AIAA 2005-6903
Infotech@Aerospace 26 - 29 September 2005, Arlington, Virginia
Radio Source Localization by a Cooperating UAV Team Eric W. Frew*, Cory Dixon†, Brian Argrow‡, and Tim Brown§ University of Colorado, Boulder, CO,80302 This paper describes the development of a networked UAV communication, command, and control (NetUAVC3) architecture. The NetUAVC3 project is divided into three stages. Stage 1 focused on developing algorithms for tying network intelligence and mission-level tasking information into automatic flight controls. Stage 2 will conclude with a demonstration of leashing UAVs to mobile nodes, and Stage 3 will conclude with a demonstration of radio source localization by a cooperating UAV team. This presentation will describe the NetUAVC3 architecture currently under development. The Stage 1 system will be presented, including the onboard flight management architecture and monitoring and command & control software that exploits the existing AUGNet mesh network. The radio localization problem, in which one or more UAVs react cooperatively to localize the location of a radio emitter, will also be introduced. Source localization is cast as a distributed estimation problem. Aircraft mobility is exploited to improve the observability, in terms of the Fisher Information Matrix, of this estimation problem. Aircraft motion is coordinated through iterative consensus by individual receding horizon controllers on each vehicle.
Nomenclature (x,y,ψ) U ui
= = = ωmax = xi,x = u = pj = Pj = P0,d0,k0,e = = tj,t zi,zi,z = u * [k ] = = Ji Wi = z, P, P = JF = Φt = v, w = Q v, Q t =
2D x-position, y-position, and heading of UAV constant UAV speed turn rate command of ith UAV maximum turn rate command vector state of ith UAV, entire UAV team input vector for entire UAV team 2-D position vector or jth radio transmitter Received power of jth transmitter Parameters of empirical radio propagation model vector state of jth radio transmitter, set of all transmitters measurement by ith UAV, measurement vector of entire UAV team control input sequence, optimal input sequence Term in RHC optimization cost optimization cost weights target location estimate, estimate covariance matrix, predicted estimate covariance matrix Fisher Information Matrix state update matrix sensor noise, process noise sensor noise covariance matrix, process noise covariance matrix
*
Assistant Professor, Aerospace Engineering Sciences,
[email protected], AIAA Member. Graduate Student, Aerospace Engineering Sciences,
[email protected], AIAA Member. ‡ Associate Professor, Aerospace Engineering Sciences,
[email protected], Senior Member. § Associate Professor, Interdisciplinary Telecommunications,
[email protected], Non-Member. †
1 American Institute of Aeronautics and Astronautics Copyright © 2005 by Eric W. Frew. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
I.
T
Introduction
he Ad-hoc UAV and Ground Network (AUGNet) is a research test bed that combines stationary and mobile ground radio nodes with airborne nodes carried by small UAVs1,2. The first combined tests were completed in October 2004. These tests included a three-UAV swarm and reported the effects of the number of radio hops on the overall performance of an ad-hoc 802.11b network, with a mix of quantitative and qualitative findings on the effects of node mobility, UAV orientation, and interference from local 802.11 networks. AUGNet research continues with the development of Networked UAV Communication, Command, and Control 3 (C ). The NetUAVC3 project is divided into three stages. Stage 1 is focused on developing algorithms for tying network intelligence and mission-level tasking information into automatic flight controls. Stage 1 research concluded with a demonstration of autonomous, data-reactive, UAV control, with data from an internally-networked suite of simple sensors. Stage 2 will conclude with a demonstration of leashing UAVs to mobile nodes, and Stage 3 will conclude with a demonstration of radio source localization by a cooperating UAV team. This paper describes the development of a control algorithm that exploits network mobility and allows an autonomous UAV team to react cooperatively to localize the location of a radio emitter. Source localization is cast as a stochastic distributed estimation problem. Aircraft mobility is exploited to improve the observability, in terms of the Fisher Information Matrix, of this estimation problem. Aircraft motion is coordinated through iterative consensus by individual receding time horizon controllers on each vehicle. The paper presents the NetUAVC3 architecture, the distributed estimation problem, the individual receding time horizon controllers, the consensus algorithm, and simulations to demonstrate system performance.
II.
