Toward Globally Optimal State Estimation Using Automatically Tightened Semidefinite Relaxations
arxiv(2023)
摘要
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.
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