Sam Drake, Kim Brown, Jeremy Fazackerley and Anthony Finn. Defence Science and Technology Organisation. PO Box 1500, Edinburgh SA 5111 Australia.
Autonomous Control of Multiple UAVs for the Passive Location of Radars Sam Drake, Kim Brown, Jeremy Fazackerley and Anthony Finn Defence Science and Technology Organisation PO Box 1500, Edinburgh SA 5111 Australia Abstract This paper describes an algorithm that has been used for the autonomous control of multiple UAVs tasked with the high level objective of locating a radar subject to a number of real world constraints. The distributed, fully autonomous, cooperative control of the multiple UAV system was executed using sensor input from a heterogenous network of miniaturised Electronic Surveillance (ES) payloads. An ES sensor onboard one UAV detected a radar target and cross-cued ES receivers onboard two other UAVs. Based on the information shared between these UAVs the target radar was approximately located by each UAV. Once the UAVs had coarsely located the target they autonomously, dynamically, and continuously adapted their flight trajectories to progressively improve the accuracy with which they were able to co-operatively locate the radar target. The UAVs were able to accurately locate the radar while simultaneously avoiding no-fly zones, one another and remaining within communication range. 1. I NTRODUCTION
techniques are used to measure the time-difference between a signal’s arrival at three or more ES receivers to provide an accurate fix almost instantaneously. Moreover, as ES sensors only have to receive and process signals they do not require large amounts of power to operate and scale well to the power constraints imposed by miniature UAVs. 50% Geolocation Uncertainty Ellipses: DF Error = 5degrees 250
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Searching for and accurately locating ground-based radar systems is an important mission in a military context. Radar sites are often associated with ground-based facilities, such as Ground-Based Air Defence Systems (GBADS). Identification, location, and prosecution of GBADS in the early phases of conflict can assist in countering their potential effects. Due to their persistence and to avoid the risk of exposing manned platforms, UAV’s are increasingly being used as a means of sensing these environments at a safe distance. Accurate location, however, requires the coordinated application of multiple sensors, and hence multiple UAVs. Large UAVs provide significant potential in this regard. Unfortunately, they require extensive infrastructure in the form of ground control systems, planning and logistics support and trained human operators. Miniature UAVs such as the Aerosonde (www.aerosonde.com) are smaller and very much less expensive, yet retain significant endurance, providing a persistent presence on the battlefield. The Defence Science And Technology Organisation (DSTO) owns six of these UAVs and is using them to explore the different cost-capability tradeoffs they present to their larger counterparts [1]. The UAVs are configured to act in concert with one another to provide the potential for economies of scale as well as the opportunity for faster, more accurate targeting [2]. For instance, multi-platform
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(a) Low accuracy stand-in UAVs 50% Geolocation Uncertainty Ellipses: DF Error = 0.5degrees 250
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(b) High accuracy stand-off UAVs Fig. 1: The 50% error ellipses are shown for a) nine low accuracy stand-in UAVs (∆) and b) 2 high accuracy stand-off UAVs (∆). The 100km×100km area of interest is bound by the solid blue line. Location is done from direction finding estimates, which can be determined by TDOA. The error ellipses are calculated using Eq.(17) of Stansfield’s paper [3].
