In this paper, we examine the problem of extrinsic calibration of multiple LIDARs on a mobile vehicle platform. To achieve fully automated and on-line calibration, the original non-linear calibration model is reformulated as a second-order cone program (SOCP). This provides an advantage over more standard linearized approaches in that a priori information such as a default LIDAR calibration, calibration tolerances, etc., can be readily modeled. Furthermore, in contrast to general non-linear methods, the SOCP relaxation is convex, returns a global minimum, and can be solved very quickly using modern interior point methods (IPM). This enables the calibration to be estimated on-line for multiple LIDARs simultaneously. Experimental results are provided where the approach is used to successfully calibrate a pair of Sick LMS291-S14 LIDARs mounted on a mobile vehicle platform. These showed the SOCP formulation yielded a more accurate reconstruction and was 1-2 orders of magnitude faster than the traditional non-linear least-squares approach.
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