Networked UAV Communication, Command, and Control Architecture
A networked communication, command, and control architecture (referred to as NetUAVC3) is under development at CU Boulder for teams of cooperating unmanned aircraft, building on previous work developing an ad-hoc UAV and ground network (AUGNet)1,2. This section provides a summary of the AUGNet system, describes the three stages of the NetUAVC3 program, and presents the intelligent flight control system that resulted from Stage 1. The AUGNet system is a wireless network based on COTS IEEE 802.11b (WiFi) hardware that combines static ground nodes, moving ground nodes, and aerial nodes carried by autonomous UAVs connected through a mesh network back-hauled to the Internet (Fig. 1). The main components of the AUGNet system include custom made mesh network radios, network monitoring software and database that can be accessed during flight experiments Fixed Site 2
Range Network
Meshed Radio UAV Nodes Network Mobile Nodes Fixed Site
Test Bed Gateway and Test Range IP Router
Table Mountain Field Site University of Colorado
Remote Monitor
Internet
Figure 1. AUGNet test bed.
Monitor
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from the Internet, routing software using the Click modular router to implement dynamic source routing (DSR), and the Ares aircraft (Fig. 2) designed and manufactured at CU Boulder. The airframe of the Ares aircraft is based on the layout of the Senior Telemaster, a popular RC model. Custom modifications include an expanded fuselage to accommodate a payload section and conversion from a tail-dragger configuration to one with tricycle gear. The monocoque fuselage, wings, main gear, and horizontal tail are made of a carbon composite laid over carboncomposite laminated plywood bulkheads and ribs. The Ares is powered by a 5-hp, two-stroke engine and has an additional payload capacity of 10.0 pounds.
Figure 2. Three Ares UAVs on the ground at the local flight test facility. The Networked UAV Communication, Command, and Control architecture (NetUAVC3) in development at CU Boulder harnesses the AUGNet networking capability to enable groups of UAVs to complete high-level mission tasks cooperatively and autonomously. The NetUAVC3 will be designed and implemented in a three stage process (Fig. 3). In Stage 1, which has been completed and will be described in more detail below, an intelligent avionics system is designed and implemented to enable single-vehicle autonomy. Subsystem development and intraplane communication and control are key elements to this stage. In Stage 2, the intelligent control capabilities created in Stage 1 will be used by a single UAV to demonstrate autonomous flight. Example applications to be demonstrated in Stage 2 include aircraft leashing (also called electronic tethering) in which a single UAV tracks a possibly moving ground node and provides a communication relay from that node to other nodes in the environment3. The inter-plane communication capability of the AUGNet system will be expanded in Stage 2 in order to enable multi-vehicle
Stage 1
Stage 2
Level 1: Intraplane subsystem comm and control Level 2: Single UAV planning, inter plane control interface
Base Demo: UAV flies to target, sends back images
Leashing algorithms
Level 3: Multi aircraft planning and decision making
Stage 3 Multi-UAV operations
Leashing flight demo
Direction finding and source localization algorithms
Direction finding flight demo
C3 via external interfaces
Figure 3. Staged approach to Networked C3 for UAV team. 3 American Institute of Aeronautics and Astronautics
control. Finally, multiple aircraft decision making and control will be demonstrated in Stage 3. The radio source localization scenario described in Section III will be implemented in Stage 3 as well as communication, command, and control of a UAV team by an external operator, i.e. reaching back from the field to an operator in a command center off site. Completion of Stage 1 of the NetUAVC3 architecture was achieved through the integration of UAV autonomous flight control, network communication, and meteorological sensor subsystems to form an intelligent informationgathering platform. The main results of this stage were design of the onboard flight management architecture, refinement of the Virtual Cockpit interface running over the mesh network, and hardware demonstration of a single UAV. A hardware-in-the-loop (HIL) laboratory test bed was also constructed so that hardware, software, and interoperability elements could be rapidly developed and tested. Onboard flight management is achieved through a modular embedded control architecture that integrates custom and COTS components. Figure 4 is a schematic of the proposed modular architecture. The subsystems are connected via a CAN bus interfaced through custom-made Naiad nodes4. The Naiad (Fig. 5) is a small interface board with the capability to act as an intelligent interpreter between the various subsystems and to perform limited amount of local computation. These distributed nodes connect the supervisory flight management computer, the low-level flight control system (which is the PiccoloPlus autopilot developed by Cloud Cap Technology), ad-hoc communication hardware, and various sensor components including the Thalassa** weather sensor package designed in house. Computer Module
Autonomous Flight Control
Supervisory Computer
Piccolo Autopilot
Naiad Node
Naiad Node
CAN Naiad Node
Naiad Node
Naiad Node
Comm Interface
Sensor
Sensor 2
Comm
…
…
Naiad Node
Sensor
Sensor Modules
Figure 4: UAV Flight Management Architecture. The Supervisory Computer module acts as a central computer to the distributed system, running high-level mission control algorithms. The purpose of this system is to collect all of the data and telemetry from the other subsystems and use this information, along with mission goals and limits, to monitor system health, turn sensors on and off, and to provide sensor reactive control commands to the autopilot system. This module will contain the sensor fusion, fault detection, and cooperative control algorithms developed for Stage 2 and Stage 3 of this project.
