# 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…

## Figures and Tables from this paper

## 12 Citations

Sparse Bounded Degree Sum of Squares Optimization for Certifiably Globally Optimal Rotation Averaging

- Computer ScienceArXiv
- 2019

This paper casts rotation averaging as a polynomial optimization problem over unit quaternions to produce the first rotation averaging method that is formally guaranteed to provide a certifiably globally optimal solution for any problem instance.

Globally Optimal Multi-Scale Monocular Hand-Eye Calibration Using Dual Quaternions

- Computer Science2021 International Conference on 3D Vision (3DV)
- 2021

This work derives a quadratically constrained quadratic program that allows a combined estimation of all extrinsic calibration parameters for monocular hand-eye calibration from per-sensor ego-motion based on dual quaternions.

A Novel Robust Approach for Correspondence-Free Extrinsic Calibration

- Computer Science2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- 2019

This paper proposes a more stable correspondence-free method with two improvements that can relax the restrictions on inputs and improve the calibration accuracy, and finds consistent sets from raw inputs using screw invariants, which significantly improve the robustness in case of outliers and data loss.

On the Tightness of Semidefinite Relaxations for Rotation Estimation

- Computer ScienceJ. Math. Imaging Vis.
- 2022

A general framework based on tools from algebraic geometry is introduced for analyzing the power of semidefinite relaxations of problems with quadratic objective functions and rotational constraints and shows that some problem classes are always tight given an appropriate parametrization.

Certifiable Outlier-Robust Geometric Perception: Exact Semidefinite Relaxations and Scalable Global Optimization

- Computer ScienceArXiv
- 2021

This work proposes the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers and proposes a sparse semidefinite programming (SDP) relaxation that is much smaller than the standard Lasserre’s hierarchy while preserving exactness.

Advances in Inference and Representation for Simultaneous Localization and Mapping

- Computer ScienceAnnual Review of Control, Robotics, and Autonomous Systems
- 2021

This article reviews recent progress in SLAM, focusing on advances in the expressive capacity of the environmental models used inSLAM systems (representation) and the performance of the algorithms used to estimate these models from data (inference).

Online multi-sensor calibration based on moving object tracking

- Computer ScienceAdv. Robotics
- 2021

The motivation comes from the practical perspective that many perception sensors of an autonomous system are part of the pipeline for detection and tracking of moving objects, and by using information already present in the system, the method provides resource inexpensive solution for the long-term reliability of the system.

Online Extrinsic Calibration Based on Per-Sensor Ego-Motion Using Dual Quaternions

- Computer ScienceIEEE Robotics and Automation Letters
- 2021

This work proposes an approach for extrinsic sensor calibration from per-sensor ego-motion estimates based on dual quaternions, enabling two different online capable solving approaches that are certifiable globally optimal and a fast local approach along with a method to verify the globality of the local approach.

Certifiably Optimal Monocular Hand-Eye Calibration

- Computer Science2020 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)
- 2020

It is proved that the technique is able to provide a certifiably globally optimal solution to both the known- and unknown-scale variants of hand-eye calibration, provided that the measurement noise is bounded.

Certifiably Optimal Mutual Localization with Anonymous Bearing Measurements

- Computer ScienceArXiv
- 2022

This paper presents a certifiably optimal algorithm that uses only anonymous bearing measurements to formulate a novel mixed-integer quadratically constrained quadratic problem (MIQCQP), relax the original nonconvex problem into a semidefinite programming (SDP) problem and obtain a cert ifiably global optimum using with off-the-shelf solvers.

## 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.