Methodologies for Decentralized Control of Networked Autonomous Vehicles Philip Haney and Jason Derenick Abstract— This paper presents two autonomous methods for cooperatively controlling a number of distributed mobile platforms in order to accurately and efficiently achieve a desired common mission objective. The first method presented is based on an information-theoretic approach utilizing a decentralized data fusion (DDF) core with information measures. This technique achieves coordinated control of distributed mobile platforms by maximizing joint information gains relative to various information metrics of interest. The second method presented is based on a distributed locational optimization approach employing Voronoi tessellations for optimal placement of resources relative to a given area of interest. This technique, referred to as Simultaneous Coverage and Tracking (SCAT), provides a framework which allows the full coupling of environment coverage, target tracking and task assignment. In this work, these state-of-the-art decentralized control methodologies are uniquely combined in order to couple their individual strengths and provide a complementary capability. A heterogeneous application example consisting of ground-based Intelligence, Surveillance and Reconnaissance (ISR) with airbased Suppression of Enemy Air Defenses (SEAD) establishes a proof-of-concept while illustrating the complementary strengths of the two presented autonomous architectures.

I. INTRODUCTION Recent advances in sensors, perception, data fusion, communications, and control have led to a trend in military systems towards increasing levels of autonomy. Missions of the future will involve multiple distributed mobile platforms that must cooperatively sense and understand their environment while efficiently exchanging and fusing data for consistent, autonomous control and resource management. Intelligent, distributed autonomous systems offer several immediate advantages such as reducing risk to personnel in hazardous situations, executing complex missions with advanced sensors and data fusion, and implementing labor intensive operations such as border surveillance. Additionally, distributed autonomous systems can be effectively used to perform tasks deemed too dangerous for either manned systems or systems controlled by a human-in-the-loop such as IED destruction and mine clearance. In this paper, the decentralized control of networked autonomous vehicles refers to the technology required to make multiple, autonomous platforms cooperatively operate in a desired fashion. In addition, the capabilities developed in this work are primarily geared to enable and support missions that require distributed and mobile operation such as Philip Haney is with BAE Systems, Technology Solutions, Burlington, MA 01803 USA (e-mail: [email protected]). Jason Derenick was working as a post-doctoral fellow in the GRASP Laboratory at the University of Pennsylvania during the completion of this work (e-mail: [email protected]).

multiplatform Intelligence, Surveillance and Reconnaissance (ISR) and Suppression of Enemy Air Defenses (SEAD). A significant amount of work has been performed over the years in the area of decentralized control of autonomous vehicles. From an information-theoretic point of view for instance, a number of pioneering efforts have been developed involving area exploration and mapping [1], [2], target localization [3], [4] and communications control [5], [6]. Similarly, recently developed Voronoi-based control methods involving coverage control [7], [8], coverage and tracking [9] and energy-aware coverage [10], [11] are also of notable recognition. However, to the best of our knowledge, the combination of information-theoretic and Voronoi-based decentralized control approaches has not been previously studied. Consequently, this paper uniquely combines and extends the results of [4], [6] and [9] in order to couple the individual strengths of these state-of-the-art decentralized control methodologies and provide a complementary capability for distinct application to cooperative, heterogeneous, ISR/SEAD related missions. The remainder of this paper is organized as follows: Section II outlines an active decentralized data fusion (DDF) core and highlights the advantages that such a distributed architecture can offer for cooperative autonomous systems. In addition, information measures for achieving coordinated control of distributed mobile platforms by maximizing information gains relative to cooperative coverage, estimation uncertainty and platform communications are also described. The Simultaneous Coverage and Tracking (SCAT) capability, which employs locational optimization and Voronoi tessellations for optimal placement of resources relative to a given area of interest, is outlined in Section III. Finally, Section IV establishes a proof-of-concept by providing simulated performance results relative to a unique, heterogeneous ground/air, ISR/SEAD application, and Section V summarizes the paper. II. ACTIVE DECENTRALIZED DATA FUSION In the field of multi-sensor data fusion, decentralized data fusion has become an attractive alternative to centralized data fusion primarily due to the inherent robustness and scalability features that decentralized architectures offer. In its most primitive form, a decentralized network exhibits sensing and processing capability at each node within the network, thereby eliminating the need and subsequent vulnerability of a central processing node. Additionally, decentralized networks maintain the capacity for each node to efficiently communicate its information with neighboring nodes ultimately generating a coherent picture of the fusion environment

