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Autonomous navigation requires an accurate model or map of the environment.While dramatic progress in the prior two decades has enabled large-scale SLAM,the majority of existing methods rely on non-linear optimization techniques tofind the MLE of the robot trajectory and surrounding environment. These methodsare prone to local minima and are thus sensitive to initialization. Severalrecent papers have developed optimization algorithms for the Pose-Graph SLAMproblem that can certify the optimality of a computed solution. Though thisdoes not guarantee a priori that this approach generates an optimal solution, arecent extension has shown that when the noise lies within a critical thresholdthat the solution to the optimization algorithm is guaranteed to be optimal. Toaddress the limitations of existing approaches, this paper illustrates that thePose-Graph SLAM and Landmark SLAM can be formulated as polynomial optimizationprograms that are SOS convex. This paper then describes how the Pose-Graph andLandmark SLAM problems can be solved to a global minimum without initializationregardless of noise level using the Sparse-BSOS hierarchy. This paper alsoempirically illustrates that convergence happens at the second step in thishierarchy. In addition, this paper illustrates how this Sparse-BSOS hierarchycan be implemented in the complex domain and empirically shows that convergencehappens also at the second step of this complex domain hierarchy. Finally, thesuperior performance of the proposed approach when compared to existing SLAMmethods is illustrated on graphs with several hundred nodes.

Guaranteed Globally Optimal Planar Pose Graph and Landmark SLAM via Sparse-Bounded Sums-of-Squares Programming