We propose a robust framework for the planar pose graph optimization contaminated by loop closure outliers. Our framework rejects outliers by first decoupling the robust PGO problem wrapped by a Truncated Least Squares kernel into two subproblems. Then, the framework introduces a linear angle representation to rewrite the first subproblem that is originally formulated with rotation matrices. The framework is configured with the Graduated Non-Convexity (GNC) algorithm to solve the two non-convex subproblems in succession without initial guesses. Thanks to the linearity properties of both the subproblems, our framework requires only linear solvers to optimally solve the optimization problems encountered in GNC. We extensively validate the proposed framework, named DEGNC-LAF (DEcoupled Graduated Non-Convexity with Linear Angle Formulation) in planar PGO benchmarks. It turns out that it runs significantly (sometimes up to over 30 times) faster than the standard and general-purpose GNC while resulting in high-quality estimates.

翻译：我们提出了一种鲁棒框架，用于处理受闭环外点污染的平面位姿图优化问题。该框架首先将基于截断最小二乘核包裹的鲁棒PGO问题解耦为两个子问题，从而剔除外点。随后，框架引入线性角度表示，将原本基于旋转矩阵表述的第一个子问题进行重写。框架采用渐进非凸性（GNC）算法，无需初始猜测即可依次求解这两个非凸子问题。得益于子问题的线性特性，我们的框架仅需线性求解器即可最优求解GNC过程中遇到的优化问题。我们在平面PGO基准测试中全面验证了所提出的方法（命名为DEGNC-LAF，即解耦渐进非凸性与线性角度公式）。结果表明，该方法运行速度显著（有时超过30倍）快于标准通用GNC，同时获得高质量估计结果。