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 In the insect, world, dragonflies are considered to be amongst thc best aerial predators, and are known to use motion camouflage techniques to mask their a p proach. How they accomplish this remains undiscovered, but using traditional guidance approaches we can attempt to simulate this behaviour.
In this paper, we consider the motion camouflage guidance problem within a linear quadratic Gaussian framework and demonstrate that the resulting guidance strategy is effective in achieving the camouflage requirements.
1 Introduction Robotic vision and navigation has a long tradition of taking inspiration from the insect world [13]. The insect visual system is both fast and precise, their simple nervous systems accomplishing difficult navigational tasks with apparent ease. Robotic implementations which take advantage of the behaviour of bees, grasshoppers and ants already exist [lo, 131. Now the study of dragonfly predation has revealed a number of potentially useful tactics that might be used by autonomous systems. Dragonfiies are the best and fastest aerial predators in the insect kingdom, and over the last 300 million years have evolved incredibly sophisticated flight and combat techniques. Having exquisite directional selectivities, dragonflies are most responsive to angular ve-
locity cues across the retina. “The dragonfly ... bas]a neural circuit capable of signalling information about moving objects separately from information about a complex moving background” [?I, Thus in order to approach or retreat from another dragonfly (or prey) unseen, they have evolved a technique that allows them to appear stationary in angular location relative to the second dragonfly. This technique is known as motion camouflage. First observed in hoverflies by Srinivasan and Davey [ll],its use was noted amongst dragonffy populations by Mizutani, et al [9]. The applicability of motion camouflage behaviour to autonomous system control is immediately apparent. For example, low observability behaviours have obvious military applications in unmanned-aerial vehicles (UAVs) and guided missiles’[15]. There are also likely to be civilian applications that wilI benefit from investigation of such motion camouflage techniques. Previous research in this area have included neuralnetwork based approaches that have attempted to mimic these observed motion camouflage behaviours in simulation [I]. However, implementing neural networks generally involves a training stage, in which the proposed controI system learns the desired behaviours. This leads to a guidance strategy tailored to the particular training set, with unknown applicability to other situations and engagements, making the neural-based approach somewhat uncertain and inefficient. Hence, solutions such as that presented in [l]provide only limited insight into the overall strategy of the insect.
We believe a more useful approach is t o formulate the probIem in a traditional optimal control form [4],In 1793
this framework, the aim would be to design an optimal control policy for the predatar which ensures certain constraints (motion camouflage requirements) are met, whilst achieving an overall objective (for example, 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 requirements. Some discussion of realistic control constraints, measurement and higher-level control issues is also provided.
Figure 1: Predator and prey positions in absolute and relative reference frames. Also shown is one camouflage constraint line
The paper is organised as follows: In Section 2, the dynamics of the motion camouflage problem are described through discrete-time dynamics. In Section 3 the motion camouflage problem is defined as an optimal control problem, in the LQG framework, and the optimal solution is presented. Motion tracking and camouflaged escape problems are also mentioned. In Section 4 some illustrative simulations are performed using the developed guidance strategies. Finally, in Section 5, some concluding remarks are made.
We assume that the motion of both the predator and prey can be represented using linear dynamics. Hence, for k = 1 , 2 , . . . , the following discrete-time state equation representation of the predator and prey dynamics i:i proposed:
where
2 Predator-Prey Dynamics of Motion
1 O A t
A state-space formulation of motion camouflage engagements is described here. A motion camouflage enigagement is assumed to involve two players (which we
0 1
0
0 0
0
0
0 0
At
The relative dynamics of the predator-prey engagement can hence be written as:
'oped framework can equally be applied to other pursuit games; including the missile (predator) and target (prey) probIem.
For the sake of simplicity, the predator-prey dynamics are considered only in two Cartesian dimensions, but the principles can easily be extended to the three . dimensional case.
