Steering laws for motion camouflage

Abstract

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 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.Comment: 8 page

Symmetry and reduction in collectives: cyclic pursuit strategies

“…Planar self-steering particles with position vectors r i are described by the curve and moving frame equations [1]…”

“…The resulting shape dynamics is cast in a natural redundant parametrization of shape space tailored to the setting of SE (2). This parametrization fits well with anticipated singularities in feedback laws, such as one associated with motion camouflage (MC) or motion parallax nulling [1]. In §3, we explicitly state the dyadic pursuit strategy we call constant bearing (CB)-of central interest in this paper-using a suitable contrast function to fix a constraint on joint state space.…”

“…For a particular choice of parameter, the CB strategy and feedback law specialize to the case of classical pursuit (CP), a topic with a rich mathematical heritage and continuing interest [3]. For comparison, we also note the motion camouflage feedback law [1]. In the biological realm, it is known that the peregrine falcon, a superior aerial predator, displays a prey-capture behaviour known as stoop, distinguished by a spiral trajectory towards prey.…”

Guidance Laws for Autonomous Underwater Vehicles

“…Hence, approaching predators can appear stationary to such prey by minimizing the relative lateral motion, only changing in size when closing in for the kill. Interestingly, this behavior can be directly related to the classical guidance laws from the missile literature (Justh & Krishnaprasad 2006). Also, such guidance laws have been successfully applied since the early 1990s to avoid computationallydemanding optimization methods associated with motion planning for robot manipulators operating in dynamic environments (Piccardo & Honderd 1991).…”

A Note on a Camouflage Pursuit Problem

“…Recently, an interesting article by Duncan Graham-Rowe [1] in the New Scientist, has explained why this strategy is now also seen as a very effective way of using missile defence systems. In two papers Justh and Krishnaprasad [4] and Wei, Justh, and Krishnaprasad [5] deal with the biological steering laws and the various pursuit strategies that are used by insects and defence systems in detail as well as giving a good overview of the subject and relevant references to the literature.They derive some approximate mathematical results which are based on these steering laws. In a series of very interesting articles Glendinning [2], [3] discussed the hidden or camouflage pursuit problem from a mathematical point of view.…”