The effect of motion formation on cooperative navigation
Abstract
The effect of formation movement on the performance of cooperative navigation is investigated in this paper. First, the inertial navigation system of each agent with a certain accuracy is modeled and simulated. Initial results showed that the navigation error of each agent increased individually over time, and this problem is more severe for agents equipped with a weaker system. Cooperative navigation is implemented for the agents to resolve this problem. It is shown that the total navigation errors are improved by observing and participating the relative distance between the agents. Various simulations and experimental tests using two real agents supported this assertation. The performance of cooperative navigation can be improved further through appropriate formation. Proper formations are investigated and evaluated through simulations. The collective covariance matrix is employed to form an objective function using an extended Kalman filter (EKF). This function has been minimized using Newton’s method, which could be the solution for the formation. The simulation results show that better accuracy can be achieved by applying the optimal formation trajectory.
Keyword : navigation, cooperative navigation, extended Kalman Filter, EKF, CNS, formation
How to Cite
Saberi Tavakkoli, M., Kahe, G., & Sadeghikia, F. (2022). The effect of motion formation on cooperative navigation. Aviation, 26(4), 224–234. https://doi.org/10.3846/aviation.2022.17552
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Causa, F., Vetrella, A. R., Fasano, G., & Accardo, D. (2018, 23–26 April). Multi-UAV formation geometries for cooperative navigation in GNSS-challenging Environments. In ION Position, Location and Navigation Symposium (PLANS). Monterey, CA, USA. IEEE. https://doi.org/10.1109/PLANS.2018.8373453
Chen, J., Wang, X., Shao, X., & Duan, D. (2010, 8–10 June). An integrated Relative Navigation system using GPS/VISNAV for ultra-close spacecraft formation flying. In 3rd International Symposium on Systems and Control in Aeronautics and Astronautics. The Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISSCAA.2010.5633067
Chen, M., Xiong, Z., Liu, J., Wang, R., & Xiong, J. (2020, June 22). Cooperative navigation of unmanned aerial vehicle swarm based on cooperative dilution of precision. International Journal of Advanced Robotic Systems, 17(3). https://doi.org/10.1177/1729881420932717
Cledat, E., & Cucci, D. A. (2017, 4–7 September). Mapping GNSS restricted environments with a drone tandem and indirect position control. In ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, IV-2/W3 (pp. 1–7). Bonn, Germany. https://doi.org/10.5194/isprs-annals-IV-2-W3-1-2017
Cutler, M., Michini, B., & How, J. P. (2013). Lightweight infrared sensing for relative navigation of quadrotors. In International Conference on Unmanned Aircraft Systems (ICUAS). IEEE. https://doi.org/10.1109/ICUAS.2013.6564807
Faghihinia, A., Amiri Atashgah, M. A., & Dehghan, S. M. (2021). Analytical expression for uncertainty propagation of aerial cooperative navigation. Aviation, 25(1), 10–21. https://doi.org/10.3846/aviation.2021.13420
Fletcher, R. (2000). Practical methods of optimization (2nd ed.). John Wiley and Sons Ltd. https://doi.org/10.1002/9781118723203
Fosbury, A. M., & Crassidis, J. L. (2008). Optimal trajectory determination for increased relative navigation observability of air vehicles. In American Institute of Aeronautics and Astronautics Guidance, Navigation and Control Conference and Exhibit (pp. 1–19). Honolulu, Hawaii. https://doi.org/10.2514/6.2008-6648
Guo, K. (4 December, 2018). Ultra-wideband-based navigation for unmanned aerial vehicles. Nanyang Technological University.
Hong, Y., & Simon, D. (2017, August 6–9). Relative navigation of non-cooperative space target based on multiple cooperative space robots. In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE 2017. Cleveland, Ohio, USA. http://proceedings.asmedigitalcollection.asme.org/
Jin, Y., Zhang, Y., Yuan, J., & Zhang, X. (12–17 May, 2019). Efficient Multi-agent cooperative navigation in unknown environments with interlaced deep reinforcement learning. In ICASSP 2019 – 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Brighton, United Kingdom. https://doi.org/10.1109/ICASSP.2019.8682555
Khambhaita, H., & Alami, R. (28 November, 2019). Viewing robot navigation in human environment as a cooperative activity. Robotics Research, 10, 285–300. https://doi.org/10.1007/978-3-030-28619-4_25
Lee, J., Kang, D. E., & Park, S. Y. (2018). Relative navigation with laser-based intermittent measurement for formation flying satellites. International Journal of Aerospace and Mechanical Engineering, 12(2), 73–77.
