be divided into graph and smoothing methods. An example of a current state-of-the-art optimization-based method is g 2 o [2]. It is a general optimization framework for nonlinear least squares problems. One of the first smoothing approaches, √ SAM, was presented in [3]. An improvement to this method, incremental smoothing and mapping (iSAM), was introduced in [4]. iSAM ex- tends √ SAM to provide an efficient solution to the full SLAM problem by updating the factorization of the sparse smoothing information matrix. The upgrade of iSAM, iSAM2, is presented in [5]. These smoothing methods are implemented in GTSAM [6], which is another state- of-the-art optimization library. An elegant example of a SLAM problem is the so- called pose SLAM, which avoids building an explicit map of the environment. The objective of pose SLAM is to estimate the trajectory of the robot given the loop closing and odometric constraints. These relative pose measurements are usually obtained from IMU, laser sensor, cameras or wheel odometry using ego-motion estimation, scan matching, iterative closest point (ICP) or some form of minimizing visual reprojection error. It is worth noting that methods in [7] and [8] present filter- based pose SLAM algorithms, but our focus in the current paper is on the approaches that implement optimization- based pose SLAM.