Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion
This enables robotic platforms to compute and certify globally optimal calibration parameters rapidly and robustly without prior estimates or operator intervention, addressing a specific need in robotics.
The authors tackled the problem of extrinsic calibration between sensors using per-sensor egomotion estimates, developing a certifiably globally optimal algorithm that solves it as a quadratically constrained quadratic program (QCQP) and achieves global optimization in less than a second with existing solvers.
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.