Planar fiducial markers are commonly used to estimate a pose of a camera relative to the marker. This information can be combined with other sensor data to provide a global or local position estimate of the system in the environment using a state estimator such as the Kalman filter. To achieve accurate estimates, the observation noise covariance matrix must be properly configured to reflect the sensor output's characteristics. However, the observation noise of the pose obtained from planar fiducial markers varies across the measurement range and this fact needs to be taken into account during the sensor fusion to provide a reliable estimate. In this work, we present experimental measurements of the fiducial markers in real and simulation scenarios for 2D pose estimation. Based on these measurements, we propose analytical functions that approximate the variances of pose estimates. We demonstrate the effectiveness of our approach in a 2D robot localisation experiment, where we present a method for estimating covariance model parameters based on user measurements and a technique for fusing pose estimates from multiple markers.

Faculty of Mechanical Engineering Brno University of Technology Technická 2896 2 616 69 Brno Czech Republic

Independent Researcher 74 401 Frenštát pod Radhoštěm Czech Republic

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Cebollada S., Payá L., Flores M., Peidró A., Reinoso O. A state-of-the-art review on mobile robotics tasks using artificial intelligence and visual data. Expert Syst. Appl. 2021;167:114195. doi: 10.1016/j.eswa.2020.114195. DOI

Rubio F., Valero F., Llopis-Albert C. A review of mobile robots: Concepts, methods, theoretical framework, and applications. Int. J. Adv. Robot. Syst. 2019;16:1729881419839596. doi: 10.1177/1729881419839596. DOI

Niloy M.A.K., Shama A., Chakrabortty R.K., Ryan M.J., Badal F.R., Tasneem Z., Ahamed M.H., Moyeen S.I., Das S.K., Ali M.F., et al. Critical Design and Control Issues of Indoor Autonomous Mobile Robots: A Review. IEEE Access. 2021;9:35338–35370. doi: 10.1109/ACCESS.2021.3062557. DOI

Jang G., Kim S., Lee W., Kweon I. Robust self-localization of mobile robots using artificial and natural landmarks; Proceedings of the 2003 IEEE International Symposium on Computational Intelligence in Robotics and Automation. Computational Intelligence in Robotics and Automation for the New Millennium (Cat. No.03EX694); Kobe, Japan. 16–20 July 2003; pp. 412–417. DOI

Popescu D.C., Cernaianu M.O., Ghenuche P., Dumitrache I. An assessment on the accuracy of high precision 3D positioning using planar fiducial markers; Proceedings of the 2017 21st International Conference on System Theory, Control and Computing; Sinaia, Romania. 19–21 October 2017; pp. 471–476. DOI

Deasy T.P., Scanlon W.G. Stepwise Algorithms for Improving the Accuracy of Both Deterministic and Probabilistic Methods in WLAN-based Indoor User Localisation. Int. J. Wirel. Inf. Netw. 2004;11:207–216. doi: 10.1007/s10776-004-1234-1. DOI

Ledergerber A., Hamer M., D’Andrea R. A robot self-localization system using one-way ultra-wideband communication; Proceedings of the 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems; Hamburg, Germany. 28 September–2 October 2015; pp. 3131–3137.

Krejsa J., Věchet S., Hrbácek J., Ripel T., Ondroušek V., Hrbácek R., Schreiber P. Presentation Robot Advee. Eng. Mech. 2011;18:307–322.

Babinec A., Jurišica L., Hubinský P., Duchoň F. Visual Localization of Mobile Robot Using Artificial Markers. Procedia Eng. 2014;96:1–9. doi: 10.1016/j.proeng.2014.12.091. DOI

Bertoni M., Michieletto S., Oboe R., Michieletto G. Indoor Visual-Based Localization System for Multi-Rotor UAVs. Sensors. 2022;22:5798. doi: 10.3390/s22155798. PubMed DOI PMC

Kayhani N., Heins A., Zhao W., Nahangi M., McCabe B., Schoellig A. Improved Tag-based Indoor Localization of UAVs Using Extended Kalman Filter; Proceedings of the ISARC. International Symposium on Automation and Robotics in Construction; Banff, AB, Canada. 21–24 May 2019; pp. 624–631. DOI

