Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion
@article{Giamou2019CertifiablyGO, title={Certifiably Globally Optimal Extrinsic Calibration From Per-Sensor Egomotion}, author={Matthew Giamou and Ziye Ma and Valentin Peretroukhin and Jonathan Kelly}, journal={IEEE Robotics and Automation Letters}, year={2019}, volume={4}, pages={367-374} }
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…
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References
SHOWING 1-10 OF 42 REFERENCES
Extrinsic Calibration from Per-Sensor Egomotion
- Computer ScienceRobotics: Science and Systems
- 2012
The algorithm takes noisy, per-sensor incremental egomotion observations as input and produces as output an estimate of the maximum-likelihood 6-DOF calibration relating the sensors and accompanying uncertainty, producing an analysis of motion degeneracy and a singularity-free optimization procedure.
Extrinsic Calibration from Per-Sensor Egomotion
- Computer Science
- 2013
The algorithm takes noisy, per-sensor incremental egomotion observations as input and produces as output an estimate of the maximum-likelihood 6-DOF calibration relating the sensors and accompanying uncertainty, producing an analysis of motion degeneracy and a singularity-free optimization procedure.
World-Base Calibration by Global Polynomial Optimization
- Computer Science2014 2nd International Conference on 3D Vision
- 2014
This paper presents a novel solution to the world-base calibration problem that is applicable in situations where a known calibration target is observed by a camera attached to the end effector of a robotic manipulator and effectively solved using Semi definite Programming.
SE-Sync: A certifiably correct algorithm for synchronization over the special Euclidean group
- Computer Science, MathematicsInt. J. Robotics Res.
- 2019
SE-Sync is able to efficiently recover certifiably globally optimal solutions of the special Euclidean synchronization problem in a non-adversarial noise regime and is significantly faster than the Gauss–Newton-based approach that forms the basis of current state-of-the-art techniques.
Lagrangian duality in 3D SLAM: Verification techniques and optimal solutions
- Computer Science2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- 2015
It is shown that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality, when the duality gap is zero, and one can compute a guaranteed optimalSLAM solution from theDual problem, circumventing non-convex optimization.
A Certifiably Globally Optimal Solution to the Non-minimal Relative Pose Problem
- Mathematics, Computer Science2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition
- 2018
This paper forms a Quadratically Constrained Quadratic Program (QCQP), which can be converted into a Semidefinite Program (SDP) using Shor's convex relaxation, and proves through exhaustive validation on both simulated and real experiments that this approach always finds and certifies the global optimum of the cost function.
Automatic Calibration of Multiple Coplanar Sensors
- Computer ScienceRobotics: Science and Systems
- 2011
It is shown that incremental pose measurements alone are sufficient to recover sensor calibration through nonlinear least squares estimation and use the Fisher Information Matrix to compute a Cramer-Rao lower bound (CRLB) for the resulting calibration.
A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group
- Computer Science, MathematicsWAFR
- 2016
SE-Sync is capable of recovering globally optimal solutions when the available measurements are corrupted by noise up to an order of magnitude greater than that typically encountered in robotics applications, and does so at a computational cost that scales comparably with that of direct Newton-type local search techniques.
Hand-eye and robot-world calibration by global polynomial optimization
- Computer Science2014 IEEE International Conference on Robotics and Automation (ICRA)
- 2014
This paper shows that the method of convex linear matrix inequality (LMI) relaxations can be used to effectively solve these problems and to obtain globally optimal solutions to hand-eye calibration problems.
Extrinsic calibration of a 2d laser-rangefinder and a camera based on scene corners
- Computer Science2015 IEEE International Conference on Robotics and Automation (ICRA)
- 2015
A new approach to extrinsic calibration of 2D laser-rangefinders and cameras which relies on the observations of orthogonal trihedrons which are profusely found as corners in human-made scenarios, which turns the calibration process fast and simpler to perform.