Abstract
This chapter presents bearing-based formation control schemes via orientation alignments. In the bearing-based control schemes, the sensing variables are bearing vectors in the aligned coordinate frames and the control variables are also bearing vectors in the aligned coordinate frames. But, as considered in the previous chapters, the initial coordinate frames of agents are not aligned. In order to align the coordinate frames, we conduct orientation alignments with simultaneous bearing-based formation control. Note that, the bearing vectors are normalized relative displacements; hence as commented in Chap. 1, the bearing vectors include the information of bearing angles. Thus, in bearing-based approaches under orientation alignment setups, the formation configuration that will be achieved is congruent up to translations and dilation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The orthogonal component is \(\delta \sin (\xi )\) and the parallel component is \(\delta \cos (\xi )\).
References
Anderson, B.D.O., Dasgupta, S., Yu, C.: Control of directed formations with a leader-first follower structure. In: Proceedings of the 46th IEEE Conference on Decision and Control, pp. 2882–2887 (2007)
Angeli, D.: An almost global notion of input to state stability. IEEE Trans. Autom. Control 49(6), 866–874 (2004)
Basiri, M., Bishop, A.N., Jensfelt, P.: Distributed control of triangular formations with angle-only constraints. Syst. Control Lett. 59(2), 147–154 (2010)
Bishop, A.N., Deghat, M., Anderson, B.D.O., Hong, Y.: Distributed formation control with relaxed motion requirements. Int. J. Robust Nonlinear Control 25(17), 3210–3230 (2015)
Cao, M., Yu, C., Anderson, B.D.O.: Formation control using range-only measurements. Automatica 47(4), 776–781 (2011)
Feingold, D.G., Varga, R.S.: Block diagonally dominant matrices and generalizations of the Gershgorin circle theorem. Pac. J. Math. 12(4), 1241–1250 (1962)
Guo, J., Zhang, C., Lin, M.: Angle-based cooperation control of triangle formation. In: Proceedings of the 34th Chinese Control Conference, pp. 7386–7391 (2015)
Kwon, S.-H., Trinh, M.H., Oh, K.-H., Zhao, S., Ahn, H.-S.: Infinitesimal weak rigidity, formation control of three agents, and extension to \(3\)-dimensional space, pp. 1–12. arXiv:1803.09545
Kwon, S.-H., Trinh, M.H., Oh, K.-H., Zhao, S., Ahn, H.-S.: Infinitesimal weak rigidity and stability analysis on three-agent formations. In: Proceedings of the SICE Annual Conference, pp. 266–271 (2018)
Park, M.-C., Ahn, H.-S.: Displacement estimation by range measurements and application to formation control. In: 2015 IEEE International Symposium on Intelligent Control, pp. 888–893 (2015)
Park, M.-C., Kim, H.-K., Ahn, H.-S.: Rigidity of distance-based formations with additional subtended-angle constraints. In: Proceedings of the International Conference on Control, Automation and Systems, pp. 111–116 (2017)
Shevitz, D., Paden, B.: Lyapunov stability theory of nonsmooth systems. IEEE Trans. Autom. Control 39(9), 1910–1914 (1994)
Summers, T.H., Yu, C., Dasgupta, S., Anderson, B.D.O.: Control of minimally persistent leader-remote-follower and coleader formations in the plane. IEEE Trans. Autom. Control 56(12), 2778–2792 (2011)
Trinh, M.-H., Mukherjee, D., Zelazo, D., Ahn, H.-S.: Finite-time bearing-only formation control. In: Proceedings of the 56th IEEE Conference on Decision and Control, pp. 1578–1583 (2017)
Trinh, M.H., Mukherjee, D., Zelazo, D., Ahn, H.-S.: Formations on directed cycles with bearing-only measurements. Int. J. Robust Nonlinear Control 28(3), 1074–1096 (2018)
Trinh, M.H., Oh, K.-K., Jeong, K., Ahn, H.-S.: Bearing-only control of leader first follower formations. In: Proceedings of the 14th IFAC Symposium on Large Scale Complex Systems: Theory and Applications, pp. 7–12 (2016)
Trinh, M.-H., Pham, V.H., Hoang, P.H., Son, J.-H., Ahn, H.-S.: A new bearing-only navigation law. In: Proceedings of the 2017 International Conference on Control, Automation and Systems, pp. 117–122 (2017)
Trinh, M.H., Zhao, S., Sun, Z., Zelazo, D., Anderson, B.D.O., Ahn, H.-S.: Bearing-based formation control of a group of agents with leader-first follower structure. IEEE Trans. Autom. Control 64(2), 598–613 (2019). https://doi.org/10.1109/TAC.2018.2836022
Zhao, S., Zelazo, D.: Bearing rigidity and almost global bearing-only formation stabilization. IEEE Trans. Autom. Control 61(5), 1255–1268 (2016)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ahn, HS. (2020). Formation Control via Bearing Measurements. In: Formation Control. Studies in Systems, Decision and Control, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-030-15187-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-15187-4_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-15186-7
Online ISBN: 978-3-030-15187-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)