Toward Globally Optimal State Estimation Using Automatically Tightened Semidefinite Relaxations
Toward Globally Optimal State Estimation Using Automatically Tightened Semidefinite Relaxations
复制标题
使用自动紧缩半定松弛实现全局最优状态估计
DOI：
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复制
发表时间：
2023
期刊：
影响因子：
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通讯作者：
T. Barfoot
中科院分区：
文献类型：
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作者：
F. Dümbgen;Connor T. Holmes;Ben Agro;T. Barfoot
近年来，机器人学中常见优化问题的半定松弛因其具有提供全局最优解的能力而受到越来越多的关注。在许多情况下，需要特定的手工制作的冗余约束来获得紧松弛，从而获得全局最优性。这些限制依赖于配方，通常通过漫长的手动过程来确定。相反，本文提出了一种自动方法来寻找一组足够的冗余约束来获得紧密性，如果它们存在的话。我们首先提出了一个有效的可行性检查，以确定给定的变量集是否可以导致紧凑的公式。其次，我们展示了如何将该方法扩展到更大规模的问题。在该过程的任何点上，我们都不必手动查找多余的约束。我们在仿真和真实数据集上展示了该方法对于基于距离的定位和基于立体的位姿估计的有效性。最后，我们复制了最近文献中提出的半定松弛，并表明我们的自动方法总是找到比先前所考虑的更小的约束集来满足紧致性。
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted redundant constraints are required to obtain tight relaxations and thus global optimality. These constraints are formulation-dependent and typically identified through a lengthy manual process. Instead, the present paper suggests an automatic method to find a set of sufficient redundant constraints to obtain tightness, if they exist. We first propose an efficient feasibility check to determine if a given set of variables can lead to a tight formulation. Secondly, we show how to scale the method to problems of bigger size. At no point of the process do we have to find redundant constraints manually. We showcase the effectiveness of the approach, in simulation and on real datasets, for range-based localization and stereo-based pose estimation. Finally, we reproduce semidefinite relaxations presented in recent literature and show that our automatic method always finds a smaller set of constraints sufficient for tightness than previously considered.
凸集图中的最短路径
DOI：
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发表时间：
2021
期刊：
ArXivorg
影响因子：
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作者：
Tobia Marcucci, Jack Umenberger
通讯作者：
Tobia Marcucci, Jack Umenberger