Fiala M. Designing Highly Reliable Fiducial Markers. IEEE Trans. Pattern Anal. Mach. Intell. 2010;32:1317–1324. doi: 10.1109/TPAMI.2009.146. PubMed DOI

Abbas S.M., Aslam S., Berns K., Muhammad A. Analysis and Improvements in AprilTag Based State Estimation. Sensors. 2019;19:5480. doi: 10.3390/s19245480. PubMed DOI PMC

Tanaka H., Sumi Y., Matsumoto Y. A solution to pose ambiguity of visual markers using Moiré patterns; Proceedings of the 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems; Chicago, IL, USA. 14–18 September 2014; pp. 3129–3134. DOI

Ch’ng S.F., Sogi N., Purkait P., Chin T.J., Fukui K. Resolving Marker Pose Ambiguity by Robust Rotation Averaging with Clique Constraints; Proceedings of the 2020 IEEE International Conference on Robotics and Automation; Paris, France. 31 May–31 August 2020.

Kalaitzakis M., Carroll S., Ambrosi A., Whitehead C., Vitzilaios N. Experimental Comparison of Fiducial Markers for Pose Estimation; Proceedings of the 2020 International Conference on Unmanned Aircraft Systems (ICUAS); Athens, Greece. 1–4 September 2020; pp. 781–789. DOI

Szentandrási I., Zachariáš M., Havel J., Herout A., Dubská M., Kajan R. Uniform Marker Fields: Camera localization by orientable De Bruijn tori; Proceedings of the 2012 IEEE International Symposium on Mixed and Augmented Reality (ISMAR); Atlanta, GA, USA. 5–8 November 2012; pp. 319–320. DOI

Neunert M., Bloesch M., Buchli J. An open source, fiducial based, visual-inertial motion capture system; Proceedings of the 2016 19th International Conference on Information Fusion (FUSION); Heidelberg, Germany. 5–8 July 2016; pp. 1523–1530.

Kalman R.E. A New Approach to Linear Filtering and Prediction Problems. Trans. ASME J. Basic Eng. 1960;82:35–45. doi: 10.1115/1.3662552. DOI

Mcgee L.A., Schmidt S.F. Discovery of the Kalman Filter as a Practical Tool for Aerospace and Industry. National Aeronautics and Space Administration; Pasadena, CA, USA: 1985.

Brablc M. Hybrid Method for Modelling and State Estimation of Dynamic Systems. Brno University of Technology; Brno, Czech Republic: 2023.

Tung C.P., Kak A. Integrating sensing, task planning, and execution for robotic assembly. IEEE Trans. Robot. Autom. 1996;12:187–201. doi: 10.1109/70.488940. DOI

Rekimoto J. Matrix: A realtime object identification and registration method for augmented reality; Proceedings of the 3rd Asia Pacific Computer Human Interaction (Cat. No.98EX110); Shonan Village Center, Japan. 17 July 1998; pp. 63–68. DOI

Stricker D., Klinker G., Reiners D. A fast and robust line-based optical tracker for augmented reality applications; Proceedings of the International Workshop on Augmented Reality (IWAR’98); San Francisco, CA, USA. 1 November 1998.

Kato H., Billinghurst M. Marker tracking and HMD calibration for a video-based augmented reality conferencing system; Proceedings of the Proceedings 2nd IEEE and ACM International Workshop on Augmented Reality (IWAR’99); San Francisco, CA, USA. 20–21 October 1999; pp. 85–94. DOI

Fiala M. ARTag, a fiducial marker system using digital techniques; Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition; San Diego, CA, USA. 20–25 June 2005; pp. 590–596. DOI

Olson E. AprilTag: A robust and flexible visual fiducial system; Proceedings of the 2011 IEEE International Conference on Robotics and Automation; Shanghai, China. 9–13 May 2011; pp. 3400–3407. DOI

Benligiray B., Topal C., Akinlar C. STag: A Stable Fiducial Marker System. Image Vis. Comput. 2017;89:158–169. doi: 10.1016/j.imavis.2019.06.007. DOI

Vávra P. Master’s Thesis. University of Technology in Brno; Brno, Czech Republic: 2019. Využití Nástroje ROS pro Řízení Autonomního Mobilního Robotu.

