Skip to main content

Accurate Estimation of 3D-Repetitive-Trajectories using Kalman Filter, Machine Learning and Curve-Fitting Method for High-speed Target Interception

  • Chapter
  • First Online:
Artificial Intelligence for Robotics and Autonomous Systems Applications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1093))

  • 1152 Accesses

Abstract

Accurate estimation of trajectory is essential for the capture of any high-speed target. This chapter estimates and formulates an interception strategy for the trajectory of a target moving in a repetitive loop using a combination of estimation and learning techniques. An extended Kalman filter estimates the current location of the target using the visual information in the first loop of the trajectory to collect data points. Then, a combination of Recurrent Neural Network (RNN) with least-square curve-fitting is used to accurately estimate the future positions for the subsequent loops. We formulate an interception strategy for the interception of a high-speed target moving in a three-dimensional curve using noisy visual information from a camera. The proposed framework is validated in the ROS-Gazebo environment for interception of a target moving in a repetitive figure-of-eight trajectory. Astroid, Deltoid, Limacon, Squircle, and Lemniscates of Bernoulli are some of the high-order curves used for algorithm validation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Abbas, M. T., Jibran, M. A., Afaq, M., & Song, W. C. (2020). An adaptive approach to vehicle trajectory prediction using multimodel kalman filter. Transactions on Emerging Telecommunications Technologies, 31(5), e3734.

    Article  Google Scholar 

  2. Anderson-Sprecher, R., & Lenth, R. V. (1996). Spline estimation of paths using bearings-only tracking data. Journal of the American Statistical Association, 91(433), 276–283.

    Article  MathSciNet  MATH  Google Scholar 

  3. Banerjee, P., & Corbetta, M. (2020). In-time uav flight-trajectory estimation and tracking using bayesian filters. In 2020 IEEE Aerospace Conference (pp. 1–9). IEEE

    Google Scholar 

  4. Barisic, A., Petric, F., & Bogdan, S. (2022). Brain over brawn: using a stereo camera to detect, track, and intercept a faster uav by reconstructing the intruder’s trajectory. Field Robotics, 2, 34–54.

    Article  Google Scholar 

  5. Beul, M., Bultmann, S., Rochow, A., Rosu, R. A., Schleich, D., Splietker, M., & Behnke, S. (2020). Visually guided balloon popping with an autonomous mav at mbzirc 2020. In 2020 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR) ( pp. 34–41). IEEE

    Google Scholar 

  6. Cascarano, S., Milazzo, M., Vannin, A., Andrea, S., & Stefano, R. (2022). Design and development of drones to autonomously interact with objects in unstructured outdoor scenarios. Field Robotics, 2, 34–54.

    Google Scholar 

  7. Chen, M., Liu, Y., & Yu, X. (2015). Predicting next locations with object clustering and trajectory clustering. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 344–356). Springer

    Google Scholar 

  8. Cheung, Y., Huang, Y. T., & Lien, J. J. J. (2015). Visual guided adaptive robotic interceptions with occluded target motion estimations. In 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 6067–6072). IEEE

    Google Scholar 

  9. Dong, G., & Zhu, Z. H. (2016). Autonomous robotic capture of non-cooperative target by adaptive extended kalman filter based visual servo. Acta Astronautica, 122, 209–218.

    Article  Google Scholar 

  10. Hadzagic, M., & Michalska, H. (2011). A bayesian inference approach for batch trajectory estimation. In 14th International Conference on Information Fusion (pp. 1–8). IEEE

    Google Scholar 

  11. Jana, S., Tony, L. A., Varun, V., Bhise, A. A., & Ghose, D. (2022). Interception of an aerial manoeuvring target using monocular vision. Robotica, 1–20

    Google Scholar 

  12. Kim, S., Seo, H., Choi, S., & Kim, H. J. (2016). Vision-guided aerial manipulation using a multirotor with a robotic arm. IEEE/ASME Transactions On Mechatronics, 21(4), 1912–1923.

    Article  Google Scholar 

  13. Kumar, A., Ojha, A., & Padhy, P. K. (2017). Anticipated trajectory based proportional navigation guidance scheme for intercepting high maneuvering targets. International Journal of Control, Automation and Systems, 15(3), 1351–1361.

    Article  Google Scholar 

  14. Levenberg, K. (1944). A method for the solution of certain non-linear problems in least squares. Quarterly of Applied Mathematics, 2(2), 164–168.

    Article  MathSciNet  MATH  Google Scholar 

  15. Li, T., Prieto, J., & Corchado, J. M. (2016). Fitting for smoothing: a methodology for continuous-time target track estimation. In 2016 International Conference on Indoor Positioning and Indoor Navigation (IPIN) (pp. 1–8). IEEE

    Google Scholar 

  16. Li, T., Chen, H., Sun, S., & Corchado, J. M. (2018). Joint smoothing and tracking based on continuous-time target trajectory function fitting. IEEE transactions on Automation Science and Engineering, 16(3), 1476–1483.

    Article  Google Scholar 

  17. Lin, L., Yang, Y., Cheng, H., & Chen, X. (2019). Autonomous vision-based aerial grasping for rotorcraft unmanned aerial vehicles. Sensors, 19(15), 3410.

    Article  Google Scholar 

  18. Liu, Y., Suo, J., Karimi, H. R., & Liu, X. (2014). A filtering algorithm for maneuvering target tracking based on smoothing spline fitting. In Abstract and Applied Analysis (Vol. 2014). Hindawi

    Google Scholar 

  19. Luo, C., McClean, S. I., Parr, G., Teacy, L., & De Nardi, R. (2013). UAV position estimation and collision avoidance using the extended kalman filter. IEEE Transactions on Vehicular Technology, 62(6), 2749–2762.

