Steering laws for motion camouflage

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Dec 2006

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 motion-camouflage feedback law for a variety of settings.

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Steering laws for motion camouflage

E.W Justh P.S Krishnaprasad - Email alerting service To subscribe to Proc. R. Soc. A go to: http://rspa.royalsocietypublishing.org/subscriptions 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)


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E.W Justh, P.S Krishnaprasad. Steering laws for motion camouflage, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006, pp. 3629-3643, 462/2076, DOI: 10.1098/rspa.2006.1742