Using Stream Functions for Complex Behavior and Path Generation

Abstract

This paper is summarized as follows: First, the previous work in stream function trajectories and the physical inspiration of incompressible fluid flow past a circular obstacle is presented. Then the algorithm is extended to include multiple obstacles, risk management, formations, and tactical maneuvers. Experimental results and analyses are provided, followed by a summary of the findings and ideas for future work. Background Potential Field Methods Potential field methods are straightforvard approaches to calculating a vector field, based on goal and obstacle locations, that the vehicle follows until it reaches the goal [5],[6],[7],[10], [1], and [12]. In these methods the vector field can develop localintermediate -equilibria vhere the vehicle appears to reach the goal state prematurely. Techniques that solve this problem produce plans that require a fully actuated robot (one that can move in any direction instantaneously) [7]. Most ground vehicles and heli- copters can folloxv these plans, but it is unreasonable to expect the same of a fixed wing aircraft because of the constraints on its movement, specifically the minimum turning radius and maximum and minimum velocity Stream Functions Stream functions are a subset of potential methods because they construct a vector field for the vehicle to folloxv to its destination. Unlike potential methods, hoxvever, stream functions do not require a fully actuated vehicle and all local equilibria are guaranteed to be saddle points, implying that the vehicle will akvays reach the goal