Skip to main content
SpringerLink
Log in

Merging Strategies, Trajectory Planning and Controls for Platoon of Connected, and Autonomous Vehicles

  • Published:
International Journal of Intelligent Transportation Systems Research Aims and scope Submit manuscript

Abstract

This paper addresses the problem of connected and autonomous vehicles (CAVs) merging into platoons in a communication- enabled environment, and studies different aspects of platoon formation, merging strategies, control approaches, and emergency braking mitigation during the merging and formation process. First it introduces a strategy and the requirements for safe and effective execution of multi-vehicles merging into a platoon. Second, several longitudinal controllers benefiting from feedforward information -via communication- have been implemented and discussed comparatively under several interesting scenarios through simulations. Third, it proposes various safe and smooth lateral trajectory plans of vehicles merging into an existing platoon. Fourth, it investigates a common emergency situation in which the preceding vehicle experiences a sudden braking while a multi-vehicle merging task is executing. A method is proposed to safely handle such scenarios. Finally, this paper presents several simulation tests to evaluate the effectiveness of the proposed strategies and methods.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Abbreviations

di :

Distance between vehicle i − 1 and i

x i :

Position of ith vehicle

v i :

Velocity of ith vehicle

ai :

Acceleration of ith vehicle

Kdi :

Vehicle’s aerodynamic drag coefficient

mi :

Vehicle’s mass

τi :

Vehicle’s engine time-constant

ηi :

Feedback linearizing law

ui :

New control input of the ith vehicle

dd :

Constant desired following distance

kp, i :

Controller proportional gains

kd, i :

Controller derivative gain

ei :

Spacing error

\( {\mathrm{k}}_{\mathrm{p},\mathrm{i}}^{\mathrm{f}} \) :

Controller proportional gains of front vehicle

\( {\mathrm{k}}_{\mathrm{p},\mathrm{i}}^{\mathrm{r}} \) :

Controller proportional gains of rear vehicles

\( {\mathrm{k}}_{\mathrm{d},\mathrm{i}}^{\mathrm{f}} \) :

Controller derivative gains of front vehicle

\( {\mathrm{k}}_{\mathrm{d},\mathrm{i}}^{\mathrm{r}} \) :

Controller derivative gains of rear vehicle

wi :

Feedforward term obtained from wireless communication

J:

Cost function

Q, r:

Weights matrices

xf, i :

Longitudinal position of end point of ith merging vehicle in platoon

yf, i :

Lateral position of end point of ith merging vehicle in platoon

CCP:

Constant-gap cycloidal polynomial

CFP:

Constant-gap 5th –order Polynomial

VCP:

Variable-gap Cycloidal polynomial

VFP:

Variable-gap 5th –order polynomial

eVF:

Empirical variable-gap 5th –order polynomial

References

  1. Burns, L.D., Jordan, W.C., Scarborough, B.A.: Transforming Personal Mobility. Columbia University, The Earth Institute (2013)

    Google Scholar 

  2. Eskandarian, A.: Handbook of Intelligent Vehicles. Springer, London (2012)

    Book  Google Scholar 

  3. C. Bergenheim, S. Shladover and E. Geolingh, "Overview of Platooning Systems," in the 19th ITS World Congress, Vienna Austria, 2012

  4. S. Halle and B. Chaib-draa, "A collaborative driving system based on multiagent modelling and simulation," Transportation Reseach Part C, Elsevier, pp. 320–345, 2005

  5. J. Bom, B. Thuilot, F. Marmoiton and P. Martinet, "A Global Control Strategy for Urban Vehicles Platooning Relying on Nonlinear Decoupling Laws," in IEEE/RSJ Conference on Intelligent Robots and Systems, Aubiere, France, 2005

  6. Alam, A., Besselink, B., Turri, V.: Heavy-duty vehicle platooning for sustainable freight transportation: a cooperative method to enhance safety and efficiency. IEEE Control. Syst. 35(6), 34–56 (2015)

    Article  MathSciNet  Google Scholar 

  7. Dao, T., Huissoon, J.P., Clark, C.M.: A strategy for optimization of cooperative platoon formation. Int. JNL. Vehicle Inform. Commun. Syst. 3(1), 28–43 (2013)

    Google Scholar 

  8. Yi, W.L., Ali, S., George, Y.G., Abhilash, P., Hongewei, Z.: "control of vehicle platoons for highway safety and efficient utility: consensus with communications and vehicle dynamics," J Syst Sci Complex. Springer. 27, 605–631 (2014)

