Disturbance scaling in bidirectional vehicle platoons with different asymmetry in position and velocity coupling
Authors
Ivo Herman, Steffi Knorn, Anders Ahlén
Abstract
This paper considers a string of vehicles where the local control law uses the states of the vehicle’s immediate predecessor and follower. The coupling towards the preceding vehicle can be chosen different to the coupling with the following vehicle, which is referred to as an asymmetric bidirectional string. Further, the asymmetry for the velocity coupling can be chosen differently to the asymmetry in the position coupling. It is investigated how the effect of the disturbance on the control errors in the string depends on the string length. It is shown, that in case of symmetric position coupling and asymmetric velocity coupling, linear scaling can be achieved. For symmetric interactions, the errors scale quadratically in the number of vehicles. When the coupling in position is asymmetric, exponential scaling may occur or the system might even become unstable. The paper thus gives a comprehensive overview of the achievable performance in linear, asymmetric, bidirectional platoons. The results reveal that symmetry in the position coupling and asymmetry in velocity coupling qualitatively improve the performance of the string. Extensive numerical results illustrate the theoretical findings.
Keywords
Port-Hamiltonian systems; Vehicular platoons; Multi-vehicle systems; Scaling; Asymmetry
Citation
- Journal: Automatica
- Year: 2017
- Volume: 82
- Issue:
- Pages: 13–20
- Publisher: Elsevier BV
- DOI: 10.1016/j.automatica.2017.04.010
BibTeX
@article{Herman_2017,
title={{Disturbance scaling in bidirectional vehicle platoons with different asymmetry in position and velocity coupling}},
volume={82},
ISSN={0005-1098},
DOI={10.1016/j.automatica.2017.04.010},
journal={Automatica},
publisher={Elsevier BV},
author={Herman, Ivo and Knorn, Steffi and Ahlén, Anders},
year={2017},
pages={13--20}
}
References
- Alam, A., Mårtensson, J. & Johansson, K. H. Experimental evaluation of decentralized cooperative cruise control for heavy-duty vehicle platooning. Control Engineering Practice vol. 38 11–25 (2015) – 10.1016/j.conengprac.2014.12.009
- Barooah, P. & Hespanha, J. P. Error Amplification and Disturbance Propagation in Vehicle Strings with Decentralized Linear Control. Proceedings of the 44th IEEE Conference on Decision and Control 4964–4969 doi:10.1109/cdc.2005.1582948 – 10.1109/cdc.2005.1582948
- Barooah, P., Mehta, P. G. & Hespanha, J. P. Mistuning-Based Control Design to Improve Closed-Loop Stability Margin of Vehicular Platoons. IEEE Transactions on Automatic Control vol. 54 2100–2113 (2009) – 10.1109/tac.2009.2026934
- Bernstein, (2009)
- Böttcher, (2005)
- Cantos, Transients in the synchronization of asymmetrically coupled oscillator arrays. European Physical Journal: Special Topics (2016)
- Hao, H. & Barooah, P. Control of large 1D networks of double integrator agents: Role of heterogeneity and asymmetry on stability margin. 49th IEEE Conference on Decision and Control (CDC) 7395–7400 (2010) doi:10.1109/cdc.2010.5717477 – 10.1109/cdc.2010.5717477
- Hao, Stability and robustness of large platoons of vehicles with double-integrator models and nearest neighbor interaction. International Journal of Robust and Nonlinear Control (2012)
- He Hao, Huibing Yin & Zhen Kan. On the robustness of large 1-D network of double integrator agents. 2012 American Control Conference (ACC) 6059–6064 (2012) doi:10.1109/acc.2012.6315531 – 10.1109/acc.2012.6315531
- Herman, I., Martinec, D., Hurak, Z. & Sebek, M. Nonzero Bound on Fiedler Eigenvalue Causes Exponential Growth of H-Infinity Norm of Vehicular Platoon. IEEE Transactions on Automatic Control vol. 60 2248–2253 (2015) – 10.1109/tac.2014.2366980
- Herman, I., Martinec, D., Hurak, Z. & Sebek, M. Scaling in Bidirectional Platoons With Dynamic Controllers and Proportional Asymmetry. IEEE Transactions on Automatic Control vol. 62 2034–2040 (2017) – 10.1109/tac.2016.2594169
- Herman, I., Martinec, D. & Veerman, J. J. P. Transients of platoons with asymmetric and different Laplacians. Systems & Control Letters vol. 91 28–35 (2016) – 10.1016/j.sysconle.2016.02.013
- Multidomain modeling of nonlinear networks and systems. IEEE Control Systems vol. 29 28–59 (2009) – 10.1109/mcs.2009.932927
- Khalil, (2001)
- Klinge, S. & Middleton, R. H. String stability analysis of homogeneous linear unidirectionally connected systems with nonzero initial conditions. IET Irish Signals and Systems Conference (ISSC 2009) 17–17 (2009) doi:10.1049/cp.2009.1694 – 10.1049/cp.2009.1694
- Knorn, S. & Ahlén, A. Deviation bounds in multi agent systems described by undirected graphs. Automatica vol. 67 205–210 (2016) – 10.1016/j.automatica.2016.01.038
- Knorn, S., Donaire, A., Agüero, J. C. & Middleton, R. H. Passivity-based control for multi-vehicle systems subject to string constraints. Automatica vol. 50 3224–3230 (2014) – 10.1016/j.automatica.2014.10.038
- Knorn, S., Donaire, A., Agüero, J. C. & Middleton, R. H. Scalability of bidirectional vehicle strings with static and dynamic measurement errors. Automatica vol. 62 208–212 (2015) – 10.1016/j.automatica.2015.09.022
- Martinec, On the necessity of symmetric positional coupling for string stability. IEEE Transactions on Automatic Control (2016)
- Middleton, R. H. & Braslavsky, J. H. String Instability in Classes of Linear Time Invariant Formation Control With Limited Communication Range. IEEE Transactions on Automatic Control vol. 55 1519–1530 (2010) – 10.1109/tac.2010.2042318
- Parlangeli, G. & Notarstefano, G. On the Reachability and Observability of Path and Cycle Graphs. IEEE Transactions on Automatic Control vol. 57 743–748 (2012) – 10.1109/tac.2011.2168912
- Ploeg, J., van de Wouw, N. & Nijmeijer, H. Lp String Stability of Cascaded Systems: Application to Vehicle Platooning. IEEE Transactions on Control Systems Technology vol. 22 786–793 (2014) – 10.1109/tcst.2013.2258346
- Seiler, P., Pant, A. & Hedrick, K. Disturbance Propagation in Vehicle Strings. IEEE Transactions on Automatic Control vol. 49 1835–1841 (2004) – 10.1109/tac.2004.835586
- Tangerman, F. M., Veerman, J. J. P. & Stosic, B. D. Asymmetric Decentralized Flocks. IEEE Transactions on Automatic Control vol. 57 2844–2853 (2012) – 10.1109/tac.2012.2199150
- Veerman, Spatial instabilities and size limitations of flocks. Networks and Heterogeous Media (2007)