Steering laws for motion camouflage
E.W Justh
P.S Krishnaprasad
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Steering laws for motion camouflage
BY E. W. JUSTH1 AND P. S. KRISHNAPRASAD1,2,*
1Institute for Systems Research, and 2Department of Electrical and Computer
Engineering, University of Maryland, College Park, MD 20742, USA
Motion camouflage is a stealth strategy observed in nature. We formulate the problem as
a feedback system for particles moving at constant speed, and define what it means for
the system to be in a state of motion camouflage. (Here, we focus on the planar setting,
although the results can be generalized to three-dimensional motion.) We propose a
biologically plausible feedback law, and use a high-gain limit to prove the accessibility of
a motion-camouflage state in finite time. We discuss connections to work in missile
guidance. We also present simulation results to explore the performance of the
motioncamouflage feedback law for a variety of settings.
1. Introduction
Motion camouflage is a stealth strategy employed by various visual insects and
animals to achieve prey capture, mating or territorial combat. In one type of
motion camouflage, the predator camouflages itself against a fixed background
object so that the prey observes no relative motion between the predator and the
fixed object. In the other type of motion camouflage, the predator approaches the
prey such that from the point of view of the prey, the predator always appears to
be at the same bearing. (In this case, we say that the object against which the
predator is camouflaged is a point at infinity.) The motion-camouflage strategy
serves to minimize motion parallax cues that moving prey would be able to extract
from the apparent relative motion of objects at various distances (Srinivasan &
Davey 1995). For example, insects with compound eyes are quite sensitive to
optical flow (which arises from the transverse component of the relative velocity
between the predator and the prey), but are far less sensitive to looming (which
arises from the component of the relative velocity between the predator and the
prey along the line joining them). More broadly, such interactions may also apply
to settings of mating activity or territorial manoeuvre as well. In Srinivasan &
Davey (1995), it was suggested that the data on visually mediated interactions
between two hoverflies Syritta pipiens, obtained earlier by Collett & Land (1975),
support a motion-camouflage hypothesis. Later, Mizutani et al. (2003), observing
the territorial aerial manoeuvres of dragonflies Hemianax papuensis, concluded
that the flight pattern is motivated by motion camouflage (see fig. 1 in Mizutani
et al. 2003). See also Srinivasan & Zhang (2004) for a review of related themes in
insect vision and flight control.
Motion camouflage can be used by a predator to stealthily pursue the prey, but
a motion-camouflage strategy can also be used by the prey to evade a predator.
The only difference between the strategy of the predator and the strategy of the
evader is that the predator seeks to approach the prey while maintaining motion
camouflage, whereas the evader seeks to move away from the predator while
maintaining motion camouflage. Besides explaining certain biological pursuit
strategies, motion camouflage may also be quite useful in certain military
scenarios (although the predator and prey labels may not be descriptive). In
some settings, as is the case in Collett & Land (1975), Srinivasan & Davey (1995)
and Mizutani et al. (2003), it is more appropriate to substitute the labels
shadower and shadowee for the predatorprey terminology.
The essential geometry of motion camouflage (see 2a) is not limited to
encounters between visual insects. In a recent work on the neuroethology of
insect-capture behaviour in echolocating bats, a strategy geometrically
indistinguishable from motion camouflage is observed (Ghose et al. 2006).
In this work, we take a structured approach to derive feedback laws for motion
camouflage, which incorporates biologically plausible (vision) sensor measurements.
We model the predator and prey as point particles moving at constant (but different)
speeds, and subject to steering (curvature) control. For an appropriate choice of
feedback control law for one of the particles (as the other follows a prescribed
trajectory), a state of motion camouflage is then approached as the system evolves.
(In the situation where the predator follows a motion-camouflage law, and the speed
of the predator exceeds the speed of the prey, the predator is able to pass close to the
prey in finite time. In practice, once the predator is sufficiently close to the prey, it
would change its strategy from a pursuit strategy to an intercept strategy.)
What distinguishes this work from an earlier study on motion-camouflage
trajectories in Glendinning (2004) is that we present biologically plausible feedback
laws leading to moti (...truncated)