Remark:
T h e dynamics are described in an Euclidean reference plane. The predator position and velocity is represented by [zp,ypl' and [kp,yp]' respectively, where I i s the transpose symboI. Simiiarly, the prey (target) position and velocity are represented by [zT,31'' and [5=,GT]' respectively. We introduce a predator and a prey state state of X p = [zp,gp,ip,3ip]', XT = [zT,gT,iT,yT]'. The control problem will be examined in t e r m of it relative state X" = X p - XT, ' (see Figure 1). e
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1. Unlike a missile guidance problem.[3], the predator is allowed control over both lateral and longitudinal accelerations. That is, control of forward
velocity is assumed possible, which is also biologically realistic. Effective motion camoufiage does not seem viable without control of forward velocity. 2. The prey dynamics (1) describe the trivial case where the prey has a constant heading and velocity. In practical situations, the prey may actually
manoeuvre; however these manoeuvres are typically not known in advance to the predator. In a manner similar to the development of the standard proportional navigation (PN) guidance law [15], we solve the motion camouflage problem assuming no prey manoeuvres and then examine the performance of the resulting guidance alge rithm when prey manoeuvres are present.
as follows:
For a pursuit where the focal point is taken to be at infinity, the constraint lines have constant slope,
2.1 Motion C a m o d a g e Constraints The objective of this paper is to develop guidance strategies for a predator that achieve engagement trajectories in which the predator appears stationary over time from the prey’s perspective, in an angular sense. This angular camouflage corresponds to constraining the motion of the predator to particular lines in 2D space, which will be termed camouflage constraint lines (CCLs). They are defined as the line between the POsition of the prey at each time instant and the chosen stationary focal point of the engagement, [fz, far]’,The slope of these CCLs provides sufficient information for the predator to adequately camouflage its motion.
Perfect camouflage is not always possible, or at least requires undesirably excessive control actions, so we represent the desire to remain close to these CCLs through the following soft running constraint term,
At this point, the precise formulation of the problem diverges depending on the particular type of engagement being modelled. Although Srinivasan, et d, [ll]distinguish between motion camouflage manoeuvres depending upon the position of the focal point, from our perspective these distinctions are trivial. For this paper, the distinguishing feature between the different algorithms will be the ultimate goal of the engagement, whether that be pursuit, tracking or escape.
It is also desirable that the energy of the control action required not be excessive, and that the predator intercept the prey at time T.
Hence, we note that on a perfectIy camouflaged path, in terms of the relative state, y:
[xl,z/r]’
T
(7) k d
’
From an optimal control perspective, it seems more natural to pose the problem using a Cartesian reference frame. However dragonflies and other animals or insects axe unlikely to operate in this stationary absolute frame, but will more probably use something akin to a polar reference frame, with themselves as the moving centre [SI.For these reasons, the motion camouflage problem will first be solved in Cartesian space, then the simulations will be modified to achieve a more biologically realistic study in Section 4.
3 Problem Formulation and Solution
In this section, the motion camouflage problem will be posed within the linear quadratic Gaussian (LQG) hamework. 3.1 Performance Index for Motion Camadage We begin by determining the slopes of the required camouflage constraint lines shown in Figure 1. For a pursuit where the focal point is not at infinity, the constraint lines at each time interval, gk, have slopes
= gkx? for k 2 1.
where T i s the time of intercept. It is assumed that T is known in advance by the predator. Assuming knowledge of T is admittedly somewhat unrealistic, but is a common strategy in missile guidance problems [15].
