Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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Brachistochrone Minimum-Time Trajectory Control Using Neural Networks

신경회로망에 의한 Brachistochrone 최소시간 궤적제어

  • Choi, Young-Kiu (Department of Electrical Engineering, Pusan National University) ;
  • Park, Jin-Hyun (Dept. of Mechatronics Eng., Kyeognam National Univ. of Science and Technology)
  • Received : 2013.08.14
  • Accepted : 2013.10.14
  • Published : 2013.12.31
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Abstract

A bead is intended to reach a specified target point in the minimum-time when it travels along a certain curve on a vertical plane with the gravity. This is called the brachistochrone problem. Its minimum-time control input may be found using the calculus of variation. However, the accuracy of its minimum-time control input is not high since the solution of the control input is based on a table form of inverse relations for some complicated nonlinear equations. To enhance the accuracy, this paper employs the neural network to represent the inverse relation of the complicated nonlinear equations. The accurate minimum-time control is possible with the interpolation property of the neural network. For various final target points, we have found that the proposed method is superior to the conventional ones through the computer simulations.

Brachistochrone 문제는 중력장내의 수직평면에 존재하는 임의의 두점을 연결하는 곡선경로를 따라 bead가 움직일 때에 가장 빠른 곡선경로를 구하는 것이며, calculus of variation에 의해 최단시간제어량을 구할 수 있지만 매우 복잡한 비선형방정식의 역관계를 테이블 형태로 구해야 하므로 그 정확도가 높지 않다. 본 논문에서는 이러한 근사해의 정확도를 높이기 위해 신경회로망을 이용하여 비선형방정식의 역관계식을 표현하였고, 신경회로망의 보간 기능으로 인해 높은 정확도의 최단시간제어가 가능하였다. 여러 가지 최종목표점에 대한 컴퓨터 시뮬레이션을 통해서 본 논문에서 제안한 방법이 기존의 방법보다 우수함을 확인할 수 있었다.

Keywords

References

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  1. 최단강하선 문제를 위한 신경회로망 최적 제어 vol.18, pp.4, 2013, https://doi.org/10.6109/jkiice.2014.18.4.818