Optimal Vehicle Trajectory Planning with Control Constraints and Recursive Implementation for Automated On-Ramp Merging

Y. Zhou, M.E. Cholette, A. Bhaskar, Edward Chin Shin Chung

Research output: Journal article publicationJournal articleAcademic researchpeer-review

75 Citations (Scopus)


This paper proposes a vehicle trajectory planning method for automated on-ramp merging. Trajectory planning tasks of an on-ramp merging vehicle and a mainline facilitating vehicle are formulated as two related optimal control problems. Rather than specifying the merge point via external computational procedures, the location and time that the on-ramp vehicle merges into the mainline are determined endogenously by the optimal control problem of the facilitating vehicle. Bounds on vehicle acceleration are explicitly considered. The Pontryagin Maximum Principle is applied to find the solutions of the optimal control problems. In order to accommodate the constantly changing external environment, the proposed optimal control method is subsequently implemented in a recursive planning framework. Because of the nature of the problem, the length of the planning horizon is time-varying, unlike the conventional model predictive control applications where the planning horizon is a fixed length. Numerical experiments are conducted to study the performances of the proposed methodology under the influence of different leading vehicle trajectories and with different lengths of the planning updating interval. In particular, an experiment involving a real-world leading vehicle trajectory and considering different traffic demand levels are presented. The proposed methodology performs well in these experiments and has demonstrated good potential in real-time applications.

Original languageEnglish
Article number8510865
Pages (from-to)3409-3420
Number of pages12
JournalIEEE Transactions on Intelligent Transportation Systems
Issue number9
Publication statusPublished - 1 Sept 2019


  • automated vehicles
  • maximum principle
  • on-ramp merging
  • optimal control
  • Trajectory planning

ASJC Scopus subject areas

  • Automotive Engineering
  • Mechanical Engineering
  • Computer Science Applications


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