These motion camouflage and control energy requirements we used to propose a performance index for the motion camouflage problem. The cost function for the problem can then be written: T-1
where
and yx is a weighting factor used to describe the importance of the camouflage requirement relative to the control energy requirement. The dynamics (3) and performance index (8) define a linear quadratic problem to which standard techniques can be applied [4]. 3.2 Optimal Motion Camouflage Guidance From [4], the optimd control solution to the linear quadratic problem is uk = -Kkxf
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(9)
2. The motion camouflage strategy developed in this paper assumes that the predator has knowledge of the correct time-horizon for the engagement. However, in the missile guidance context, this type of time-horizon assumption is known to be invalid [33. In dragonfly engagements, it is not yet known how the insect might estimate this required information. The standard time-togo estimate of range divided by the range rate, see [15,3], does not seems appropriate for the developed motion camouflage guidance law because the trajectory is not direct to the prey [3].
where Kk is given by
Kk = [(Bp)'pkBp+R]I' (Bp)'phA
(10)
and Pk is given by the appropriate discretetime E c cati equation solved backwards in time,
PN = Q N Pk-1 =A'[pk -
(( B P ) ' 9 E p + R)-'( Bp)'pk]A (11)
+Qk--l.
3.3 Other Engagement Goals 3.3.1 Tracking: Dragonflies have been observed to fly in tandem during territorial disputes, perhaps to prove aerial and tactical superiority. The challenger will attempt to match or outperform the others' manoeuvres. The goal whilst tracking another dragonfly is for the challenger to remain a t a fixed distance from the other insect, and the cost is determined by how far the challenger deviates from this desired vector. , The tandem or tracking flight problem can again be considered within an LQG framework. The requirement to remain a t a fixed distance &om the prey can be represented by introducing a new relative state, X Q , offset from the prey location as foiIows:
xo = X R + Id,,
d,, 0,OJ'
(12)
where [d,, d,]' is the desired displacement vector.
A guidance strategy can then be developed as a standard infinite-horizon LQG tracking problem. 3.3.2 Escape: A third type of behaviour observed in dragonfly engagements is camouflaged escape. In a similar manner to camouflaged attack, the prey retreats from the predator so that it appears at a 'constant angular location.
4 Results 4.1 General Example: Pursuit
Simulation studies of the proposed motion camouflage guidance were first performed in the setting of a generic pursuit problem, without the consideration of realistic biological constraints. Using a weighting factor of yx = 1 x lo8, and initial prey and predator states of [loo, -10,400,2500]' and [0,0,2500,450]' respectively, the proposed motion camouflage guidance algorithm was used to guide the predator to a non-manoeuvring target. Figure 2 shows the resulting camouflaged trajectories when the initial location of the predator, (0, 0), is used as the focal point. Figure 4 shows the resulting camouflaged trajectories when a point between the predator and the prey, (-45, -1), is used as a focal point. The algorithm will work irregardless of the choice of focal point. However, since Srinivasan, et al [ll] demonstrated that the fscal point does ndt have to correspond t o a real object, just a point in space, it seems logical to choose a point along the initial predator / prey sight line. 36
This escape behaviour is the subject of current investigations and is not considered further here.
..I
25
Remarks: Engagements between two dragonflies have been observed to involve periods of one engagement behaviour before a distinct change to another behaviour. For example, initially one dragonfly may use a tracking strategy, presumably to assess aerial superiority, before the tactics change to a motion camouflaged attack. At other periods the same dragonfly might perform the prey role in the encounter. The issue of designing a higher-level controller that selects the appropriate guidance strategy for each dragonfly in an encounter (tracking, attack or escape) cam probably be considered within a dynamic game framework
PI.
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Figure 2: Motion camouflage: the focal point is
at
the
predatbr's initid position.
The deviations of the predator from the C C L slopes
to exhibit types of manoeuvres that have also been observed in dragonfly prey. Redistically representing in simulation the likely nature of the predator measurement process is a more difficult task.
for the above engagement can be seen in Figure 3.
It is likely that dragonflies have an excellent estimation of the angular velocity of their prey 1121. However, insects have small heads relative to typical engagement ranges, which when combined with their low resolution eyes, means binocular stereopsis is not an effective method for them use when obtaining range information. Thus it seems that their range estimation may be poor at best. However, stereopsis is not the only possible visual mechanism for measuring range.
