We propose a novel approach to Graduated Non-Convexity (GNC) and demonstrate its efficacy through its application in robust pose graph optimization, a key component in SLAM backends. Traditional GNC methods often rely on heuristic methods for GNC schedule, updating control parameter {\mu} for escalating the non-convexity. In contrast, our approach leverages the properties of convex functions and convex optimization to identify the boundary points beyond which convexity is no longer guaranteed, thereby eliminating redundant optimization steps in existing methodologies and enhancing both speed and robustness. We show that our method outperforms the state-of-the-art method in terms of speed and accuracy when used for robust back-end pose graph optimization via GNC. Our work builds upon and enhances the open-source riSAM framework. Our implementation can be accessed from: https://github.com/SNU-DLLAB/EGNC-PGO

翻译：我们提出了一种新颖的渐进非凸优化（GNC）方法，并通过其在鲁棒位姿图优化（SLAM后端的关键组成部分）中的应用证明了其有效性。传统GNC方法通常依赖启发式策略来调整控制参数μ以逐步提升非凸性。相比之下，我们的方法利用凸函数与凸优化的性质，识别出凸性不再保证的边界点，从而消除现有方法中的冗余优化步骤，同时提升速度与鲁棒性。实验表明，在基于GNC的鲁棒后端位姿图优化任务中，我们的方法在速度和精度上均优于当前最先进方法。本研究基于并改进开源riSAM框架。代码开源地址：https://github.com/SNU-DLLAB/EGNC-PGO