throughout the network without requiring any knowledge of the network topology. In the context of intelligent unmanned systems, this “commonality” feature of DDF encourages consistent and intelligent global decision making in the sense that when all platforms have a common understanding of the fusion environment, then inherently more accurate and intelligent global decisions can be consistently made. Figure 1 provides a high-level illustration of the Active DDF architecture. Essentially, each platform in the DDF network utilizes the information form of the Kalman filter outlined in Subsection II-A - to generate a local estimate of the fusion environment based on observations received from on-board sensors. These local estimates are then shared with neighboring platforms, and a global estimate of the fusion environment is inherently constructed [12]. Since communications are typically constrained to neighboring platforms, it should be noted that in order for the global estimate to be properly computed, each platform must communicate not just its own local estimate, but its local estimate assimilated with estimates received from other platforms. Consequently, care must be taken to prevent platforms from processing redundant information. If not correctly handled, the re-fusion of information will degrade the overall fusion quality leading to errors in the global estimate of the fusion environment. As a result, methods such as channel filters [13] or covariance intersection [14] need to be incorporated in order to estimate and account for any correlation in the shared data. Finally, as a consistent and common understanding of the fusion environment is developed across the DDF network, intelligent and coordinated control of the platforms can be realized in order to cooperatively achieve a shared objective. Platform Control

instance, given N sensors and assuming standard Kalman filter notation, the posterior information state and information matrix can be calculated using [4] ˆ k,k = y ˆ k,k−1 + y

N X

ij,k

j=1

Yk,k = Yk,k−1 +

N X

(1) Ij,k

j=1

where ˆ k,k ˆ k,k = P−1 y k,k x Yk,k = P−1 k,k

(2)

and ij,k and Ij,k are the information state and information matrix contributions from sensors j = 1, ..., N defined as ′

ij,k = Hj,k R−1 j,k zj,k ′

Ij,k = Hj,k R−1 j,k Hj,k .

(3)

Consequently, as can be seen in (1), the simple additive nature of the information filter makes it highly attractive for multi-sensor, decentralized estimation. Additionally, since the information form of DDF is inherently informationcentric, information-based metrics provide natural quantitative utilities for controlling platforms with limited sensing and communications capabilities in order to maximize a desired information gain. As will be discussed in the ensuing subsections, the information metrics investigated for this work - specifically geared towards ISR/SEAD-related applications - are cooperative coverage control, uncertainty control and communications control.

Maximize Information Utility

u* = arg max J ( f ( I , u )) u

Platform Actuation

Sensory Data

Decentralized Data Fusion

Sensory Perception

Global Estimate

z1(k)

Data Registration & Alignment Object Recognition & Perception

M zN(k)

Channel Estimate

yˆ (k | k) Y(k | k)

Sensory Information

å

Prediction

Δyˆ ch (k | k) ΔYch (k | k) Channel Filters

Predicted Global Estimate

i1(k) I1(k)

yˆ (k | k - 1) Y(k | k - 1)

M

å Local Estimate

~ y(k | k) - yˆ ch1 (k | k) Y(k | k) - Ych1 (k | k)

Comms Mgmt

~ y(k | k) Y(k | k)

iN(k) IN(k)

~ y(k | k) - yˆ ch m (k | k) Y(k | k) - Ych m (k | k)

M Platform Control Maximize Information Utility

u* = arg max J ( f ( I , u )) u

Platform Actuation

Sensory Data

Decentralized Data Fusion

Sensory Perception

Global Estimate

Sensory Information

z1(k)

Data Registration & Alignment Object Recognition & Perception

Fig. 1.