Miniature UAVs are not yet considered a practical replacement for the larger strategic UAVs. However, by networking
2. U NCONSTRAINED T RAJECTORY P LANNING Consider the situation in which three UAVs are trying to determine the location of an enemy radar. One method by which the location of the radar can be determined is by time difference of arrival (TDOA) or equivalently range difference of arrival (RDOA) (comprehensive reviews of these techniques can be found in [7] and [8]). Figure 2 shows the location error ellipse for TDOA. The location uncertainty depends on both the geometry of the receivers and the measurement noise of the time of arrival; the uncertainty in the UAV positions is assumed to have a negligible effect. It can be shown that the error ellipse is minimised if the UAVs are spread evenly in angle around the radar, the range has no major effect on the error ellipse, see [8] for details. For the UAVs to spread around the radar there are two basic paths they can take: 1) Head straight for the radar and, as soon as 1 often called virtual forces but we avoid this use as it implies that we determine the acceleration of the UAV by calculating the force and dividing by the mass
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(a) Good geometry 150 Radar UAV 1 σ error ellipse 100
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their sensors we may derive greater capability. As an example, figure 1 shows a comparison between the 50% uncertainty bounds for locating emissions of interest from two platforms with 0.5degree error direction finding (DF) capability and nine platforms with 5.0degree error DF capability, respectively. The more accurate sensors are normally placed on board high-value assets and must therefore standoff at a nominal range of 100km, whereas the less capable sensors, which are significantly smaller and cheaper, are placed on more expendable platforms and may therefore stand-in (their cost means that we are also able to afford more of them). Analysis of figure 1 shows that the system using the less accurate networked sensors has average errors around an order of magnitude smaller than those of the more expensive system. The question addressed in this paper is: “Given a team of UAVs what control strategy simultaneously maximises the radar location accuracy, satisfies the operational constraints and does so without placing an onerous workload on the operator (who must supervise multiple UAVs)?” There are a number of methods for solving constrained optimisation problems such as this: simulated annealing, grid search, virtual potential fields and virtual vector fields1 [4]. The method we chose is based on virtual vector fields because a) it is a computationally simple, b) it is scalable c) it is easily adapted to new constraints or desired behaviours and d) it is able to cope with a dynamically changing environment. The VVF method has been successfully employed by the robotics community for a wide variety of scenarios [5], [6] but, to the best of our knowledge, it has not been formulated in a completely generic form that can be applied to any desired behaviour or constraint, in application to the problem of determining flight trajectories of UAVs for the passive location of radars. In section 3 of this paper we write the equation for an arbitrary VVF and in section 4 we show how this general form can be tailored to the specific case of using UAVs for the passive location of radars.
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(b) Bad geometry Fig. 2: TDOA location uncertainty ellipse for 2(a) good geometry and 2(b) bad geometry. The ellipses are calculated for a clock error of σt = 50ns using Eq.(16) of Torrieri’s paper [8].
they are within a certain range, encircle it (we refer to these as direct flight paths); 2) Spread around the radar straight away (we refer to these as circular flight paths). Figure 3 shows how the error ellipse varies as a function of time for the two fundamental flight paths. From this figure we can conclude that the best flight path for the UAVs depends on the team objective. If the objective is to achieve the minimum error ellipse as soon as possible the direct path should be taken. If, on the other hand, the object is to achieve maximum accuracy at any instant then the circular flight path is better. In this paper we are interested in algorithms that give good location accuracy in a rapidly changing environment as the UAV team may be tasked with locating another radar at a different location at any moment. If the reassignment occurs before the UAVs can get sufficiently close to the radar by flying a direct path then the team would achieve better location accuracy by flying the circular path. For this reason we concentrate on algorithms that are circular rather than direct.
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(a) Two possible formations for the UAVs: The direct flight paths maximises the location accuracy as soon as possible; whereas circular flight paths maximise the location accuracy at every instant.
The VVF is expressed by the canonical power law ³ r ´p ρˆ , (1) f = s where • r is the interval over which the field acts. For example this interval might be the physical separation or angular separation. • s is the coupling, which determines the interval at which the field magnitude is one. • p is the stiffness, i.e. the gradient of the field when r = s, see figure 4. The sign of p determines whether the field is monotonically increasing (p > 0), or monotonically decreasing (p < 0). ˆ defines the direction of the field. • ρ 2 p=1 p=2 p = 10 p = 100
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(b) Mean radius for radar location error ellipse for direct and circular formations Fig. 3: A comparison of the radar location error ellipses for two different UAV formations. For circular formations UAV1 remains fixed.
3. G ENERALISED V IRTUAL V ECTOR FIELDS FOR CONSTRAINED TRAJECTORIES
While the a priori mission objectives may allow us to determine the (closed loop) optimal flight paths for the UAVs [9], [10], operational constraints may make these flight paths undesirable. For example the planned flight path (based on a closed loop solution) may cross a threat area that was identified after the initial flight plan was loaded. If this is deemed unsafe then the UAVs must dynamically replan their trajectories to avoid this area. The exclusion of the no-fly zone on the solution space places constraints on the allowed solutions to the optimisation problem, for this reason such problems are referred to as constrained optimisation problems. As we mentioned in the introduction there are a number of techniques for solving constrained optimisation problems but we use the virtual vector field method as it is fast, scalable and flexible.
