Formation control for meter-scale UAVs

E.W. Justh and P.S. Krishnaprasad
Collaborators:
Fumin Zhang (University of Maryland, College Park)
Jeff Heyer, Larry Schuette, Jason Fox (Naval Research Laboratory, Washington, DC)

Project Background and Goals

We are studying novel control laws for meter-scale UAVs (unmanned aerial vehicles). We model vehicles as point particles traveling at unit speed and subject to steering (i.e., curvature) control, in the planar setting. The control laws we seek are steering laws which are functions of the relative positions and orientations of the vehicles. We then attempt to prove that these control laws lead to stable formation-maintaining behavior. Shape-space notions and a Lie group formulation of the dynamics play central roles in this work.

Methodology/Procedure

What distinguishes this work is an emphasis on the geometry that emerges from the assumption of constant-speed motion. In particular, we are led to consider gyroscopic forces of interaction, which conserve the kinetic energy of each particle. In mechanics, gyroscopic forces arise from vector potentials, so our work is in distinct contrast with the scalar synthetic potentials commonly used in robotics to navigate toward a target while avoiding obstacles. Although our focus is on the theoretical aspects of the formation control problem, we are also strongly influenced by practical issues - primarily by the requirement to develop laws which can be implemented simply and inexpensively in small, expendable vehicles with stringent payload constraints.

Project Results

We have three main results so far: one characterizes the set of all possible relative equilibria, independent of the specific control law; the second is a global convergence result for two vehicles with a specific control law; and the third is a nonlinear convergence result for a specific multi-vehicle control law. We are currently working on additional analysis for both the planar and three-dimensional setting, and on formulating and analyzing a continuum version of the models.

Significance

In addition to the UAV application, this work may have implications for biological swarming or schooling systems. From a practical point of view, one of the main strengths of our modeling approach for UAVs is that it seems to be a natural framework in which to address the issue of "steering cost." Steering (i.e., banking to change heading direction) for meter-scale UAVs leads to sideslip, so that additional thrust is required to recover altitude. Minimizing steering thus increases the time the UAV can spend in powered flight, as well as the range it can cover on its limited energy supply.
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justh@isr.umd.edu
Last Updated: May 28, 2003.