M zN(k)

iN(k) IN(k)

å

Prediction Predicted Global Estimate

i1(k) I1(k)

M

Channel Estimate

yˆ (k | k) Y(k | k)

yˆ (k | k - 1) Y(k | k - 1)

å Local Estimate

~ y(k | k) Y(k | k)

Δyˆ ch (k | k) ΔYch (k | k) Channel Filters

~ y(k | k) - yˆ ch1 (k | k) Comms Mgmt

Y(k | k) - Ych1 (k | k)

~ y(k | k) - yˆ ch m (k | k) Y(k | k) - Ych m (k | k)

Active Decentralized Data Fusion Architecture

A. Information Filter The information filter is equivalent to the Kalman filter in the sense that they share a specific duality enabling one form to be directly derived from the other. However, instead of working directly with the states, the information filter recasts the estimates in terms of information quantities. The significance of the information filter primarily lies in the fact that it provides an inherently straightforward method for fusing multiple observations from multiple sensors. For

B. Cooperative Coverage Control In the context of ISR/SEAD related applications, an apriori area of interest typically needs to be “mapped” in order to extract desired intelligence relative to some designated mission objective. As a result, in this work, the notion of coverage control refers to the cooperative ability of a number of mobile platforms to share past sensing locations with their peers in order to minimize redundancy and improve mission efficiency during this mapping process. Consequently, assuming a-priori knowledge of a desired area of interest, a grid-based approach can be leveraged to recursively estimate the probability of coverage for the ith grid cell, p(xi ), using a simple linear filter given as


 p xi |Z k = p xi |Z k−1 + α p (zk |xi ) − p xi |Z k−1 (4) where Z k = {z1 , z2 , · · · , zk } is a sequence of observations collected by a given platform, p (zk |xi ) is the corresponding sensor model, and α is the filter gain (0 < α < 1). From (4), the expected gain in coverage information can be computed for a given platform location, uk , using i h  (5) Icvg (uk ) = − log p xiuk |Z k

where xiuk signifies the ith grid cell which corresponds to platform location uk . As a result, global coverage can be cooperatively achieved by using (5) in the following optimization [1] u∗k = arg max {Icvg (uk )} uk ∈U

(6)

which essentially drives the platforms to the locations which maximize the expected gain in coverage information. C. Cooperative Uncertainty Control In order for an ISR mission to be successful, any actionable intelligence gained from the mapping process needs to be as accurate as necessary relative to the overall mission objectives. Consequently, in this work, the concept of cooperative uncertainty control is the process by which mobile sensing platforms dynamically position themselves such that any uncertainty related to a target or entity of interest is reduced to an acceptable level. As outlined in Subsection IIA, since the Kalman filter and information filter are inversely related, this desired reduction of target uncertainty in a Kalman-sense can be directly mapped into a gain in Fisher information. As a result, given a sequence of target location observations, Zk = {z1 , z2 , · · · , zk }, it is assumed that a target state of interest, x, can be recursively estimated using Bayes Theorem. If it is additionally assumed that the target state is normally distributed, p (x) ∼ N [¯ x, P], then differentiating the log-likelihood form of Bayes Theorem twice reveals the Fisher information observation update as ′

−1 −1 P−1 k,k = Pk,k−1 + Hk Rk Hk → Yk,k = Yk,k−1 + Ik . (7)

From (7), it can be seen that the gain in Fisher information (i.e., reduction in target uncertainty) is essentially driven by the observed information. As a result, the expected gain in Fisher information can be computed for a given platform location, uk , using [4]   1 |Yk,k | Itgt (uk ) = log 2 |Y |   k,k−1 (8) |Yk,k−1 + Ik (uk )| 1 . = log 2 |Yk,k−1 | Consequently, from (8), target uncertainty can be reduced using the following optimization which ultimately drives the platforms to the locations where the maximum expected gain in Fisher information was observed [4] u∗k = arg max {Itgt (uk )} . uk ∈U

(9)

with the rest of the network. Consequently, in this work, the notion of communications control refers to the ability of a platform to remain connected to the mobile network throughout the duration of a desired mission. As a result, to achieve this it is first assumed that the signal-to-noise ratio of a RF communication link can be modeled using the following relationship [6] Sij (pi , pj ) =

