A solution for dubins path problem with uncertainties using world cup optimization and chebyshev polynomials

Abstract

In this paper, an efficient numerical approach is developed for solving the baseline problem with interval uncertainties. Interval arithmetic is also utilized for developing the proposed method in the presence of uncertainties with only lower and upper bounds of parameters. In the proposed method, the equation of motion, performance index, and boundary conditions are first changed into some algebraic equations. This process converts the problem into an optimization problem. The presented technique is based on an interval extension of Chebyshev polynomials where its coefficients are achieved by world cup optimization algorithm, as a new optimization algorithm. The proposed method approximates the control and state variables as a function of time. The proposed solution is based on state parameterization, such that the state variable is approximated by the proposed interval Chebyshev polynomials with unknown interval coefficients. Finally, by solving the baseline problem in the presence of interval uncertainties, the reliability and effectiveness of the proposed method are demonstrated.