Pacific Journal of Mathematics

Optimal paths for a car that goes both forwards and backwards.

J. A. Reeds and L. A. Shepp

Article information

Source
Pacific J. Math., Volume 145, Number 2 (1990), 367-393.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102645450

Mathematical Reviews number (MathSciNet)
MR1069892

Subjects
Primary: 49N55
Secondary: 53A04: Curves in Euclidean space 70Q05: Control of mechanical systems [See also 60Gxx, 60Jxx] 93C10: Nonlinear systems

Citation

Reeds, J. A.; Shepp, L. A. Optimal paths for a car that goes both forwards and backwards. Pacific J. Math. 145 (1990), no. 2, 367--393. https://projecteuclid.org/euclid.pjm/1102645450


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References

  • [1] E. J. Cockayne and G. W. C. Hall, Plane motion of particle subject to curvature constraints, SIAM J. Control, 13 (1975), 197-220.
  • [2] E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
  • [3] J. Dieudonne, Treatise on Analysis, vol. Ill, Academic Press, New York, 1972.
  • [4] L. E. Dubins, On curvesof minimal length with a constraint on average curvature and with prescribedinitial and terminal positions and tangents, Amer. J. Math., 79(1957), 497-516.
  • [5] L. E. Dubins, On plane curves with curvature, Pacific J. Math., 11 (1961), 471-482.
  • [6] W. H. Fleming, Functions of Several Variables, Addison-Wesley, Reading, Mass., 1966.
  • [7] M. G. Krein and A. A. Nudelman, The Markov Moment Problem and Extremal Problems, American Mathematical Society, Providence, 1977.
  • [8] A. A. Markov, Some examples of the solution of a special kind of problem on greatest and least quantities, (in Russian) Soobshch. Karkovsk. Mat. Obshch., 1(1887), 250-276.
  • [9] Z. A. Melzak, Plane motion with curvaturelimitations, J. Soc. Ind. Appl. Math., 9(1961), 422-432.