**
Naiad and Thalassa are Neptune’s first and second moons, respectively. 4 American Institute of Aeronautics and Astronautics
(a) Figure 5. Top and Bottom view of two Naiad boards. The onboard flight management architecture was integrated with the AUGNet networking capability to establish the NetUAVC3 architecture for Stage 1 testing. Figure 6 shows a schematic of this architecture, including onboard embedded computing, mesh networking, the network monitor that is run off site through a back-haul Internet connection, and the Virtual Cockpit interface also used through the network on site to control the aircraft. Results of Stage 1 tests will be published in future work.
Figure 6: Networked UAV C3 architecture for Stage 1 deployment.
III.
Radio Source Localization
Radio source localization by a team of autonomous aircraft consists of dual estimation and cooperative control problems. This section describes the radio source localization problem and our solution method that combines distributed estimation with communication-based decentralized receding horizon control. We consider a team of N aircraft whose motion resulting from low-level flight control is described by the standard planar kinematic model: x&i = U ⋅ cosψ i y& i = U ⋅ sinψ i ψ& i = ui
(1) ui ≤ ω max
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where x i = [xi , yi ,ψ i ] is the state of the ith vehicle, U is the constant vehicle speed, and u i is the aircraft turn rate command bounded by the maximum turn rate ω max . Let x = (x1 , L , x N )T denote the state of the entire team and u = (u1 , L , u N )T denote the control input vector for the entire team. Next consider a set of M radio emitters located at positions p j = x j , y j in the environment. The power Pj (p r ) received at position p r = (xr , y r ) from the jth emitter using the practical radio propagation model is
(
)
e ⎛ ⎛d ⎞ ⎞ log Pj (p r ) = log⎜ P0 ⋅ ⎜ 0 ⎟ ⎟ + v = k 0 − e ⋅ log d + v ⎜ ⎝ d ⎠ ⎟⎠ ⎝
(
) (
(2)
)
where P0 and d 0 are reference power and distance, d = x r − x j 2 + y r − y j 2 is the distance between the emitter and receiver, 2 < e < 6 is the propagation decay exponent, assuming e is constant in the environment k 0 = log P0 ⋅ d 0e lumps the constant parameters together, and v is Gaussian fast fading noise. The variable Pi , j will denote the power of the jth emitter received at the location of the ith aircraft. Let the state of the jth transmitter be denoted t j = x j , y j , e, k 0 T and the state of all M transmitters be denoted t = (t1 , L t M )T . Let the position of all transmitters be denoted p t = ( p1 , L , p M )T . Figure 7 shows the results of radio power measurements versus separation distance for the meshed radio nodes used in the NetUAVC3 project. In this case, the fir empirical model has parameters k0 = 3822.0 mW, e = 3.582, and the fast fading noise has a standard deviation σ = 1.96 mW.
(
)
-8
15
Recieved Power vs. Range
x 10
Power Estimate: Exponential Decay Model -30
Node 80 Node 82
Average Best Fit Model
-40
Rx Power [dBm]
Recieved Power [mW]
-50
10
5
-60 -70 -80 -90 -100
0 200
400
600
800 1000 Distance [m]
1200
-110
1400
0
500
1000 1500 Distance [m]
2000
2500
a.
b. Figure 7. Measurements of received radio power versus distance for the NetUAVC3 meshed radio nodes. a.) Raw data, b.) Exponential model fit. Each aircraft is equipped with a receiver that can detect and measure the power of radio transmission signals. In some instances the receivers can only measure the total power received and the measurement z i taken by the ith aircraft is
zi =
M
∑ Pi, j .
(3)
j =1
In other cases the receivers can distinguish between transmissions from different sources in which case the measurement taken by the ith aircraft is the vector
z i = (Pi ,1 ,L Pi , M )T . Let z = (z1 , L , z N )T or z = (z1 , L z N )T denote the measurement vector obtained by the entire UAV team.