    Article  Google Scholar 

  20. Ma, H., Wang, M., Fu, M., & Yang, C. (2012). A new discrete-time guidance law base on trajectory learning and prediction. In AIAA Guidance, Navigation, and Control Conference (p. 4471)

    Google Scholar 

  21. Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the society for Industrial and Applied Mathematics, 11(2), 431–441.

    Article  MathSciNet  MATH  Google Scholar 

  22. Mehta, S. S., Ton, C., Kan, Z., & Curtis, J. W. (2015). Vision-based navigation and guidance of a sensorless missile. Journal of the Franklin Institute, 352(12), 5569–5598.

    Article  MathSciNet  MATH  Google Scholar 

  23. Pang, B., Ng, E. M., & Low, K. H. (2020). UAV trajectory estimation and deviation analysis for contingency management in urban environments. In AIAA Aviation 2020 Forum (p. 2919)

    Google Scholar 

  24. Prevost, C. G., Desbiens, A., & Gagnon, E. (2007). Extended kalman filter for state estimation and trajectory prediction of a moving object detected by an unmanned aerial vehicle. In 2007 American Control Conference (pp. 1805–1810). IEEE

    Google Scholar 

  25. Qu, L., & Dailey, M. N. (2021). Vehicle trajectory estimation based on fusion of visual motion features and deep learning. Sensors, 21(23), 7969.

    Article  Google Scholar 

  26. Roh, G. P., & Hwang, S. W. (2010). Nncluster: an efficient clustering algorithm for road network trajectories. In International Conference on Database Systems for Advanced Applications (pp. 47–61). Springer

    Google Scholar 

  27. Schulz, J., Hubmann, C., Löchner, J., & Burschka, D. (2018). Multiple model unscented kalman filtering in dynamic bayesian networks for intention estimation and trajectory prediction. In 2018 21st International Conference on Intelligent Transportation Systems (ITSC) (pp. 1467–1474). IEEE

    Google Scholar 

  28. Shamwell, E. J., Leung, S., & Nothwang, W. D. (2018). Vision-aided absolute trajectory estimation using an unsupervised deep network with online error correction. In 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 2524–2531). IEEE

    Google Scholar 

  29. Shrivastava, A., Verma, J. P. V., Jain, S., & Garg, S. (2021). A deep learning based approach for trajectory estimation using geographically clustered data. SN Applied Sciences, 3(6), 1–17.

    Article  Google Scholar 

  30. Strydom, R., Thurrowgood, S., Denuelle, A., & Srinivasan, M. V. (2015). UAV guidance: a stereo-based technique for interception of stationary or moving targets. In Conference Towards Autonomous Robotic Systems (pp. 258–269). Springer

    Google Scholar 

  31. Su, K., & Shen, S. (2016). Catching a flying ball with a vision-based quadrotor. In International Symposium on Experimental Robotics (pp. 550–562). Springer

    Google Scholar 

  32. Sung, C., Feldman, D., & Rus, D. (2012). Trajectory clustering for motion prediction. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 1547–1552). IEEE

    Google Scholar 

  33. Thomas, J., Loianno, G., Sreenath, K., & Kumar, V. (2014). Toward image based visual servoing for aerial grasping and perching. In 2014 IEEE International Conference on Robotics and Automation (ICRA) (pp. 2113–2118). IEEE

    Google Scholar 

  34. Tony, L. A., Jana, S., Bhise, A. A., Gadde, M. S., Krishnapuram, R., Ghose, D., et al. (2022). Autonomous cooperative multi-vehicle system for interception of aerial and stationary targets in unknown environments. Field Robotics, 2, 107–146.

    Article  Google Scholar 

  35. Yan, L., Jg, Zhao, Hr, Shen, & Li, Y. (2014). Biased retro-proportional navigation law for interception of high-speed targets with angular constraint. Defence Technology, 10(1), 60–65.

    Article  Google Scholar 

  36. Zhang, X., Wang, Y., & Fang, Y. (2016). Vision-based moving target interception with a mobile robot based on motion prediction and online planning. In 2016 IEEE International Conference on Real-time Computing and Robotics (RCAR) (pp. 17–21). IEEE

    Google Scholar 

  37. Zhang, Y., Wu, H., Liu, J., & Sun, Y. (2018). A blended control strategy for intercepting high-speed target in high altitude. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 232(12), 2263–2285.

    Article  Google Scholar 

  38. Zhao, M., Shi, F., Anzai, T., Takuzumi, N., Toshiya, M., Kita, I., et al. (2022). Team JSK at MBZIRC 2020: interception of fast flying target using multilinked aerial robot. Field Robotics, 2, 34–54.

    Google Scholar 

Download references

Acknowledgements

We would like to acknowledge the Robert Bosch Center for Cyber Physical Systems, Indian Institute of Science, Bangalore, and Khalifa University, Abu Dhabi, for partial financial support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Debasish Ghose .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Agrawal, A., Bhise, A., Arasanipalai, R., Tony, L.A., Jana, S., Ghose, D. (2023). Accurate Estimation of 3D-Repetitive-Trajectories using Kalman Filter, Machine Learning and Curve-Fitting Method for High-speed Target Interception. In: Azar, A.T., Koubaa, A. (eds) Artificial Intelligence for Robotics and Autonomous Systems Applications. Studies in Computational Intelligence, vol 1093. Springer, Cham. https://doi.org/10.1007/978-3-031-28715-2_4

Download citation

Publish with us

Policies and ethics