    MATH  Google Scholar 

  9. Goli, M., Eskandarian, A.: The Effect of Information, and Communication Topologies on Input-to-State Stability of Platoon. ITSC IEEE, Rio de Janeiro (2016)

    Book  Google Scholar 

  10. Blum, J.J., Eskandarian, A., Hoffman, L.J.: Challenges of intervehicle ad hoc networks. IEEE Trans. Intell. Transp. Syst. 5(4), 347–351 (2004)

    Article  Google Scholar 

  11. F. Michaud, P. Lepage, P. Frenette, D. Létourneau and N. Gaubert, "Coordinated maneuvering of automated vehicles in platoon," IEEE Transactions on Intelligent Transportation Systems, vol. 7, no. 4, 2006

    Article  Google Scholar 

  12. A. Kurt, K. Redmill and U. Ozguner, "WiP Abstract: Coordinated Autonomous Driving with 100 Connected Vehicles," in IEEE ICCPS, Philadelphia, PA, 2013

  13. K. S. Chang, W. Li, A. Shaihbahait, F. Assaderaghi and P. Varaiya, "A Preliminary Implementation for Vehicle Platoon Control System," in American Control Conference, 1991

  14. Ghasemi, A., Kazemi, R., Azadi, S.: Stable decentralized control of platoon of vehicles with heterogeneous information feedback. IEEE Trans. Veh. Technol. 62(9), 4299–4308 (2013)

    Article  Google Scholar 

  15. Xiao, L., Gao, F.: Practical string stability of platoon of adaptive cruise control vehicles. IEEE Trans. ITS. 12(4), 1184–1194 (2011)

    Google Scholar 

  16. J. Zhang and P. Ioannou, "Adaptive Vehicle Following Control System with Variable Time Headways," in IEEE Conference on Decision and Control, 2005

  17. X. Y. Lu, S. Shladover and J. K. Hedrick, "Heavy-Duty Truck Control: Short Inter-Vehicle Distance Following," in American Control Conference, Boston, Massachusetts, 2004

  18. Swaroop, D., Hedrick, J.K.: String stability of interconnected systems. IEEE Trans. Autom. Control. 41(3), 349–357 (1996)

    Article  MathSciNet  Google Scholar 

  19. D. Swaroop, "String Stability of Interconnected Systems: an Application to Platooning in Automated Highway," UC Berkeley, 1997

  20. J. Hedrick and D. Swaroop, "Dynamic Coupling between Vehicles under Automatic Control," in 13th IAVSD Symposium, 1993

  21. A. Stotsky, C. C. Chien and P. Ioannou, "Robust Platoon-Stable Controller Design for Autonomous Intelligent Vehicles," in IEEE Conferenec on Decision and Control, Lake Buena Vista, FL, 1994

  22. Ploeg, J., Shukla, D.P., van de Wouw, N., Nijmeijer, H.: Controller synthesis for string stability of vehicle platoons. IEEE Trans. Intel. Trans. Syst. 15(2), 854–865 (2014)

    Article  Google Scholar 

  23. Kosmatopoulos, E.B., Ioannou, P.A.: Collision avoidance analysis for lane changing and merging. IEEE Trans. Veh. Technol. 49(6), 2295–2308 (2000)

    Article  Google Scholar 

  24. D. Soudbakhsh and A. Eskandarian, "a Collision Avoidance Steering Controller Using Linear Quadratic Regulator," in SAE Int. Conf., Detroit, 2010

  25. A. Bayuwindra, Ø. L. Aakre, J. Ploeg and H. Nijmeijer, "Combined Lateral and Longitudinal CACC for a Unicycle-Type Platoon," in IEEE IV, 2016

  26. P. Petrove and F. Nashashibi, "Adaptive Steering Control for Autonomous Lane Change Maneuver," in IEEE IV, Gold Coast, Australia, 2013

  27. C. Hatipoglu, U. Ozguner and K. A. Unyelioglu, "on Optimal Design of a Lane Change Controller," in Intelligent Vehicles Symposium, Detroit, MI, 1995

  28. Hatipoglu, C., Ozguner, U., Redmill, K.A.: Automated lane change controller design. IEEE Trans. Intell. Transp. Syst. 4(1), 13–22 (2003)

    Article  Google Scholar 

  29. C. Hatipoglu, K. Redmill and U. Ozguner, "Steering and Lane Change: a Working System," in IEEE Conference on Intelligent Transportation System, Boston, MA, 1997