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(4)
The radio localization problem can now be broken down into two related problems. The first is estimation of the state of all transmitters t = E [t | z, x] . Although the position estimate pt = E [p t | z, x] of the transmitters is often the desired variable, the addition state components are often needed to calculate the result. In certain cases the positions can be determined without estimating the entire radio propagation function. The second problem is determination of the control input u * = arg min J (x,t , u ) that optimizes some combination of performance and information criteria. Descriptions of solutions to each problem are presented below.
A. Distributed Receding Horizon Control A distributed receding horizon control (DRHC) policy is used to calculate control inputs for the UAV team. The main steps of the basic RHC policy are (i) calculating the optimal control sequence u * [k + i ] = u * [k + 1], L , u * [k + Th ] starting from state x i [k ] , over a finite planning horizon 2 ≤ Th < ∞ ; (ii) implementing the optimal control input over some control horizon k ≤ t ≤ k + Tc where 1 ≤ Tc ≤ Th ; and (iii) repeating steps 1 and 2 for x i [k + Tc ] at time k + Tc . The RHC approach is well suited to cooperative radio localization since uncertainty in the sensor information will necessitate continual adaptation of the UAV routes as more information is obtained. The basic RHC policy is extended to cooperating vehicles through a distributed process, also referred to as communication-based decentralization5, that works well for small numbers of vehicles ( rsafe
(10)
which keeps the UAV some distance away from the radio source estimates, both for some level of safety and to avoid mathematical singularities in the estimation equations. We model the target dynamics with the state update matrix Φ t such that p target [k + 1] = Φ t ⋅ p target [k ] + w
(11)
[
]
where w is zero mean, Guassian white process noise with covariance Q t = E w ⋅ w t . For a stationary object the state update matrix is the identity matrix ( Φ t = I ) and we assume no process noise ( Q t = 0 ). In order to predict the evolution of the target estimate we assume an idealized (efficient) version of the radio localization problem. We use the Fisher Information Matrix (which is equivalent to the inverse of the Posterior Cramer-Rao Lower Bound) to describe the information gained about a target by assuming the target estimate is exact over the finite planning horizon and we know exactly how the aircraft moves. The Fisher Information Matrix is calculated from the following recursion6:
(
J F [k + 1] = Q t + Φ t ⋅ J k−1 [k ]⋅ Φ Tt
)
−1
+ J Z [k + 1]
J Z [k + 1] = H[k + 1] ⋅ Q z ⋅ H T [k + 1]
H[k + 1] =
dz (x[k + 1]) dt
(12) (13) (14)
where t represents the sate of all transmitters, not time. The recursion is initialized by the inverse of the covariance matrix J F [k 0 ] = P −1 [k 0 ]
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(15)
and the future covariance matrix is approximated by
P [k + i ] = J −1 F [k + i ] .
(16)
The solution to the receding horizon optimization problem (5) is currently obtained through an exhaustive enumerative search over some discretized input space. This approach allows for optimal solutions of each subproblem, but limits the planning horizon to 2-4 sample times. Figure 9b shows a time sequence of plots from a simulation of the DRHC planning algorithm with two UAVs and a single radio source. The triangle markers represent the UAVs which begin at positions (60, 650) and (60, 600) meters and have speed 20 m/s. The single target is located at the origin with k 0 = 100 and e = 2.0 . The shaded region in the subplots of Fig. 9b represents the 3 − σ uncertainty ellipse of the position components of the Fisher Information Matrix of the target. For comparison, Fig. 9a shows a simulation in which the two UAVs use individual RHC planning without distributed cooperation. In this case, both UAVs head toward the left of the target position. By cooperating, the UAVs head in opposite directions, maximizing the baseline of the underlying trilateration process.
a.
b.
Figure 9. Time sequences of two UAVs minimizing the FIM of a static target. a.) No cooperation, individual RHC only. b.) Cooperation using the DRHC algorithm. The shaded region represents the 3 − σ bound of the target FIM. B. Cooperative Estimation Cooperative estimation of the state t of all transmitters assumes a fully connected communication graph between all UAV team members. Through this graph, all measurements zi are assumed to synchronously reach one or more fusion centers that carry out the estimation process. The problem of localizing an unknown radio transmitter from multiple spatially-distributed measurements of that source is mathematically equivalent to the problem of locating a radio receiver based on measurements taken from multiple known transmitters (Fig. 10). The latter problem has received considerable attention in the mobile networking community7-10. Example solution methods exist based on multidimensional scaling, optimization, Bayesian inference, point matching, and pattern recognition7. Most applications considered in the mobile networking community occur indoors using COTS wireless Internet devices based on IEEE 802.11b (WiFi) or Bluetooth8, 9. The indoor environments often add large amounts of uncertainty or variability, due to multi-path and other interference source, to the propagation of radio signals. Thus these approaches typically characterize the environment in advance by deriving “fingerprints” of various radio nodes. By comparison, the application of interest here considers a radio source about which nothing is known in advance. Although fingerprinting cannot be done a
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priori, the outdoor environment reduces the variable fading effects in the signal propagation. Furthermore, measurement of the same transmitted signal by multiple receivers enables estimation of some of these noise sources.