Martin, S. M. (2011, May 9). Closely coupled GPS/INS relative positioning for automated vehicle. Auburn University.
Mokhtarzadeh, H., & Gebre-Egziabher, D. (2016). Performance of networked dead reckoning navigation system. IEEE Transactions on Aerospace and Electronic Systems, 52(5), 2539–2553. https://doi.org/10.1109/TAES.2016.150180
Montenbruck, O., Ebinuma, T., Lightsey, E. G., & Leung, S. (2002, October). A real-time kinematic GPS sensor for spacecraft relative navigation. Aerospace Science and Technology, 6(6), 435–449. https://doi.org/10.1016/S1270-9638(02)01185-9
Noureldin, A., Karamat, T., & Georgy, J. (2013). Fundamentals of inertial navigation, satellite-based positioning and their integration. Springer. https://doi.org/10.1007/978-3-642-30466-8
Roumeliotis, S. I., & Bekey, G. A. (2002). Distributed multirobot localization. IEEE Transactions on Robotics and Automation, 18(5), 781–795. https://doi.org/10.1109/TRA.2002.803461
Rutkowski, A. J., Barnes, J. E., & Smith, A. T. (2016). Path planning for optimal cooperative navigation. In 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS). IEEE. https://doi.org/10.1109/PLANS.2016.7479721
Sanderson, A. C. (1998). A distributed algorithm for cooperative navigation among multiple mobile robots. Advanced Robotics, 12, 335–349. https://doi.org/10.1163/156855398X00235
Sheikh, S. I., Ray, P. S., Weiner, K., Wolff, M. T., & Wood, K. S. (2007). Relative navigation of spacecraft utilizing bright, aperiodic celestial sources. In 63rd Annual Meeting of the Institute of Navigation (pp. 444–453). The Institute of Navigation.
Sivaneri, V. O., & Gross, J. N. (2017, December). UGV-to-UAV cooperative ranging for robust navigation in GNSS-challenged environments. Aerospace Science and Technology, 71, 245–255. https://doi.org/10.1016/j.ast.2017.09.024
Summerfield, N. S., Deokar, A. V., Xu, M., & Zhu, W. (2020, 6 February). Should drivers cooperate? Performance evaluation of cooperative navigation on simulated road networks using network DEA. Journal of the Operational Research Society, 72. https://doi.org/10.1080/01605682.2019.1700766
Thomason, J., Murray, M., Cakmak, M., & Zettlemoyer, L. (2020). Vision-and-dialog navigation. In Conference on Robot Learning, PMLR. ArXiv.
