2004 5th Asian Control Conference Biologically Inspired Guidance for Motion Camouflage Nicole E Carey*, Jason J Ford+ and Javaan S Chahlt *Centre for visual SCknCeS, Research school of Biologkal sciences, Australian National University. e-mail: [email protected] Weapons Systems Division, Defence Science and Technology Organisation, and the School of Information Technology and Electrical Engineering, the Australian Deknce Force Academy. e-mail: [email protected] Weapons Systems Division, Defence Science and Technology Organisation, and the Centre for Visual Sciences, Research SchooI of Biological Sciences, Australian National University. e-mail: javaan@~iorobotics.anu.edu.au Abstract locity cues across the retina. “The dragonfly ... bas] a neural circuit capable of signalling information about In the insect, world, dragonflies are considered to be moving objects separately from information about a amongst thc best aerial predators, and are known to complex moving background” [?I, Thus in order to use motion camouflage techniques to mask their ap approach or retreat from another dragonfly (or prey) proach. How they accomplish this remains undiscov- unseen, they have evolved a technique that allows them ered, but using traditional guidance approaches we can to appear stationary in angular location relative to the attempt to simulate this behaviour. second dragonfly. This technique is known as motion camouflage. First observed in hoverflies by Srinivasan In this paper, we consider the motion camouflage and Davey [ll],its use was noted amongst dragonffy guidance problem within a linear quadratic Gaussian populations by Mizutani, et al [9]. framework and demonstrate that the resulting guid- ance strategy is effective in achieving the camouflage The applicability of motion camouflage behaviour to requirements. autonomous system control is immediately apparent. For example, low observability behaviours have obvi- ous military applications in unmanned-aerial vehicles (UAVs) and guided missiles’[15]. There are also likely 1 Introduction to be civilian applications that wilI benefit from inves- tigation of such motion camouflage techniques. Robotic vision and navigation has a long tradition of Previous research in this area have included neural- taking inspiration from the insect world [13]. The network based approaches that have attempted to insect visual system is both fast and precise, their mimic these observed motion camouflage behaviours simple nervous systems accomplishing difficult naviga- in simulation [I]. However, implementing neural net- tional tasks with apparent ease. Robotic implementa- works generally involves a training stage, in which the tions which take advantage of the behaviour of bees, proposed controI system learns the desired behaviours. grasshoppers and ants already exist [lo, 131. Now the This leads to a guidance strategy tailored to the partic- study of dragonfly predation has revealed a number of ular training set, with unknown applicability to other potentially useful tactics that might be used by au- situations and engagements, making the neural-based tonomous systems. approach somewhat uncertain and inefficient. Hence, Dragonfiies are the best and fastest aerial predators solutions such as that presented in [l] provide only lim- in the insect kingdom, and over the last 300 million ited insight into the overall strategy of the insect. years have evolved incredibly sophisticated flight and We believe a more useful approach is to formulate the combat techniques. Having exquisite directional selec- probIem in a traditional optimal control form [4], In tivities, dragonflies are most responsive to angular ve- 1793 this framework, the aim would be to design an opti- mal control policy for the predatar which ensures cer- tain constraints (motion camouflage requirements) are met, whilst achieving an overall objective (for exam- ple, attack, tracking, or escape). This optimal control approach is not necessarily expected to represent the mechanism used by the insect, but simply provides a useful frame in which to develop strategies that mimic the observed insect behaviour, and perhaps provide some insight into the essential features of the problem. The key contribution of this paper is to describe and solve several varieties of motion camouflage behaviours within a linear quadratic Gaussian (LQGJ framework [8], and to find optimal strategies for achieving both the motion constraints and the overdI engagement re- quirements. Some discussion of realistic control con- straints, measurement and higher-level control issues Figure 1: Predator and prey positions in absolute and is also provided. relative reference frames. Also shown is one The paper is organised as follows: In Section 2, the camouflage