publication . Preprint . Conference object . 2006

Motion camouflage in three dimensions

Puduru Reddy; Justh, E. W.; Krishnaprasad, P. S.;
Open Access English
  • Published: 07 Mar 2006
Abstract
We formulate and analyze a three-dimensional model of motion camouflage, a stealth strategy observed in nature. A high-gain feedback law for motion camouflage is formulated in which the pursuer and evader trajectories are described using natural Frenet frames (or relatively parallel adapted frames), and the corresponding natural curvatures serve as controls. The biological plausibility of the feedback law is discussed, as is its connection to missile guidance. Simulations illustrating motion camouflage are also presented. This paper builds on recent work on motion camouflage in the planar setting [1]. [1] E.W. Justh and P.S. Krishnaprasad (2005). "Steering laws ...
Subjects
free text keywords: Mathematics - Optimization and Control, 93C10 (Primary), 93D30 (Secondary), Frenet–Serret formulas, Pursuer, Motion control, Missile guidance, Control theory, Motion camouflage, law.invention, law, Biological plausibility, Computer science

[1] A.J. Anderson and P.W. McOwan, “Model of a predatory stealth behavior camouflaging motion,” Proc. Roy. Soc. Lond. B Vol. 270, No. 1514, pp. 489-495, 2003. [OpenAIRE]

[2] A.J. Anderson and P.W. McOwan, “Motion camouflage team tactics,” Evolvability & Interaction Symposium (see http://www.dcs.qmul.ac.uk/˜aja/TEAM MC/team mot cam.html), 2003.

[3] R.L. Bishop, “There is more than one way to frame a curve,” The American Mathematical Monthly, Vol. 82, No. 3, pp. 246-251, 1975.

[4] T.S. Collett and M.F. Land, “Visual control of flight behaviour in the hoverfly, Syritta pipiens,” J. comp. Physiol., vol. 99, pp. 1-66, 1975. [OpenAIRE]

[5] K. Ghose, T. Horiuchi, P.S. Krishnaprasad and C. Moss, “Echolocating bats use a nearly time-optimal strategy to intercept prey,” PLoS Biology, to appear, 2006.

[6] P. Glendinning, “The mathematics of motion camouflage,” Proc. Roy. Soc. Lond. B, Vol. 271, No. 1538, pp. 477-481, 2004.

[7] E.W. Justh and P.S. Krishnaprasad, “Natural frames and interacting particles in three dimensions,” Proc. 44th IEEE Conf. Decision and Control, 2841-2846, 2005 (see also arXiv:math.OC/0503390v1). [OpenAIRE]

[8] E.W. Justh and P.S. Krishnaprasad, “Steering laws for motion camouflage,” preprint, 2005 (arXiv:math.OC/0508023). [OpenAIRE]

[9] A.K. Mizutani, J.S. Chahl, and M.V. Srinivasan, “Motion camouflage in dragonflies,” Nature, Vol. 423, p. 604, 2003.

[10] J.H. Oh and I.J. Ha, “Capturability of the 3-dimensional pure PNG law,” IEEE Trans. Aerospace. Electr. Syst., vol. 35, No. 2, pp. 491-503, 1999.

[11] N.A. Shneydor, Missile Guidance and Pursuit, Horwood, Chichester, 1998.

[12] S.H. Song and I.J. Ha,“A Lyapunov-like approach to performance analysis of 3-dimensional pure PNG laws,” IEEE Trans. Aerospace and Electronic Systems, Vol. 30, pp. 349-358, 1994.

[13] M.V. Srinivasan and M. Davey, “Strategies for active camouflage of motion,” Proc. Roy. Soc. Lond. B, Vol. 259, No. 1354, pp. 19-25, 1995.

[14] M.V. Srinivasan and S. Zhang, “Visual Motor Computations in Insects,” Ann. Rev. Neurosci., Vol. 27, pp. 679-696, 2004.

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Abstract
We formulate and analyze a three-dimensional model of motion camouflage, a stealth strategy observed in nature. A high-gain feedback law for motion camouflage is formulated in which the pursuer and evader trajectories are described using natural Frenet frames (or relatively parallel adapted frames), and the corresponding natural curvatures serve as controls. The biological plausibility of the feedback law is discussed, as is its connection to missile guidance. Simulations illustrating motion camouflage are also presented. This paper builds on recent work on motion camouflage in the planar setting [1]. [1] E.W. Justh and P.S. Krishnaprasad (2005). "Steering laws ...
Subjects
free text keywords: Mathematics - Optimization and Control, 93C10 (Primary), 93D30 (Secondary), Frenet–Serret formulas, Pursuer, Motion control, Missile guidance, Control theory, Motion camouflage, law.invention, law, Biological plausibility, Computer science

[1] A.J. Anderson and P.W. McOwan, “Model of a predatory stealth behavior camouflaging motion,” Proc. Roy. Soc. Lond. B Vol. 270, No. 1514, pp. 489-495, 2003. [OpenAIRE]

[2] A.J. Anderson and P.W. McOwan, “Motion camouflage team tactics,” Evolvability & Interaction Symposium (see http://www.dcs.qmul.ac.uk/˜aja/TEAM MC/team mot cam.html), 2003.

[3] R.L. Bishop, “There is more than one way to frame a curve,” The American Mathematical Monthly, Vol. 82, No. 3, pp. 246-251, 1975.

[4] T.S. Collett and M.F. Land, “Visual control of flight behaviour in the hoverfly, Syritta pipiens,” J. comp. Physiol., vol. 99, pp. 1-66, 1975. [OpenAIRE]

[5] K. Ghose, T. Horiuchi, P.S. Krishnaprasad and C. Moss, “Echolocating bats use a nearly time-optimal strategy to intercept prey,” PLoS Biology, to appear, 2006.

[6] P. Glendinning, “The mathematics of motion camouflage,” Proc. Roy. Soc. Lond. B, Vol. 271, No. 1538, pp. 477-481, 2004.

[7] E.W. Justh and P.S. Krishnaprasad, “Natural frames and interacting particles in three dimensions,” Proc. 44th IEEE Conf. Decision and Control, 2841-2846, 2005 (see also arXiv:math.OC/0503390v1). [OpenAIRE]

[8] E.W. Justh and P.S. Krishnaprasad, “Steering laws for motion camouflage,” preprint, 2005 (arXiv:math.OC/0508023). [OpenAIRE]

[9] A.K. Mizutani, J.S. Chahl, and M.V. Srinivasan, “Motion camouflage in dragonflies,” Nature, Vol. 423, p. 604, 2003.

[10] J.H. Oh and I.J. Ha, “Capturability of the 3-dimensional pure PNG law,” IEEE Trans. Aerospace. Electr. Syst., vol. 35, No. 2, pp. 491-503, 1999.

[11] N.A. Shneydor, Missile Guidance and Pursuit, Horwood, Chichester, 1998.

[12] S.H. Song and I.J. Ha,“A Lyapunov-like approach to performance analysis of 3-dimensional pure PNG laws,” IEEE Trans. Aerospace and Electronic Systems, Vol. 30, pp. 349-358, 1994.

[13] M.V. Srinivasan and M. Davey, “Strategies for active camouflage of motion,” Proc. Roy. Soc. Lond. B, Vol. 259, No. 1354, pp. 19-25, 1995.

[14] M.V. Srinivasan and S. Zhang, “Visual Motor Computations in Insects,” Ann. Rev. Neurosci., Vol. 27, pp. 679-696, 2004.

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