| Abstract: | We consider the problem of distributed pose graph optimization (PGO) that has important applications in multirobot simultaneous localization and mapping (SLAM). We propose the majorization minimization (MM) method for distributed PGO ( MM--PGO ) that applies to a broad class of robust loss kernels. The MM--PGO method is guaranteed to converge to first-order critical points under mild conditions. Furthermore, noting that the MM--PGO method is reminiscent of proximal methods, we leverage Nesterov's method and adopt adaptive restarts to accelerate convergence. The resulting accelerated MM methods for distributed PGO—both with a master node in the network ( AMM--PGO∗ ) and without ( AMM--PGO# )—have faster convergence in contrast to the MM--PGO method without sacrificing theoretical guarantees. In particular, the AMM--PGO# method, which needs no master node and is fully decentralized, features a novel adaptive restart scheme and has a rate of convergence comparable to that of the AMM--PGO∗ method using a master node to aggregate information from all the nodes. The efficacy of this work is validated through extensive applications to 2-D and 3-D SLAM benchmark datasets and comprehensive comparisons against existing state-of-the-art methods, indicating that our MM methods converge faster and result in better solutions to distributed PGO. |
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