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Fig. 4: Plot of the magnitude of the VVF kff k as a function of the interval ( rs ) for a variety of stiffness values p.
4. TAILORING THE V IRTUAL V ECTOR F IELDS FOR AUTONOMOUS C ONTROL OF UAV S The desired, potentially time varying, behaviours of the UAVs are: 1) Achievement Orientation a) Improve geometry b) Improve signal quality 2) Social Awareness a) Maintain communication links b) Avoid Collision with other aircraft c) Avoid no-fly zones/threats 3) Self protection a) Avoid detection from hostile radar b) Encircle radar at constant distance Each of the desired behaviours can be mapped directly to a VVF by Eq.(1). 1a Improve geometry In TDOA, direction finding (DF) and many other passive location techniques the estimated position uncertainty is minimised if the receivers are spread evenly in angle about the radar. The
SNR VVF has influence only when good geometry is achieved its magnitude is one, regardless of the UAV’s location, i.e.,
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The direction of the improve signal to noise ratio VVF is towards the radar hence, lr − ri ρˆ ≡ , (8) kll r − r i k
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location error depends only on the angular separation of the UAVs with respect to the radar, hence r ≡ θij
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where θij is the angular separation between the i’th and j’th UAVs with respect to the radar, see figure 5. The magnitude of the field is normalised to one when all the UAVs are spread evenly in angle about the radar so 2π , (3) N where N is the number of UAVs. Furthermore the magnitude of the field should decrease as the UAVs spread further apart in angle, i.e., s≡
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As the received power of the communication link drops off as 1/krr j − r i k2 the VVF has the inverse behaviour, i.e., p≡2
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The direction of the i’th UAV’s maintain communications VVF needs to be towards the j’th UAV that we are trying to communicate with, hence rj − ri . (13) ρˆij ≡ krr j − r i k By combining Eqs. (10) to (13) we find that the VVF associated with the maintain communication links behaviour is N X (rr j − r i )krr j − r i k . (14) f 2a i = rcl j=1,j6=i
2b Avoid Collision Collision between UAVs will almost certainly result in the loss of the UAV. This is clearly undesirable. To minimise the likelihood of the this occurring the UAVs should maintain a minimum safe distance from each other and any other aircraft known to be in the area. The avoid collision VVF depends only on the separation between UAVs, hence r ≡ krr j − r i k
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where r i is the location of the UAV of interest and r j is the location of the j’th UAV that we are trying to avoid. The minimum safe distance sets the scale parameter s ≡ rsd
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There are two primary concepts associated with collision avoidance 1) deconfliction and 2) evasive maneuvers [11]. Deconfliction is a medium range task that attempts to avoid a collision while still allowing the UAV to complete its mission. Evasive maneuvers are last minute emergency acts aimed solely at preventing aircraft loss, they do not take mission completion into its avoidance decisions. As deconfliction has a medium to long range influence it is best represented by a small stiffness, e.g. p = 1. On the other hand evasive maneuvers can be modelled by a strong field over a short range, e.g. p = 10. We have found by simulation that deconfliction is better at meeting the mission objectives and ensuring the survivability of the UAV hence we have chosen p≡1
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for the avoid collision VVF. The direction of the VVF should be away from the other UAV, so rj − ri ρˆ ≡ − (18) krr j − r i k By combining Eqs. (15) to (18) we find that the VVF associated with the avoid collision behaviour is f 2b i =−
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2c Avoid No-Fly zones No-fly zones can exist for a number of reasons. For example communications black spots, heavily populated areas, air space restrictions, etc. The avoid no-fly zone VVF depends only on the separation between UAVs and the centre of the no-fly zone (NFZ), hence r ≡ krr i − z k k , (20)
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where rnfz is the radius of the no-fly zone and rt the turn radius of the UAV. If the UAVs are far enough away from the NFZ they should not influence the overall VVF, hence it should be a monotonically decreasing function, i.e., p