Vetrella, A. R., Fasano, G., & Accardo, D. (2016, 7–10 June). Cooperative navigation in GPS-Challenging environments exploiting position broadcast and vision-based tracking. In 2016 International Conference on Unmanned Aircraft Systems (ICUAS). Arlington, VA USA. IEEE. https://doi.org/10.1109/ICUAS.2016.7502647
Vetrella, A. R., Opromolla, R., Fasano, G., Accardo, D., & Grassi, M. (2017, 9–13 January). Autonomous flight in GPS-Challenging environments exploiting multi-UAV cooperation and vision-aided navigation. In AIAA SciTech Forum. AIAA Information Systems-AIAA Infotech @ Aerospace. https://doi.org/10.2514/6.2017-0879
Vetrella, A. R., Fasano, G., & Accardo, D. (2018). Attitude estimation for cooperating UAVs based on tight integration of GNSS and vision measurements. Aerospace Science and Technology, 84, 966–979. https://doi.org/10.1016/j.ast.2018.11.032
Wang, X. (2011, April). Improved adaptive filter with application to relative navigation. GPS Solutions, 15(2), 121–128. https://doi.org/10.1007/s10291-010-0175-7
Wang, X., Gong, D., Xu, L., Shao, X., & Duan, D. (2011a, June–July). Laser radar based relative navigation using improved adaptive Huber filter. Acta Astronautica, 68(11–12), 1872–1880. https://doi.org/10.1016/j.actaastro.2011.01.002
Wang, X., Shao, X., Gong, D., & Duan, D. (2011b, April). GPS/VISNAV integrated relative navigation and attitude determination system for ultra-close spacecraft formation flying. Journal of Systems Engineering and Electronics, 22(2), 283–291. https://doi.org/10.3969/j.issn.1004-4132.2011.02.015
Chen, J., Wang, X., Shao, X., & Duan, D. (2010, 8–10 June). An integrated Relative Navigation system using GPS/VISNAV for ultra-close spacecraft formation flying. In 3rd International Symposium on Systems and Control in Aeronautics and Astronautics. The Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISSCAA.2010.5633067
Chen, M., Xiong, Z., Liu, J., Wang, R., & Xiong, J. (2020, June 22). Cooperative navigation of unmanned aerial vehicle swarm based on cooperative dilution of precision. International Journal of Advanced Robotic Systems, 17(3). https://doi.org/10.1177/1729881420932717
Cledat, E., & Cucci, D. A. (2017, 4–7 September). Mapping GNSS restricted environments with a drone tandem and indirect position control. In ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, IV-2/W3 (pp. 1–7). Bonn, Germany. https://doi.org/10.5194/isprs-annals-IV-2-W3-1-2017
Cutler, M., Michini, B., & How, J. P. (2013). Lightweight infrared sensing for relative navigation of quadrotors. In International Conference on Unmanned Aircraft Systems (ICUAS). IEEE. https://doi.org/10.1109/ICUAS.2013.6564807
Faghihinia, A., Amiri Atashgah, M. A., & Dehghan, S. M. (2021). Analytical expression for uncertainty propagation of aerial cooperative navigation. Aviation, 25(1), 10–21. https://doi.org/10.3846/aviation.2021.13420
Fletcher, R. (2000). Practical methods of optimization (2nd ed.). John Wiley and Sons Ltd. https://doi.org/10.1002/9781118723203
Fosbury, A. M., & Crassidis, J. L. (2008). Optimal trajectory determination for increased relative navigation observability of air vehicles. In American Institute of Aeronautics and Astronautics Guidance, Navigation and Control Conference and Exhibit (pp. 1–19). Honolulu, Hawaii. https://doi.org/10.2514/6.2008-6648
Guo, K. (4 December, 2018). Ultra-wideband-based navigation for unmanned aerial vehicles. Nanyang Technological University.
Hong, Y., & Simon, D. (2017, August 6–9). Relative navigation of non-cooperative space target based on multiple cooperative space robots. In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE 2017. Cleveland, Ohio, USA. http://proceedings.asmedigitalcollection.asme.org/
Jin, Y., Zhang, Y., Yuan, J., & Zhang, X. (12–17 May, 2019). Efficient Multi-agent cooperative navigation in unknown environments with interlaced deep reinforcement learning. In ICASSP 2019 – 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Brighton, United Kingdom. https://doi.org/10.1109/ICASSP.2019.8682555
Khambhaita, H., & Alami, R. (28 November, 2019). Viewing robot navigation in human environment as a cooperative activity. Robotics Research, 10, 285–300. https://doi.org/10.1007/978-3-030-28619-4_25
Lee, J., Kang, D. E., & Park, S. Y. (2018). Relative navigation with laser-based intermittent measurement for formation flying satellites. International Journal of Aerospace and Mechanical Engineering, 12(2), 73–77.
Martin, S. M. (2011, May 9). Closely coupled GPS/INS relative positioning for automated vehicle. Auburn University.