Pij (pi , pj ) N (pi )

(10)

where Pij (pi , pj ) is the power received by platform i at position pi from platform j at position pj , and N (pi ) is the environmental noise observed by platform i at position pi . Using this simplistic model for SNR, the ShannonHartley Theorem states that the channel capacity, Ci,j , for an average SNR, Si,j , can be computed using the following log2 relationship [6] Cij (pi , pj ) = B log2 (1 + Sij (pi , pj ))

(11)

where B is the channel bandwidth. Therefore, using the above formulation, communications-connectivity can be maintained for a linked network chain using the following optimization which essentially drives the platforms to the locations which maximize the minimum individual channel capacities [6] u∗j = arg max min {Cij (pi , pj ) , Cjl (pj , pl )} uj ∈U

(12)

for: |i − j| = 1, |j − l| = 1, i 6= j 6= l. III. SIMULTANEOUS COVERAGE AND TRACKING Three critical components in the field of cooperative autonomous control are: (i) environment coverage, (ii) target tracking, and (iii) task assignment. These three problems essentially encompass the fundamental subtasks which must be solved in order to successfully detect and track multiple targets in a pre-defined area of interest. For instance, when the number of targets and their locations is unknown, environment coverage is required in order to maximize the probability of target detection. However, once targets have been detected, task assignment is then necessary to manage the conflicting roles of simultaneously tracking a given number of targets while maintaining uniform coverage of the environment. Consequently, the Simultaneous Coverage and Tracking (SCAT) capability outlined in [9] fully couples the fundamental subtasks of environment coverage, target tracking and task assignment by employing locational optimization and Voronoi tessellations for optimal placement of resources relative to a given area of interest.

D. Cooperative Communications Control

A. SCAT - Environment Coverage

A critical component for achieving accurate and efficient coordinated control relative to a desired mission objective is the capability of the mobile network to generate a common and coherent picture of the fusion environment. In order to do this, however, the platforms must be able to efficiently and consistently communicate their assimilated information

The problem of locational optimization considers the cost function Z min f (d (q, pi )) φ (q) dq (13) H (P) = Q i∈{1,...,n}

which is comprised of the following entities:

An integral across some environment, Q ⊂ RN , in which Q may be non-convex [8], • The minimization of the integrand relative to an available set of platform/sensor locations, ′ pi ∈ Q for i = i h ′ ′ ′ 1, 2, ..., n, with P = p1 p2 , ..., pn ∈ Q×, ..., ×Q representing the platform/sensor configuration, N • A distance function, d : R × RN → R≥0 , which measures the distance between points, q ∈ Q, and platform locations, pi ∈ Q, • A monotonically increasing function, f : R → R, which measures the degradation in sensor performance as a function of distance, • A density function, φ : Q → R≥0 , which provides a weight for each point, q ∈ Q, reflecting either the probability of occurrence of events in different regions, or a measure of relative importance of different regions within the environment, Q. To achieve environment coverage using the SCAT algorithm, the locational optimization cost function in (13) is minimized by partitioning the environment, Q, into nonoverlapping Voronoi cells using [9] •

min H (P) = min P

P

n Z X i=1

f (d (q, pi )) φ (q) dq

(14)

Vi

where each Voronoi cell is defined as Vi = {q ∈ Q|f (d (q, pi )) ≤ f (d (q, pj )) ∀j 6= i}

(15)

C. SCAT - Task Assignment In essence, the fundamental purpose of SCAT is to simultaneously track dynamic targets invading an area of interest, Q, while maintaining uniform coverage throughout that same area of interest. Consequently, for a given number of targets, K, a task assignment problem needs to be formulated such that K + 1 tasks can be simultaneously maintained (i.e., K target tasks and 1 uniform coverage task). A target task is only generated for targets inside the area of interest, Q, however, the number of tracking tasks, K, can change over time as targets enter and/or leave the area of interest. As a result, this task assignment problem is essentially modeled by composing a series of radial basis functions which provide the importance of each target relative to coverage. These radial basis functions, centered at the positions of the targets within the environment, are combined to generate the following time-varying density function for insertion into (17) [9] φ (q, t) =

n Z X i=1

2

kq − pi k φ (q) dq.

