Analytical expression for uncertainty propagation of aerial cooperative navigation
Abstract
In this paper, the propagation of uncertainty in a cooperative navigation algorithm (CNA) for a group of flying robots (FRs) is investigated. Each FR is equipped with an inertial measurement unit (IMU) and range-bearing sensors to measure the relative distance and bearing angles between the agents. In this regard, an extended Kalman filter (EKF) is implemented to estimate the position and rotation angles of all the agents. For further studies, a relaxed analytical performance index through a closed-form solution is derived. Moreover, the effects of the sensors noise covariance and the number of FRs on the growth rate of the position error covariance is investigated. Analytically, it is shown that the covariance of position error in the vehicles equipped with the IMU is proportional to the cube of time. However, the growth rate of the navigation error is, considerably more rapid compared to a mobile robot group. Furthermore, the covariance of position error is independent of the path and noise resulting from the relative position measurements. Further, it merely depends on both the size of the group and noise characteristics of the accelerometers. Lastly, the analytical results are validated through comprehensive Guidance, Navigation, and Control (GNC) in-the-loop simulations.
Keyword : closed-form solution, cooperative navigation, flying robots, inertial navigation, performance analysis
How to Cite
Faghihinia, A., Amiri Atashgah, M. A., & Dehghan, S. M. M. (2021). Analytical expression for uncertainty propagation of aerial cooperative navigation. Aviation, 25(1), 10-21. https://doi.org/10.3846/aviation.2021.13420
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Bayat, M., & Atashgah, M. A. (2017). An augmented strapdown inertial navigation system using jerk and jounce of motion for a flying robot. The Journal of Navigation, 70(4), 907–926. https://doi.org/10.1017/S0373463317000017
Chakraborty, A., Sharma, R., & Brink, K. M. (2019). Cooperative localization for multirotor unmanned aerial vehicles. In AIAA Scitech 2019 Forum, (January), 1–19. https://doi.org/10.2514/6.2019-0684
Chakraborty, A., Taylor, C. N., Sharma, R., & Brink, K. M. (2016). Cooperative localization for fixed wing unmanned aerial vehicles. In Proceedings of the IEEE/ION Position, Location and Navigation Symposium, PLANS 2016, 106–117. https://doi.org/10.1109/PLANS.2016.7479689
Enayatollahi, F., & Atashgah, M. A. A. (2018). Wind effect analysis on air traffic congestion in terminal area via cellular automata. Aviation, 22(3), 102–114. https://doi.org/10.3846/aviation.2018.6252
Gao, R., & Chitre, M. (2010). Cooperative positioning using range-only measurements between two AUVs. In OCEANS’10 IEEE, OCEANSSYD 2010. Sydney. https://doi.org/10.1109/OCEANSSYD.2010.5603615
Goel, S., Kealy, A., Gikas, V., Retscher, G., Toth, C., Brzezinska, D. G., & Lohani, B. (2017). Cooperative localization of unmanned aerial vehicles using GNSS, MEMS inertial, and UWB sensors. Journal of Surveying Engineering, 143(4), 4017007. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000230
Goel, S., Kealy, A., & Lohani, B. (2016). Cooperative UAS localization using lowcost sensors. In ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences, III–1(July), 183–190. https://doi.org/10.5194/isprsannals-III-1-183-2016
Kemsaram, N., Thatiparti, V. R. K., Guntupalli, D. R., & Kuvvarapu, A. (2017). Design and development of an on-board autonomous visual tracking system for unmanned aerial vehicles. Aviation, 21(3), 83–91. https://doi.org/10.3846/16487788.2017.1378265
Koifman, M., & Bar-Itzhack, I. Y. (1999). Inertial navigation system aided by aircraft dynamics. IEEE Transactions on Control Systems Technology, 7(4), 487–493. https://doi.org/10.1109/87.772164
Kurazume, R., Nagata, S., & Hirose, S. (1994, May). Cooperative positioning with multiple robots. In Proceedings of the 1994 IEEE International Conference on Robotics and Automation, 1250–1257. https://doi.org/10.1109/ROBOT.1994.351315
Lee, C.-Y. (2020). Cooperative drone positioning measuring in internet-of-drones [Conference presentation]. 2020 IEEE 17th Annual Consumer Communications & Networking Conference (CCNC), 1–3. IEEE. https://doi.org/10.1109/CCNC46108.2020.9045111
Martinelli, A., Pont, F., & Siegwart, R. (2005). Multi-robot localization using relative observations. In Proceedings – IEEE International Conference on Robotics and Automation, 2005(April), 2797–2802. https://doi.org/10.1109/ROBOT.2005.1570537
Martinelli, A., & Siegwart, R. (2005). Observability analysis for mobile robot localization [Conference presentation]. 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, 1264–1269. https://doi.org/10.1109/IROS.2005.1545153
Mourikis, A. I., Member, S., & Roumeliotis, S. I. (2006). Performance Analysis of Multirobot Cooperative Localization. 22(4), 666–681. https://doi.org/10.1109/TRO.2006.878957
Rekleitis, I. M., & Roumeliotis, S. I. (2003). Analytical expressions for positioning uncertainty propagation in networks of robots [Conference presentation]. IEEE Mediterranean Conference on Control and Automation, 131–136.
