Formation control for meter-scale UAVs
E.W. Justh and P.S. Krishnaprasad
- 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.
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.
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.
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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Last Updated: May 28, 2003.