On the Existence and Uniqueness of Minimum Time Optimal Trajectory for a Micro Air Vehicle under Wind Conditions

Ram V. Iyer, Rachelle Arizpe, Phillip R. Chandler

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

An important subproblem in the area of cooperative control of multiple, autonomous, unmanned air vehicles is the determination of the minimum-time optimal paths for the agents to fly from one destination to the next. The tasks for the air vehicles are usually tightly coupled in time, and hence estimates of the times taken for each air vehicle to fly from one destination to the next is highly critical for correct assignment of tasks. In this article, we discuss the existence and uniqueness of minimum time solutions for the trajectory planning problem for a Micro Air Vehicle (MAV) under wind conditions. We show that there exists a minimum time solution for the trajectory planning problem with a minimum turn radius constraint for the air vehicle, and for a non-zero, time-varying wind vector field satisfying certain easily checked sufficient conditions. We also prove uniqueness for almost every combination of initial and final conditions in the case of a wind vector field that can vary with time but is constant in the spatial variable at each time instant.

Original languageEnglish
Title of host publicationEmergent Problems in Nonlinear Systems and Control
EditorsM. Thoma, F. Allgower, M. Morari
Pages57-77
Number of pages21
DOIs
StatePublished - 2009

Publication series

NameLecture Notes in Control and Information Sciences
Volume393
ISSN (Print)0170-8643

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