A state-constrained optimal control based trajectory planning strategy for cooperative freeway mainline facilitating and on-ramp merging maneuvers under congested traffic

Yue Zhou, Edward Chung, Ashish Bhaskar, Michael E. Cholette

Research output: Journal article publicationJournal articleAcademic researchpeer-review

42 Citations (Scopus)


This paper presents a trajectory planning strategy for connected automated vehicles (CAVs) to cooperatively carry out mainline facilitating (i.e. gap development) and on-ramp merging maneuvers. The trajectory planning tasks of the mainline facilitating vehicle and the merging vehicle are formulated as two related optimal control problems. The motivation behind the proposed strategy is to restrain a facilitating maneuver's impact on following traffic. To this end, the proposed strategy bounds the speed of the facilitating maneuver from below and meanwhile ensures that the task of gap development can still be fulfilled. Because of the existence of the speed bound, the optimal control problem of the facilitating vehicle becomes constrained in state, in addition to the control constraints. A Pontryagin Maximum Principle (PMP) with state constraints is applied to rigorously derive the analytical solution. The main difficulty of the analytical procedure exists in the fact that the first-order necessary condition on the extremality of the Hamiltonian cannot yield useful information on the property of the optimal control history with regard to making the optimal speed trajectory to satisfy the speed constraint. As a result, additional conditions have to be explored, notably the so-called “jump conditions”, among others. Taking advantage of the analytical solution, the proposed strategy is then implemented under a model predictive control framework. Simulation assessments of the proposed strategy are conducted at two levels – individual vehicle level and traffic flow level. At the individual vehicle level, the proposed strategy shows potential to reduce the risk of rear-end collision between the facilitating vehicle and the following vehicle, the most vulnerable pair of vehicles under the influence of gap development. At the traffic flow level, coupled with Aimsun, the proposed strategy is assessed under mixed traffic flow conditions, with various penetration rates of CAVs. The results show that it has potential to generate lower speed variations of traffic flow, a critical factor in traffic flow safety. Meanwhile it does not show negative impact on traffic efficiency in the simulation, and is likely to improve traffic efficiency in the real world. A sensitivity analysis of the effect of the facilitating maneuver's lower speed bound is also conducted. Although there exist several limitations with this study, it sheds some light on future research.

Original languageEnglish
Pages (from-to)321-342
Number of pages22
JournalTransportation Research Part C: Emerging Technologies
Publication statusPublished - Dec 2019


  • Connected automated vehicles
  • Cooperative on-ramp mering
  • Gap development
  • Pontryagin Maximum Principle
  • State-constrained optimal control
  • Traffic safety

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Transportation
  • Computer Science Applications


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