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Journal of Intelligent & Robotic Systems

, Volume 88, Issue 2–4, pp 495–511 | Cite as

Tightly Bounding the Shortest Dubins Paths Through a Sequence of Points

  • Satyanarayana G. Manyam
  • Sivakumar Rathinam
  • David Casbeer
  • Eloy Garcia
Article

Abstract

This article addresses an important path planning problem for robots and Unmanned Aerial Vehicles (UAVs), which is to find the shortest path of bounded curvature passing through a given sequence of target points on a ground plane. Currently, no algorithm exists that can compute an optimal solution to this problem. Therefore, tight lower bounds are vital in determining the quality of any feasible solution to this problem. Novel tight lower bounding algorithms are presented in this article by relaxing some of the heading angle constraints at the target points. The proposed approach requires us to solve variants of an optimization problem called the Dubins interval problem between two points where the heading angles at the points are constrained to be within a specified interval. These variants are solved using tools from optimal control theory. Using these approaches, two lower bounding algorithms are presented and these bounds are then compared with existing results in the literature. Computational results are presented to corroborate the performance of the proposed algorithms; the average reduction in the difference between upper bounds and lower bounds is 80 % to 85 % with respect to the trivial Euclidean lower bounds.

Keywords

Dubins paths Curvature constrained paths Lower bounds Pontryagin’s minimum principle Dubins interval problem 

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Copyright information

© Springer Science+Business Media Dordrecht (outside the USA) 2017

Authors and Affiliations

  1. 1.Control Science Center of ExcellenceAir Force Research LaboratoryWPAFBUSA
  2. 2.Department of Mechanical EngineeringTexas A & M UniversityCollege StationUSA

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