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 require a lengthy manual process to find. 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 manually find redundant constraints. 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 finds a smaller set of constraints sufficient for
tightness than previously considered.Comment: 18 pages, 20 figure