Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion

TL;DR

This paper introduces a fast, certifiably globally optimal algorithm for extrinsic sensor calibration using egomotion data, leveraging QCQP and SDP techniques to guarantee optimality and robustness.

Contribution

It formulates the calibration problem as a QCQP and applies SDP relaxation to achieve certifiable global optimality with rapid computation, outperforming local methods.

Findings

Global optimality achieved in less than a second

Robust performance across noise levels and measurement counts

Validated on extensive simulations and real datasets

Abstract

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.