T1
R1 R3
T3
T
R T2
R2
Figure 10. Localization of an unknown radio transmitter is equivalent to determining the location of a radio receiver from multiple measurements from known transmitters.
The radio source localization estimator has not currently been developed. A maximum-likelihood estimator will be designed that fuses synchronous measurements from multiple distributed UAVs. Previous work locating nodes in wireless sensor networks will be extended to the scenario described here. The use of multiple-model and hybrid estimation techniques11 will be incorporated when the number of transmitting radio sources is also unknown.
IV.
Conclusion
This paper describes the development of a networked UAV communication, command, and control (NetUAVC3) architecture. The three stages of the NetUAVC3 project were described, including the onboard flight management architecture and monitoring and command & control software that resulted from completion of Stage 1. The radio localization problem, in which one or more UAVs react cooperatively to localize the location of a radio emitter, was also introduced. Source localization is cast as a distributed estimation problem. Aircraft mobility is exploited to improve the observability, in terms of the Fisher Information Matrix, of this estimation problem. Aircraft motion is coordinated through iterative consensus by individual receding horizon controllers on each vehicle. Future work will develop the cooperative estimation algorithm needed to fuse synchronous measurements from multiple UAVs.
V.
References
1
Brown, T.X., Argrow, B., and Dixon, C., "Ad Hoc UAV Ground Network (AUGNet)," AIAA 3rd "Unmanned Unlimited" Technical Conference, Workshop and Exhibit, AIAA, 2004. 2 Brown, T.X., Doshi, S., and Jadhav, S., "Test Bed for a Wireless Network on Small UAVs," AIAA 3rd "Unmanned Unlimited" Technical Conference, Workshop, and Exhibit, AIAA, 2004. 3 Dixon, C., Frew, E.W., and Argrow, B., "Radio leashing unmanned aircraft," AIAA Infotech@Aerospace, 2005. 4 Elston, J., Argrow, B., and Frew, E., "A distributed avionics package for small UAVs," AIAA Infotech@Aerospace, 2005. 5 Richards, A., and How, J., "Implementation of robust decentralized model predictive control," AIAA Guidance, Navigation, and Control Conference, 2005. 6 Hernandez, M.L., "Optimal sensor trajectories in bearings-only tracking," Proceedings of the Seventh International Conference on Information Fusion, FUSION 2004, Jun 28-Jul 1 2004, Vol. 2, International Society of Information Fusion, Fairborn, OH 45324, United States, Stockholm, Sweden, 2004, pp. 893-900. 7 Elnahrawy, E., Li, X., and Martin, R.P., "The limits of localization using signal strength: A comparative study," 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, IEEE SECON 2004, Oct 4-7 2004, Institute of Electrical and Electronics Engineers Inc., New York, NY 10016-5997, United States, Santa Clara, CA, United States, 2004, pp. 406-414. 8 Bandara, U., Hasegawa, M., and Inoue, M., "Design and implementation of a Bluetooth signal strength based location sensing system," Proceedings - 2004 IEEE Radio and Wireless Conference, RAWCON, Sep 19-22 2004, Institute of Electrical and Electronics Engineers Inc., New York, NY 10016-5997, United States, Atlanta, GA, United States, 2004, pp. 319-322.
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9 Ladd, A.M., Bekris, K.E., and Rudys, A., "Robotics-based location sensing using wireless ethernet," MOBICOM'02, 2002, pp. 227-227-238. 10 Doherty, L., Pister, K.S.J., and El Ghaoui, L., "Convex position estimation in wireless sensor networks," 20th Annual Joint Conference of the IEEE Computer and Communications Societies, Apr 24-26 2001, Vol. 3, Institute of Electrical and Electronics Engineers Inc, Anchorage, AK, 2001, pp. 1655-1663. 11 Hofbaur, M.W., and Williams, B.C., "Hybrid estimation of complex systems," IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), Vol. 34, No. 5, 2004, pp. 2178-91.
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