(16)

Vi

Extending (16) to allow for time-dependent coverage through the density function, φ, gives [9] H (P, t) =

n Z X i=1

2

kq − pi k φ (q, t) dq

(17)

(18)

where αk and β are tuning constants defining the importance of a given task. As can be seen in Figure 2, the parameter αk defines the importance of tracking target k, while the parameter β defines the importance of uniform coverage. The proper choices and definitions of αk , β and φk are mission/application specific and are typically governed by a number of scenario-related factors such as target threat-levels and/or system sensing and communication capabilities. K

f (q, t ) = å a k fk (q, t ) + b k =1

weight for uniform coverage

Density Function

weight for tracking kth target

B. SCAT - Target Tracking

H (P) =

αk φk (q, t) + β

k=1

and the collection of all Voronoi cells is referred to as the Voronoi tessellation. Consequently, minimizing over the environment relative to the available platforms/sensors reveals that a given point, q, within the environment, Q, essentially becomes the responsibility of the platform, pi , which provides the best sensing performance at that point.

To achieve target tracking using the SCAT algorithm, the cost function outlined in (13) is restricted to the planar case (i.e., N = 2) with d defined as the Euclidean distance, f (x) = x2 , and the environment, Q, is convex. In this restricted setting, the cost function can be written as [9]

K X

0.3 0.2 0.1 0 20

β 20

0 Y

Fig. 2.

0 -20 -20

X

Illustration of SCAT Task Assignment Model

The final requirement for implementing the SCAT capability is the implementation of a decentralized controller capable of maintaining all platforms/sensors in a configuration which minimizes H (P, t). D. SCAT - Exponential Controller As shown in [9], the optimal configuration of the SCAT algorithm occurs when each platform is located at the centroid of its corresponding Voronoi cell, defined as

Vi

which, as will be outlined in the next subsection, ultimately provides the ability to dynamically track targets invading the environment.

pi = CVi ∀i where

(19)

TABLE I G ROUND -BASED ISR PARAMETERS

CVi = LVi /MVi (centroid of ith Voronoi cell) Z L Vi = qφ (q) dq (q-weighted sum of ith Voronoi cell) Vi Z MV i = φ (q) dq (mass of ith Voronoi cell). Vi

(20) Consequently, optimal deployment for the time-varying density function defined in (18) requires that each platform track its corresponding Voronoi centroid over time. The exponential controller proposed to achieve this is outlined in [9] and given as

ui =

(LVi + Ri − MVi pi ) 

2 kLVi + Ri − MVi pi k

2

2

kMVi kCVi − pi k + Fi



(21) where Ri can be thought of as a disturbance to the centroid position due to the moving boundaries of the Voronoi regions, and Fi accounts for the time-varying nature of φ (q, t) and is defined as

Fi = (CVi − pi )

′

Z

(2q − CVi − pi ) φ˙ (q, t) dq.

(22)

Vi

From the above, it can be seen that the exponential controller defined in (21) essentially drives a given platform, pi , to the centroid of its corresponding Voronoi cell, CVi , while simultaneously accounting for time-varying targets through the function Fi . IV. SIMULATED PERFORMANCE RESULTS The autonomous, cooperative capabilities developed in this work were evaluated relative to a unique, heterogeneous scenario consisting of ground-based ISR and air-based SEAD. The con-ops of the scenario are outlined below: •

•

•

A strike aircraft is required to pass through an area of interest containing an enemy integrated air defense system (IADS). The primary mission is to survey the area of interest using cooperative, ground-based ISR and generate a map of any detected RF emitters. This emitter map is then communicated to a fleet of UAVs providing cooperative SEAD for the strike aircraft as it passes through the area of interest containing the enemy IADS.

Phase 1 of the mission involves ground-based ISR using Active Decentralized Data Fusion with cooperative coverage, uncertainty and communications control. For this phase of the mission, the primary goal is to jointly survey the regionof-interest while maintaining communications-connectivity and ultimately driving down the emitter location uncertainties to reasonable values. The simulated parameters used for Phase 1 of the mission are outlined in Table I. Simulation snapshots are provided in Figures 3-4.

