发表机构
University of Toronto Robotics Institute; University of Toronto（多伦多大学机器人研究所; 多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出中央路径验证器（CP-Cert），针对机器人学中SDP松弛退化问题优化可验证方法，将其应用于位姿配准与点云关联，速度比现有方法快三个数量级，构建了异常值鲁棒的位姿估计流水线并验证于真实数据。
AI 中文摘要
可验证方法已成为使用凸半定规划（SDP）松弛保证非凸问题解全局最优性的手段。这些方法中性能最优者采用局部求解器获取候选解，再通过高效线性代数技术验证其最优性。然而，对于机器人学中许多受关注的问题，这种“先局部求解再验证”的方法会因松弛的一种退化形式而受阻，仅剩下对松弛进行高成本优化这一途径。本文提出中央路径验证器（CP-Cert），这是一种专门为验证表现出该退化形式问题的候选最优解而定制的可验证方法。以一个候选解为起点，该方法寻找可行空间中一个邻近区域——即中央路径，在此处可轻易获得有效验证。该方法通过利用间接线性代数技术、问题稀疏性和并行性保持高效性。我们将CP-Cert应用于矩阵加权位姿配准和点云数据关联，其新颖的SDP松弛本身具有研究价值。在模拟示例中，我们探究了这种新颖松弛的特性，并表明CP-Cert快速且可扩展，运行时间比最先进的直接求解器快三个数量级。最后，我们将这些贡献整合为一条可验证、异常值鲁棒的位姿估计流水线，并将其应用于真实世界数据。
英文摘要
Certifiable methods have arisen as a means to guarantee global optimality of solutions to non-convex problems using convex semidefinite programming (SDP) relaxations. The most performant of these methods use a local solver to obtain the candidate solution, and then certify its optimality using efficient linear algebra techniques. However, for many problems of interest in robotics, this local-solve-then-certify approach is impeded by a form of degeneracy in the relaxation, leaving a costly optimization of the relaxation as the only recourse. In this paper, we introduce our Central-Path Certifier (CP-Cert), a certifiable method explicitly tailored to certify candidate optima to problems that exhibit this form of degeneracy. Using a candidate as a starting point, our approach seeks a nearby region of the feasible space -- known as the central path -- where a valid certificate can be readily obtained. The approach is kept efficient by exploiting indirect linear algebra techniques, problem sparsity, and parallelism. We apply CP-Cert to both matrix-weighted pose registration and pointcloud data association, whose novel SDP relaxation is of independent interest. On simulated examples, we explore the properties of this novel relaxation and show that CP-Cert is fast and scalable, achieving runtimes that are up to three orders of magnitude faster than state-of-the-art direct solvers. Finally, we combine these contributions into a certifiable, outlier-robust pose-estimation pipeline, which we apply to real-world data.