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ov
20
40
lime
1~
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140
120
Figure 3: Deviation from camouflage constraint slope
A variety of initial conditions and focal point locations were tested, and the proposed control law could successfully camouflage a predator for any prey trajectory.
;1
There are two weH-supported hypotheses about how dragonflies might accomplish range estimation. One, explored more fully in [SI, proposes that dragonflies, like hoverflies, make some broad assumptions about the likely size o f t h e prey they are tracking, and then infer range from these assumptions. Some supporting evidence €or this is the tendency of dragonflies to pursue objects such as aeroplanes for a short time. Another passibility is that postdated by Weber, et al [14], wherein dragonflies make assumptions about the speed capabilities of the sighted prey and infer the range from image motion cues. This corresponds with other research indicating the visual fields of dragonflies are most receptive to movement 171, and thus angular velocities and accelerations can be calculated, leading to a fairly accurate estimation of range.
To partially represent the measurement process available to dragonflies, a polar system representation of information was incorporated into the simulation. Although filtering was not added, this poIar representation allowed noise t~ be introduced into range and angle measurements in a crude manner, in order to partially represent the effect of a state estimation process.
. ...
Figure 4: Motion camouflage: focal point lies between
15-
initial predator and prey positions
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Prey Predator CamoullagaComiramt Lines
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4.2 Mimicking Dragonfly Encounters: Realistic .
.
Constraints In order that the simulation should more realistically mimic the dynamic behaviour of dragonfly engagements, certain modification were made to the simulations (including motion constraints, prey manoeuvres, and measurement issues).
The added motion constraints include maximum Iimits on the allowable insect accelerations and velocities which match the dynamic behaviour observed in dragonfly engagements. The prey dynamics were modified
Figure 5: Mimicking Dragonffy engagements.
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Figure 5 shows an example of the closed-loop motion camouflage behaviour, with focal point (O,O), when these considerations are incorporated in the simulation. This figure demonstrates that when some realistic constraints are introduced into the simulations, and the velocity and acceleration limits axe met, the predator dynamics deviates from the CCLs for at least some parts of the engagement. Figure 6 shows the d e
Figure 6: Deviation from the camouflage constraint
prey trajectory from changes to the prey’s current behaviour (ie. wing beats etc.). 4.3 Examples of Tracking Behaviour The results of a typical tracking manoeuvre, with a
displacement of 14,c m be seen in Figure 7. 73,
I
Figure 7:Tracking: the predator maintains a fixed distance from the target at all times
slopes
viation from the desired slope for this encounter with constraints. As can be seen, the error is minimal until ,anextreme mmeouver is made by the prey, whereupon the predator has difficulty maintaining camouflage. Remarks: *
1. A systematic approach to estimating the required state information from the partial observations available to the dragonfly was not implemented in this study. A Kalman filtering approach to state estimation would be one obvious approach. The primary reason state estimation was not investigated is that the actual set of measurements available to a dragonfly is not yet known. An interesting unanswered question is: what is the minimum set of information that allows the dragonfly to successfully perform the described motion camouflage behaviour? 2. A second, more subtle issue, is prediction of future prey motion. It appears that some sort of prediction of future prey behaviour is required for successful guidance. However, it is known that when a predator dragonfly encounters an aerially and tactically capable prey, the predator’s behaviour is more complicated than the presented simple motion camouflage strategy [9]. Although not currently possibly to verify, the predator dragonfly may obtain cues about future
5 Conclusion This paper presented a brief description of parts of the motion camouflage behaviour observed during the predatory behaviour of dragonfly insects. It was shown how this motion camouflage guidance behaviour could tie mimicked via the solution to a linear quadratic Gaussian control problem. Tracking behaviour was ;dso considered. The presented motion camouflage guidance strategies were examined in simulation studies involving a variety of camouflage focal points. These provide a prelimh a r y illustration of the capabilities of the approach.
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