  30. C. Wonshik and M. Tomizuka, "Vehicle Lane Change Maneuver in Automated Highway Systems," UC Berkeley, Berkeley, 1994

  31. Hsu, H.C.-H., Liu, A.: Kinematic design for platoon-lane-change maneuvers. IEEE Trans. Intel. Trans. Syst. 9(1), 185–190 (2008)

    Article  Google Scholar 

  32. R. Rai, B. Sharma and J. Vanualailai, "Real and Virtual Leader-Follower Strategies in Lane Changing, Merging and Overtaking Maneuvers," in APWC on CSE, Nadi, Fiji, 2015

  33. M. Goli and A. Eskandarian, "Evaluation of Lateral Trajectories with Different Controllers for Multi-Vehicle Merging in Platoon," in ICCVE, Vienna, Austria, 2014

  34. M. Goli and A. Eskandarian, "A Systematic Multi-Vehicle Platooning and Platoon Merging: Strategy, Control, and Trajectory Generation," in ASME, DSCC 2014, San Antonio, Texas, 2014

  35. Stankovic, S.S., Stanojevic, M.J., Siljak, D.D.: Decentralized overlapping control of a platoon of vehicles. IEEE Trans. Control Syst. Technol. 8(5), 816–832 (2000)

    Article  Google Scholar 

  36. J. K. Hedrick, D. McMahon, V. Narendran and D. Swaroop, "Longitudinal Vehicle Controller Design for IVHS Systems," in American Control Conference, Boston, MA, 1991

  37. J. Ploeg, B. T. M. Scheepers, E. v. Nunen and H. N. Nathan van de Wouw, "Design and experimental evaluation of cooperative adaptive cruise control," in IEEE Conference on Intelligent Transportation Systems, Washington, DC, 2011

  38. F. Morbidi, P. Colaneri and T. Stanger, "Decentralized Optimal Control of a Car Platoon with Guaranteed String Stability," in European Control Conference, Zurich, Switzerland, 2013

  39. W. Nelson, "Continuous-Curvature Paths for Autonomous Vehicles," in IEEE Int. Conf. Rob. Autom., 1989

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, DC, USA

    Mohammad Goli

  2. Department Head and Rebecca and Nicholas Des Champs Professor, Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA

    Azim Eskandarian

Authors
  1. Mohammad Goli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Azim Eskandarian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Goli.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

In addition to the control design analysis presented in the paper, the Appendix includes further conditions for stability of the platoon’s string.

8.1 Stability conditions for bilateral PD controller

The vehicle following stability and the string stability of controller in section 3.2 are detailed in [14].

Theorem 1: The dynamic Eq. (4) is stable if and only if

$$ {k}_{d,i}^r>{\tau}_i{k}_{p,i}^r $$

As for the platoon string stability, the following definition is adopted:

$$ {\left\Vert \frac{V_i}{V_{i-1}}\left( j\omega \right)\right\Vert}_{\infty}\le 1,\kern1.75em \forall \omega >0. $$

It is proved in [14], that if the following conditions are met, the platoon is string stable:

$$ {k}_{p,i}^r>\frac{\Delta _i^p}{\sqrt{2}}, $$
$$ {k}_{d,i}^r<\frac{0.25}{\tau_i}-0.5{\Delta }_i^d, $$
$$ {\left({k}_{d,i}^r\right)}^2>2{k}_{p,i}^r+{\Delta }_i^p+0.5{\Delta _i^p}^2 $$

8.2 String stability conditions for optimal controller

Considering the following definition sensitivity function as introduced in section 3.1.1:

$$ {\mathcal{S}}_i(s)=\frac{A_i(s)}{A_{i-1}(s)}\kern1em 2\le i\le \mathrm{N} $$

In the above definition acceleration is taken as the basis for string stability. The string stability condition can then be stated as:

$$ {\left\Vert {\mathcal{S}}_i\left( j\omega \right)\right\Vert}_{{\mathcal{H}}_{\infty }}\le 1\kern0.75em 2\le i\le \mathrm{N} $$

By modifying the proposition 1 in [38] to match the constant spacing policy used in this paper, the car platoon is string stable if the following two conditions are satisfied:

$$ {\left({k}_3-1\right)}^2-2\tau {k}_2-{k}_F^2\ge 0 $$
$$ {k}_1\left({k}_3-1\right)+{k}_1{k}_F\ge 0 $$

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goli, M., Eskandarian, A. Merging Strategies, Trajectory Planning and Controls for Platoon of Connected, and Autonomous Vehicles. Int. J. ITS Res. 18, 153–173 (2020). https://doi.org/10.1007/s13177-019-00188-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13177-019-00188-z

Keywords

Search

Navigation