constraint line dynamics of the motion camouflage problem are de- scribed through discrete-time dynamics. In Section 3 the motion camouflage problem is defined as an opti- We assume that the motion of both the predator and mal control problem, in the LQG framework, and the prey can be represented using linear dynamics. Hence, optimal solution is presented. Motion tracking and for k = 1,2,. , the following discrete-time state equa- camouflaged escape problems are also mentioned. In tion representation of the predator and prey dynamics Section 4 some illustrative simulations are performed i:i proposed: using the developed guidance strategies. Finally, in Section 5, some concluding remarks are made. where 2 Predator-Prey Dynamics of Motion 1OAt 0 00 A state-space formulation of motion camouflage en- 01 0 At gagements is described here. A motion camouflage en- 00 igagement is assumed to involve two players (which we 0 'oped framework can equally be applied to other pur- The relative dynamics of the predator-prey engage- suit games; including the missile (predator) and target ment can hence be written as: (prey) probIem. For the sake of simplicity, the predator-prey dynam- ics are considered only in two Cartesian dimensions, but the principles can easily be extended to the three Remark: . dimensional case. 1. Unlike a missile guidance problem.[3], the preda- The dynamics are described in an Euclidean reference tor is allowed control over both lateral and longi- plane. The predator position and velocity is repre- tudinal accelerations. That is, control of forward sented by [zp,ypl' and [kp,yp]' respectively, where velocity is assumed possible, which is also bio- I is the transpose symboI. Simiiarly, the prey (tar- logically realistic. Effective motion camoufiage get) position and velocity are represented by [zT,3'1' does not seem viable without control of forward and [5=,GT]' respectively. We introduce a predator velocity. state of Xp = [zp,gp,ip,3ip]',and a prey state XT = [zT,gT,iT,yT]'.The control problem will be 2. The prey dynamics (1) describe the trivial case e examined in term of it relative state X" = Xp- XT, where the prey has a constant heading and veloc- ' (see Figure 1). ity. In practical situations, the prey may actually 1794 manoeuvre; however these manoeuvres are typi- as follows: cally not known in advance to the predator. In a manner similar to the development of the stan- dard proportional navigation (PN) guidance law [15], we solve the motion camouflage problem as- For a pursuit where the focal point is taken to be at suming no prey manoeuvres and then examine infinity, the constraint lines have constant slope, the performance of the resulting guidance alge rithm when prey manoeuvres are present. 2.1 Motion Camodage Constraints Hence, we note that on a perfectIy camouflaged path, The objective of this paper is to develop guidance in terms of the relative state, strategies for a predator that achieve engagement tra- jectories in which the predator appears stationary over y: = gkx? for k 2 1. time from the prey’s perspective, in an angular sense. This angular camouflage corresponds to constraining Perfect camouflage is not always possible, or at least re- the motion of the predator to particular lines in 2D quires undesirably excessive control actions, so we rep- space, which will be termed camouflage constraint lines resent the desire to remain close to these CCLs through (CCLs). They are defined as the line between the PO- the following soft running constraint term, sition of the prey [xl,z/r]’ at each time instant and T the chosen stationary focal point of the engagement, (7) ’ [fz, far]’,The slope of these CCLs provides sufficient kd information for the predator to adequately camouflage its motion. where T is the time of intercept. It is assumed that T is known in advance by the predator. Assuming knowl- At this point, the precise formulation of the prob- edge of T is admittedly somewhat unrealistic, but is a lem diverges depending on the particular type of en- common strategy in missile guidance problems [15]. gagement being modelled. Although Srinivasan, et d, [ll]distinguish between motion camouflage manoeu- It is also desirable that the energy of the control ac- vres depending upon the position of the focal point, tion required not be excessive, and that the predator from our perspective these distinctions are trivial. For intercept the prey at time T. this paper, the distinguishing feature between the dif- These motion camouflage and control energy require- ferent algorithms will be the ultimate goal of the en- ments we used to propose a performance index for the gagement, whether that be pursuit, tracking or escape. motion camouflage problem. The cost function for the can From