  We present a certifiably globally optimal algorithm for determining the
extrinsic calibration between two sensors that are capable of producing
independent egomotion estimates. This problem has been previously solved using
a variety of techniques, including local optimization approaches that have no
formal global optimality guarantees. We use a quadratic objective function to
formulate calibration as a quadratically constrained quadratic program (QCQP).
By leveraging recent advances in the optimization of QCQPs, we are able to use
existing semidefinite program (SDP) solvers to obtain a certifiably global
optimum via the Lagrangian dual problem. Our problem formulation can be
globally optimized by existing general-purpose solvers in less than a second,
regardless of the number of measurements available and the noise level. This
enables a variety of robotic platforms to rapidly and robustly compute and
certify a globally optimal set of calibration parameters without a prior
estimate or operator intervention. We compare the performance of our approach
with a local solver on extensive simulations and multiple real datasets.
Finally, we present necessary observability conditions that connect our
approach to recent theoretical results and analytically support the empirical
performance of our system.