Parameter Area-of-Interest Number of Emitters Number of UGVs UGV Velocity UGV Location Uncertainty UGV Sensor Detection Range UGV Sensor Detection Angle UGV Sensor Range Uncertainty UGV Sensor Angle Uncertainty UGV Communications Range UGV Communications Xmit Frequency

Value 1600 meters x 4000 meters 10 3 20 meters/second 0.5 meters (GPS) 300 meters 180 degrees 0.1 meter/meter (1-σ) 2 degrees (1-σ) 800 meters 10 Hz

Phase 2 of the mission involves air-based SEAD using Simultaneous Coverage and Tracking and the emitter map generated from Phase 1 of the mission. For this phase of the mission, the primary goal is to shield the strike aircraft from being detected as it flies through the area of interest containing the enemy IADS. To accomplish this, the SCAT environment, Q, and corresponding UAVs are colocated with the strike aircraft so that as the strike aircraft progresses through the area of interest, the Voronoi cells are continuously adapted relative to the emitter map providing cooperative and global SEAD for the strike aircraft. The simulated parameters used for Phase 2 of the mission are outlined in Table II. It should be noted that the SCAT β and αk parameters provided in Table II were selected to provide the desired trade-off between coverage and tracking relative to the specific mission objectives. In addition, the SCAT radial basis functions, φk , were defined to reflect the expected region of influence corresponding to the emitters needing to be neutralized. Simulation snapshots for Phase 2 of the mission are provided in Figures 5-6. TABLE II A IR -BASED SEAD PARAMETERS Parameter SCAT Environment (Q) Strike Aircraft Velocity Strike Aircraft Location Uncertainty Number of UAVs UAV Velocity UAV Location Uncertainty UAV Range of Influence Emitter Detection Range SCAT Coverage Weight (β) SCAT Tracking Weight (αk )

Value 1000 meters x 1000 meters 100 meters/second 0.5 meters (GPS) 3 200 meters/second 0.5 meters (GPS) 450 meters 500 meters 1 1.25

From Figures 3-6, it can be seen that the cooperative capabilities of Active Decentralized Data Fusion coupled with Simultaneous Coverage and Tracking successfully achieve the mission objective of shielding the strike aircraft as it passes through the area of interest containing the enemy IADS. V. SUMMARY AND ADDITIONAL WORK This work has established a proof-of-concept for combining the complementary strengths of two autonomous methods which cooperatively control a number of distributed mobile platforms relative to a common mission objective.

UAV

Active Decentralized Data Fusion was shown to achieve autonomous and intelligent control by maximizing the joint information gain relative to various information metrics of interest such as coverage, target uncertainty and communications. Similarly, Simultaneous Coverage and Tracking was shown to achieve autonomous and intelligent control via locational optimization and Voronoi tessellations. The complementary strengths of the two methods were illustrated via a unique, heterogeneous, ground/air, ISR/SEAD application scenario. Anticipated future efforts involve characterizing the robustness and various performance trends of the combined autonomous methods such as coverage time, localization accuracy, communications connectivity and shielding success relative to the number of platforms, platform velocities, sensor accuracies and communications capabilities. Additionally, the development of self-localization methods, such as SLAM, for operation in GPS-denied environments is also of interest. Finally, identifying the optimal SCAT parameter values relative to a desired mission objective is an area of continued exploration.

SCAT Environment

Strike Aircraft UAV Region of Influence

Emitter Emitter Detection Range

Flight Path

Fig. 5.

Strike Aircraft Entering Area of Interest

Suppressed Emitters

Uncovered Area of Interest

Large Emitter Location Uncertainty at Initial Detection

Fig. 6.

Emitter

Comms-Connectivity

Covered Area of Interest

Sensor Detection Range

Ground Platform

Fig. 3.

Initial Mapping of Area of Interest

[4] [5] [6] [7] [8]

[9]

[10] Fig. 4.

Intermediate Mapping of Area of Interest [11]

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