Journal of Scientific Computing

, Volume 54, Issue 2–3, pp 622–644 | Cite as

Optimal Trajectories of Curvature Constrained Motion in the Hamilton–Jacobi Formulation



We propose a PDE approach for computing time-optimal trajectories of a vehicle which travels under certain curvature constraints. We derive a class of Hamilton–Jacobi equations which models such motions; it unifies two well-known vehicular models, the Dubins’ and Reeds–Shepp’s cars, and gives further generalizations. Numerical methods (finite difference for the Reeds–Shepp’s car and semi-Lagrangian for the Dubins’ car) are investigated for two-dimensional domains and surfaces.


Viscosity Solution Optimal Path Jacobi Equation Jacobi Formulation Path Planning Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors thank Professors S. Osher, P. Souganidis and A. Vladimirsky for helpful discussions, and Dr. Y. Landa and Mr. H. Shen for taking part in the early stages of this project. Takei was supported by ONR Grants N00014-07-1-0810 and N00014-08-1-1119, and the CHASE MURI Grant 556016. Tsai was supported by a Sloan Fellowship, National Science Foundation Grants DMS-0914465, DMS-0914840, and a MURI sub-contract from Univ. of S. Carolina Grant No. W911NF-07-1-0185. Takei thanks Prof. Claire Tomlin and the Hybrid Systems Lab at UC Berkeley for their hospitality during the completion of this work.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer SciencesUC BerkeleyBerkeleyUSA
  2. 2.Department of MathematicsUniversity of TexasAustinUSA

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