A Comprehensive Differential Game Theoretic Solution to a Game of Two Cars

Ritwik Bera (), Venkata Ramana Makkapati () and Mangal Kothari ()
Additional contact information
Ritwik Bera: Indian Institute of Technology Kanpur
Venkata Ramana Makkapati: Georgia Institute of Technology
Mangal Kothari: Indian Institute of Technology Kanpur

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 3, No 12, 818-836

Abstract: Abstract In this paper, a pursuit-evasion game involving two non-holonomic agents is examined using the theory of differential games. It is assumed that the two players move on the Euclidean plane with fixed but different speeds and they each have a lower bound on their achievable turn radii. Both players steer at each instant by choosing their turn radii value and directions of turn. By formulating the game as a game of kind, we characterize the regions of initial conditions that lead to capture as well as the regions that lead to evasion, when both the players play optimally. The game is then formulated as a game of degree to obtain time-optimal paths for the pursuer and evader inside a capture region. Besides, all possible scenarios are considered for both players that differ in speed ratios and maneuverability constraints. Solutions are provided for those cases using appropriate simulation parameters, which aid in understanding the characteristics of the game of two cars under a wide range of constraints.

Keywords: Differential games; Min–Max strategies; Non-holonomic constraints; Barriers; Collision avoidance (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-017-1134-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1134-z

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-017-1134-z

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().