This paper presents a non-iterative pose-graph optimization algorithm for fast 2D simultaneous localization and mapping (SLAM). The graph-SLAM approach addresses the SLAM problem using a factor graph structure. For a pose-only SLAM problem, landmarks are not explicitly modeled and are not a part of the SLAM problem. Conventional pose-graph optimization methods minimize the error by an iterative local linearization process. The proposed method reformulates the pose-graph optimization problem as a combination of two linear least-squares problems. The position and angle term in a pose vector are optimized separately, and the iterative linearization process is removed. Due to an approximation in the reformulation of the pose-graph optimization problem, there is a tradeoff between the accuracy and the computational complexity. The simulation is conducted to demonstrate the efficiency of the proposed method. For comparison, the conventional manifold based pose-graph optimization algorithm is implemented. The results of simulations which optimized 1,079 poses show that the proposed method is more than 25 times faster than the conventional method. However, the localization accuracy is approximately 10% lower than the conventional method.
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