TY - GEN

T1 - On the Existence and Uniqueness of Minimum Time Optimal Trajectory for a Micro Air Vehicle under Wind Conditions

AU - Iyer, Ram V.

AU - Arizpe, Rachelle

AU - Chandler, Phillip R.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70350138167&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03627-9_4

DO - 10.1007/978-3-642-03627-9_4

M3 - Conference contribution

AN - SCOPUS:70350138167

SN - 9783642036262

T3 - Lecture Notes in Control and Information Sciences

SP - 57

EP - 77

BT - Emergent Problems in Nonlinear Systems and Control

A2 - Thoma, M.

A2 - Allgower, F.

A2 - Morari, M.

ER -