Mokhtarzadeh, H., & Gebre-Egziabher, D. (2016). Performance of networked dead reckoning navigation system. IEEE Transactions on Aerospace and Electronic Systems, 52(5), 2539–2553. https://doi.org/10.1109/TAES.2016.150180
Montenbruck, O., Ebinuma, T., Lightsey, E. G., & Leung, S. (2002, October). A real-time kinematic GPS sensor for spacecraft relative navigation. Aerospace Science and Technology, 6(6), 435–449. https://doi.org/10.1016/S1270-9638(02)01185-9
Noureldin, A., Karamat, T., & Georgy, J. (2013). Fundamentals of inertial navigation, satellite-based positioning and their integration. Springer. https://doi.org/10.1007/978-3-642-30466-8
Roumeliotis, S. I., & Bekey, G. A. (2002). Distributed multirobot localization. IEEE Transactions on Robotics and Automation, 18(5), 781–795. https://doi.org/10.1109/TRA.2002.803461
Rutkowski, A. J., Barnes, J. E., & Smith, A. T. (2016). Path planning for optimal cooperative navigation. In 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS). IEEE. https://doi.org/10.1109/PLANS.2016.7479721
Sanderson, A. C. (1998). A distributed algorithm for cooperative navigation among multiple mobile robots. Advanced Robotics, 12, 335–349. https://doi.org/10.1163/156855398X00235
Sheikh, S. I., Ray, P. S., Weiner, K., Wolff, M. T., & Wood, K. S. (2007). Relative navigation of spacecraft utilizing bright, aperiodic celestial sources. In 63rd Annual Meeting of the Institute of Navigation (pp. 444–453). The Institute of Navigation.
Sivaneri, V. O., & Gross, J. N. (2017, December). UGV-to-UAV cooperative ranging for robust navigation in GNSS-challenged environments. Aerospace Science and Technology, 71, 245–255. https://doi.org/10.1016/j.ast.2017.09.024
Summerfield, N. S., Deokar, A. V., Xu, M., & Zhu, W. (2020, 6 February). Should drivers cooperate? Performance evaluation of cooperative navigation on simulated road networks using network DEA. Journal of the Operational Research Society, 72. https://doi.org/10.1080/01605682.2019.1700766
Thomason, J., Murray, M., Cakmak, M., & Zettlemoyer, L. (2020). Vision-and-dialog navigation. In Conference on Robot Learning, PMLR. ArXiv.
Vetrella, A. R., Fasano, G., & Accardo, D. (2016, 7–10 June). Cooperative navigation in GPS-Challenging environments exploiting position broadcast and vision-based tracking. In 2016 International Conference on Unmanned Aircraft Systems (ICUAS). Arlington, VA USA. IEEE. https://doi.org/10.1109/ICUAS.2016.7502647
Vetrella, A. R., Opromolla, R., Fasano, G., Accardo, D., & Grassi, M. (2017, 9–13 January). Autonomous flight in GPS-Challenging environments exploiting multi-UAV cooperation and vision-aided navigation. In AIAA SciTech Forum. AIAA Information Systems-AIAA Infotech @ Aerospace. https://doi.org/10.2514/6.2017-0879
Vetrella, A. R., Fasano, G., & Accardo, D. (2018). Attitude estimation for cooperating UAVs based on tight integration of GNSS and vision measurements. Aerospace Science and Technology, 84, 966–979. https://doi.org/10.1016/j.ast.2018.11.032
Wang, X. (2011, April). Improved adaptive filter with application to relative navigation. GPS Solutions, 15(2), 121–128. https://doi.org/10.1007/s10291-010-0175-7
Wang, X., Gong, D., Xu, L., Shao, X., & Duan, D. (2011a, June–July). Laser radar based relative navigation using improved adaptive Huber filter. Acta Astronautica, 68(11–12), 1872–1880. https://doi.org/10.1016/j.actaastro.2011.01.002
Wang, X., Shao, X., Gong, D., & Duan, D. (2011b, April). GPS/VISNAV integrated relative navigation and attitude determination system for ultra-close spacecraft formation flying. Journal of Systems Engineering and Electronics, 22(2), 283–291. https://doi.org/10.3969/j.issn.1004-4132.2011.02.015