López-Cerón A., Cañas J.M. Accuracy analysis of marker-based 3D visual localization; Proceedings of the XXXVII Jornadas de Automática Jornadas de Automática 2016; Madrid, Spain. 7–9 September 2022.

Abawi D., Bienwald J., Dorner R. Accuracy in optical tracking with fiducial markers: An accuracy function for ARToolKit; Proceedings of the Third IEEE and ACM International Symposium on Mixed and Augmented Reality; Arlington, VA, USA. 5 November 2004; pp. 260–261. DOI

Pentenrieder K., Meier P., Klinker G. Analysis of Tracking Accuracy for Single-Camera Square-Marker-Based Tracking; Proceedings of the Dritter Workshop Virtuelle und Erweiterte Realitt der GIFachgruppe VR/AR; Koblenz, Germany. 25–26 September 2006.

Tanaka H., Sumi Y., Matsumoto Y. Avisual marker for precise pose estimation based on lenticular lenses; Proceedings of the 2012 IEEE International Conference on Robotics and Automation; Saint Paul, MN, USA. 14–18 May 2012; pp. 5222–5227. DOI

Uchiyama H., Saito H. Random dot markers; Proceedings of the 2011 IEEE Virtual Reality Conference; Singapore. 19–23 March 2011; pp. 35–38. DOI

Mateos L.A. AprilTags 3D: Dynamic Fiducial Markers for Robust Pose Estimation in Highly Reflective Environments and Indirect Communication in Swarm Robotics. arXiv. 2020 doi: 10.48550/ARXIV.2001.08622.2001.08622 DOI

Zheng J., Bi S., Cao B., Yang D. Visual Localization of Inspection Robot Using Extended Kalman Filter and Aruco Markers; Proceedings of the 2018 IEEE International Conference on Robotics and Biomimetics; Kuala Lumpur, Malaysia. 12–15 December 2018; pp. 742–747. DOI

Chavez A.G., Mueller C.A., Doernbach T., Birk A. Underwater navigation using visual markers in the context of intervention missions. Int. J. Adv. Robot. Syst. 2019;16:1729881419838967. doi: 10.1177/1729881419838967. DOI

Bradski G. The OpenCV Library. Dobb’s J. Softw. Tools. 2000;25:120–123.

Koenig N., Howard A. Design and use paradigms for Gazebo, an open-source multi-robot simulator; Proceedings of the 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566); Sendai, Japan. 28 September–2 October 2004; pp. 2149–2154. DOI

Blanco-Claraco J.L. A tutorial on SE(3) transformation parameterizations and on-manifold optimization. arXiv. 20212103.15980

Petersen K.B., Pedersen M.S. The Matrix Cookbook. Tech. Univ. Den. 2012;7:510.

Quigley M., Conley K., Gerkey B., Faust J., Foote T., Leibs J., Wheeler R., Ng A. ROS: An open-source Robot Operating System; Proceedings of the ICRA Workshop on Open Source Software; Kobe, Japan. 12–17 May 2009;

Madgwick S.O.H., Harrison A.J.L., Vaidyanathan R. Estimation of IMU and MARG orientation using a gradient descent algorithm; Proceedings of the 2011 IEEE International Conference on Rehabilitation Robotics; Zurich, Switzerland. 29 June–1 July 2011; pp. 1–7. PubMed DOI

Meeussen W. REP 105—Coordinate Frames for Mobile Platforms (ROS.org) 2010. [(accessed on 7 February 2023)]. Available online: https://www.ros.org/reps/rep-0105.html.

Moore T., Stouch D. A Generalized Extended Kalman Filter Implementation for the Robot Operating System; Proceedings of the 13th International Conference on Intelligent Autonomous Systems (IAS-13); Padova, Italy. 15–18 July 2014.