Share This Article:

A Video Game Based on Elementary Differential Equations

Abstract Full-Text HTML XML Download Download as PDF (Size:194KB) PP. 250-262
DOI: 10.4236/ica.2013.43030    4,842 Downloads   8,075 Views  

ABSTRACT

In this paper a prey-predator video game is presented. In the video game two predators chase a prey that tries to avoid the capture by the predators and to reach a location in space (i.e. its “home”). The prey is animated by a human player (using a joypad), the predators are automated players whose behaviour is decided by the video game engine. The purpose of the video game is to show how to use mathematical models to build a simple prey-predator dynamics representing a physical system where the movements of the game actors satisfy Newton’s dynamical principle and the behaviour of the automated players simulates a simple form of intelligence. The game is based on a simple set of ordinary differential equations. These differential equations are used in classical mechanics to describe the dynamics of a set of point masses subject to a force chosen by the human player, elastic forces and friction forces (i.e. viscous damping). The software that implements the video game is written in C++ and Delphi. The video game can be downloaded from:

http://www.ceri.uniroma1.it/ceri/zirilli/w9

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Giacinti, F. Mariani, M. Recchioni and F. Zirilli, "A Video Game Based on Elementary Differential Equations," Intelligent Control and Automation, Vol. 4 No. 3, 2013, pp. 250-262. doi: 10.4236/ica.2013.43030.

References

[1] F. Bellotti, R. Berta and A. De Gloria, “Designing Effec tive Serious Games: Opportunities and Challenges for Research,” Special Issue: Creative Learning with Serious Games, Journal of Emerging Technologies in Learning, Vol. 5, No. 3, 2010, pp. 22-35.
[2] F. Bellotti, R. Berta, A. De Gloria and L. Primavera, “Adaptive Experience Engine for Serious Games,” IEEE Transactions on Computational Intelligence and AI in Games, Vol. 1, No. 4, 2009, pp. 264-280. doi:10.1109/TCIAIG.2009.2035923
[3] M. Athans, “On Optimal Allocation and Guidance Laws for Linear Interception and Rendez Vous Problems,” IEEE Transactions on Aerospace and Electronics Sys tems, Vol. 7, No. 5, 1971, pp. 843-853. doi:10.1109/TAES.1971.310324
[4] R. Isaacs, “Differential Games,” Dover Publication, New York, 1999.
[5] A. A. Melikyan, “Primary Strategies of Simple Pursuit in Differential Games on Two-Sided Plane Figures,” Journal of Applied Mathematics and Mechanics, Vol. 68, No. 4, 2004, pp. 545-554. doi:10.1016/j.jappmathmech.2004.07.007
[6] V. Kokkeviv, “Practical Physics for Articulated Charac ters,” Game Developers Conference, San Jose, 24-26 2004, pp. 1-16. http://www.red3d.com/cwr/games/#ai-papers
[7] I. Millington, “Game Physics Engine Developments,” El sevier Inc., San Francisco, 2007.
[8] S. I. Nishimura and T. Ikegami, “Emergence of Collective Strategies in a Prey-Predator Game Model,” Artificial Life, Vol. 3, No. 4, 1997, pp. 243-260. doi:10.1162/artl.1997.3.4.243
[9] I. Millington, “Artificial Intelligence for Games,” Morgan Kaufmann Publications, Elsevier, San Francisco, 2006.
[10] V. Y. Glizer and V. Turetsky, “Complete Solution of a Differential Game with Linear Dynamics and Bounded Controls,” Applied Mathematics Research Express, Vol. 2008, No. 1, 2008, 49 p. doi:10.1093/amrx/abm012

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.