Rekleitis, I. M., Dudek, G., & Milios, E. E. (2002). Multi-robot cooperative localization: A study of trade-offs between efficiency and accuracy [Conference presentation]. IEEE International Conference on Intelligent Robots and Systems, 3, 2690–2695. https://doi.org/10.1109/IRDS.2002.1041676
Roumeliotis, S. I., & Bekey, G. A. (2000). Distributed multi-robot localization. In Distributed autonomous robotic systems 4 (pp. 179–188). Springer. https://doi.org/10.1007/978-4-431-67919-6_17
Roumeliotis, S. I., & Rekleitis, I. M. (2003). Analysis of multirobot localization uncertainty propagation [Conference presentation]. IEEE International Conference on Intelligent Robots and Systems, 2, 1763–1770. https://doi.org/10.1109/IROS.2003.1248899
Ryan, A., Zennaro, M., Howell, A., Sengupta, R., & Hedrick, J. K. (2004). An overview of emerging results in cooperative UAV control [Conference presentation]. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No. 04CH37601), 1, 602–607. IEEE. https://doi.org/10.1109/CDC.2004.1428700
Sharma, R., Beard, R. W., Taylor, C. N., & Quebe, S. (2012). Graph-based observability analysis of bearing-only cooperative localization. IEEE Transactions on Robotics, 28(2), 522–529. https://doi.org/10.1109/TRO.2011.2172699
Sharma, R., Quebe, S., Beard, R. W., & Taylor, C. N. (2013). Bearing-only cooperative localization. Journal of Intelligent & Robotic Systems, 72(3–4), 429–440. https://doi.org/10.1007/s10846-012-9809-z
Sharma, R., & Taylor, C. (2008). Cooperative navigation of MAVs in GPS denied areas [Conference presentation]. IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, (4), 481–486. https://doi.org/10.1109/MFI.2008.4648041
Sharma, R., & Taylor, C. N. (2009). Vision based distributed cooperative navigation for MAVs in GPS denied areas [Conference presentation]. AIAA Infotech at Aerospace Conference and Exhibit and AIAA Unmanned...Unlimited Conference, (April). https://doi.org/10.2514/6.2009-1932
Shin, E.-H., & El-Sheimy, N. (2001). Accuracy improvement of low cost INS/GPS for land applications. Graduate Studies.
Simon, D. (2006). Optimal state estimation: Kalman, H infinity, and nonlinear approaches. John Wiley & Sons. https://doi.org/10.1002/0470045345
Sullivan, N., Grainger, S., & Cazzolato, B. (2018). Analysis of cooperative localisation performance under varying sensor qualities and communication rates. Robotics and Autonomous Systems, 110, 73–84. https://doi.org/10.1016/j.robot.2018.09.010
Titterton, D., & Weston, J. (2004). Strapdown inertial navigation technology. In Strapdown Inertial Navigation Technology, 17. https://doi.org/10.1049/PBRA017E
Wanasinghe, T. R., Mann, G. K. I., & Gosine, R. G. (2016). Decentralized cooperative localization approach for autonomous multirobot systems. Journal of Robotics, 2016. https://doi.org/10.1155/2016/2560573