Feature-Based SLAM: Why Simultaneous Localisation and Mapping?

In this paper; we first prove an interesting result for point feature based SLAM. "When the covariance matrices of feature observation errors are isotropic; the robot poses and feature positions obtained in each Gauss-Newton iteration (when solving a reformulated least squares optimisation based SLAM) are independent of the feature positions in the previous step". That is; even if we reset the feature positions to different random values before each iteration; the results after the iteration never change. Building on this finding; we propose an algorithm to solve the robot poses only ("localisation") and show that the algorithm generates exactly the same robot poses in each iteration as the Gauss-Newton method (SLAM). The optimal feature positions can be easily recovered using a closed-form formula after the optimal robot poses are obtained. Similarly; when the covariance matrices of odometry translation errors are also isotropic; we can prove that the SLAM results are independent of both the feature positions and the robot positions. Thus; we can have an "rotation-only algorithm" which generates the same robot rotations as the full SLAM. Again; the optimal robot positions and the optimal feature positions can be computed from the obtained optimal robot rotations using a closed-form formula. We have used multiple 2D and 3D SLAM datasets to demonstrate our research findings. The video shows the interesting convergence results can be found at https://youtu.be/j1T8toqGtDE. We expect the findings in this paper can help SLAM researchers to further understand the special structure of the SLAM problems and to further develop more efficient and reliable SLAM algorithms.