Path generation for flying robots in mountainous regions

In this paper, a new path planning method is proposed to resolve the problem of two-dimensional terrain following flight of flying robots in mountainous regions. The performance criteria considered for this mission design could include either the minimum vertical acceleration or the minimum flying time. To impose the terrain following/terrain avoidance constraints, various approaches such as least square method, Fourier series method, Gaussian estimation method, and Chebyshev orthogonal polynomial are explored. The resulting optimal control problem is discretized by employing a numerical technique namely direct collocation and then transformed into a nonlinear programming problem. The efficacy of the proposed method is demonstrated by extensive simulations, and particularly, it has been verified that this method is able to produce a solution that satisfies all hard constraints of the underlying problem.