Parametrization of nonlinear trajectory for time optimal 2D path planning for Unmanned Aerial Vehicles

Abstract

This paper presents an effective path decision method to find a two-dimension path that is time optimal and obstacIe free using parametrization in Complex domain. Such a path is used only for moving forward vehicIes with constant velocity and non-holonomic kinematic constraints such as VA V (Vnmanned Aerial Vehicles). Each start and goal point of a vehicIe in a planar domain with randomly selected heading angle demonstrates this problem, wh ich is sometimes referred to as Dubins's circIe problems. Due to the nonlinearity of problems, researchers have recommended common approaches, incIuding optimal control using cost functions and numerical solutions of nonlinear functions. These approaches do involve additional restrictions that previous research has highlighted. However; the author here suggests a simpler, more effective and more generalized method, based on problems identified in complex domain using parameterization.Keywords-parametrization; complex domain; time optimal; unmanned aerial vehicle I. INTRODUCTlONPath-planning for the forward motion of non-holonomic vehicles is somewhat different from holonomic systems such as holonomic manipulators and ornni-directional mobile robots; in other words, simple control and decision schemes cannot be directly applied with success to vehicles with nonholonomic constraints. For example, two-wheel differential mobile robots or UA Vs work this way, because constraints such as minimum turning radius or curvature induced from constant velocity cannot be integrated to position level. In addition, its movement is only forward in the cases ofUA Vs. This geometrie problem is so called "piano-mover problem" in a configuration space such as a two-dimensional space. In this paper, we confine and solve this path-planning problem with simple kinematics of UA Vs using parametrization in Complex domain . B ACKGROUTNDPath-planning problems of non-holonomic vehicles could be categorized into three major groups according to approaches taken to solve them. The first one is calculusbased; the second, graph-based, and the last, uses numerical methods. The calculus-based path-planning method requires severe computationalloads [1]- [3]. The path-planning based

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