Brachistochrone on a 2D curved surface using optimal control and spline-based dem map data

Natasha C. Wright, Michael P. Hennessey, Cheri Shakiban

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Based on a bivariate spline representation of United States Geological Survey (USGS) digital elevation model (DEM) data, the brachistochrone on a 2D curved surface without friction was solved numerically using dynamic and control models in MATLAB® in conjunction with the Spline Toolbox for surface modeling. This extends in a natural manner previous work by several of the authors (Hennessey and Shakiban) on both the 1D and 2D curved surface brachistochrone using optimal control and resulting in a twopoint boundary value problem. DEM data permits an accurate representation of the surface in question (30 m resolution data for Lone Mountain in MT) and the Spline Toolbox provides a sufficiently smooth version of the surface, including access to spatial partial derivatives needed in the minimum-time control law. Step-by-step results are reported, including the surface representation details, the minimum-time route and travel time, evaluation of the generalized = 1 Legendre-Clebsch optimality condition, and comparison with competing routes, namely the constant yaw rate and constant bearing angle routes.

Original languageEnglish (US)
Title of host publicationASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012
Pages703-709
Number of pages7
DOIs
StatePublished - Dec 1 2012
Externally publishedYes
EventASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012 - Fort Lauderdale, FL, United States
Duration: Oct 17 2012Oct 19 2012

Publication series

NameASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012
Volume2

Other

OtherASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012
CountryUnited States
CityFort Lauderdale, FL
Period10/17/1210/19/12

Keywords

  • And DEM
  • Brachistochrone
  • MATLAB
  • Optimal control
  • Splines

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