Dynamic Resource Networks: Coordination and Control of Networks with Mobile Actuators and Sensors

Transcription

1 Dynamc Resource Networks: Coordnaton and Control of Networks wth Moble Actuators and Sensors Kevn L. Moore, Ph.D., P.E.¹ G.A. Dobelman Dstngushed Char and Professor of Engneerng Dvson of Engneerng Colorado School of Mnes ¹Some work performed at the Johns Hopkns Unversty Appled Physcs Laboratory and the Utah State Unversty Center for Self- Organzng and Intellgent Systems

2 Outlne Introductory Comments Dynamc Resource Networks DSN) General Ideas Motvatng Examples A Framework for Dffuson Problems A Coordnated Optmzaton Approach Consensus Varables and Extensons Example Decentralzed, cooperatve adaptve schedulng Hgher-order Consensus Example Flockng-lke behavor n coordnated moton Dstrbuted Computaton Global Optmzaton va Coordnaton Example Data exfltraton problem

3 Networked Sensors Through hstory, many technologes have become ubqutous: Mcroprocessors, Motors Today a new technology has the same promse; Networked sensors Due to advances n n bology, electroncs, nanotechnology, wreless communcatons, computng, networkng, and robotcs, we can now: Desgn advanced sensors and sensor system Use wreless communcatons, or telemetry, to more effectvely communcate sensor data from a dstance than ever before Buld networks of sensors, usng wreless communcatons and computer networkng technology, that can provde the capablty to obtan spatally-dstrbuted measurements from low-power sensors whch communcate and relay nformaton between each other Develop reconfgurable, or adaptable, networks of dstrbuted sensors by provdng moblty or actuaton to the ndvdual sensors n the network

4 Technology Enables Paradgm Change Smaller, larger, more complex: smaller becomes larger Nano-tech, MEMS, molecular computng devces Advances n sensors, communcatons, nanotechnology, and bology enable the the concept nformaton about everythng avalable everywhere Informaton s no longer a smple sensor output, but becomes multmodal/mult-meda Result s more complex engneered systems, wth mplcatons for Hardware: dstrbuted wreless) and embedded Software: parallel, dstrbuted, ntellgent algorthms Systems: dstrbuted and embedded, ssues nclude: Informaton management Informaton processng Decson makng Systems and control thnkng becomes key

5 Paradgm Change Brngs Challenges Key challenge: the classcal, lumped parameter ODE/PDE paradgm of systems and control s nadequate for future progress. Essentally every thng done n the last [50] years of control theory rests on a common presumpton of centralty [that all the nformaton avalable about the system, and the calculatons based on ths nformaton, take place at a sngle locaton] Survey of decentralzed control methods for large scale systems, Sandell, Varaya, Athans, Sarnov, IEEE Transactons on Automatc Control, Aprl From an algorthmc perspectve, we need to turn to spataltemporal methodologes.

6 Paradgm Change Brngs Opportunty One perspectve on future challenges and opportuntes for sensor networks can be summarzed by: Only through control wll sensor networks acheve ther value, Mchael Bruns, VP A&D AS Process Automaton, Semens AG, DE, comments durng Plenary Lecture, Wednesday, July 6, 2005 IFAC World Congress, Prague. From ths perspectve, I would lke to comment on deas related to what Dynamc Resource Networks, whch ncludes the dea of Moble Actuator/Sensor Networks, or MASNET

7 Dynamc Resource Networks Network of enttes Communcaton nfrastructure Entty-level functonalty Impled global functonalty Not necessarly homogeneous Resource: Prmarly consderng enttes that are sensors Bgger pcture ncludes actors as well Dynamc Enttes may be moble Communcaton topology mght be tme-varyng Data actvely and delberately shared among enttes Decson-makng and learnng

8 A Prototypcal Problem Gven: Network of dstrbuted, statc sensors Each nstantated wth a perfect classfer that allows successful target dentfcaton f gven perfect measurements Each receves corrupted sgnatures due to sensor placement n the envronment Each sensor has a lmted detecton range and a lmted communcaton range and BW between sensors Each sensor s connected to some of the other sensors; assume at least one spannng tree exsts n the graph; also assume that at least range between communcatng sensors s known Each sensor can compute the bearng and possble classfcaton of three domnant targets n ts regon of detecton Multple movng targets Moton vector velocty, atttude) Characterstc sgnature e.g., tank, car, motorcycle, etc.) wth spatally-lmted range of nfluence Fnd: Estmated moton vector and classfcaton of all targets movng through the sensor feld

9 A Dual to the Prototypcal Problem Gven: Network of dstrbuted, statc targets Each has a characterstc sgnature wth spatally-lmted range of nfluence, each related to the other n some known) way e.g., fxed network of weather statons for ecologcal montorng n the wlderness) Each target s connected to some of the other sensors; assume at least one spannng tree exsts n the graph Some targets have hgher-level communcatons Sngle movng sensor Instantated wth a perfect classfer that allows successful classfcaton of the phenomena represented by the targets f gven perfect measurements Receves corrupted sgnatures due to sensor placement n the envronment Fnd: Classfcaton of the phenomena represented by the targets

10 A Set of Related Problems Sensors: Passve lsten only) or Actve llumnates and lstens) Homogeneous or heterogeneous Moble or Fxed Sngle or Multple Isolated or Networked) Target: Passve must be llumnated) or Actve generates sgnature) Homogeneous or heterogeneous Moble or Fxed Sngle or Multple Isolated or Networked) Sngle Entty Statonary Passve Actve Moble Multple Enttes Isolated/Networked

11 Dynamc Resource Networks Defne seven types of resources: UGS: Unattended ground sensor UGA: Unattended ground system wth drect acton capablty e.g., autonomous artllery) UGS-n: Local network of multple UGS UAV-s: UAV used as a sensor UAV-a: UAV wth drect acton capablty e.g., strke) UGV-s: UGV used as sensor UGV-a: UGV wth drect acton capablty UAV-s UAV-a UGA UGS-n UGV-s UGS UGV-a Each entty s characterzed by Type Acton Regon Sensor regon of attracton blue) Actor regon of nfluence red) Communcaton Envelope yellow) Moblty Vector green)

12 Motvatng Example 1 Autonomous swarm for plume trackng Sensor-carryng UAVs and UGVs assess and track the development of a hazardous plume resultng from a CBR terrorsm act.

13 Motvatng Example 2 Autonomous confederaton buldng, adaptve to changes n battlefeld condtons Confederaton B Confederaton A Confederaton B Target Cluster A Target Cluster B Confederaton A Target Cluster A Target Cluster B

14 Motvatng Example Three -1 Data exfltraton applcaton Sensor clusters are deployed by hand Not all clusters can communcate wth each other Exact cluster locatons are not known UAVs execute a cooperatve search to fnd the clusters Search begns wth a pre-planned raster scan Search s refned based on cluster dscovery results After dscovery, UAVs cooperate to collect data from all the clusters n some optmal way UAVs confgure to provde maxmum coverage of clusters or An optmal path s planned to travel between clusters

15 Motvatng Example Three -2 Adaptaton occurs n response to changes n the UAV resources or the sensor clusters: Perodcally, one of the UAVs returns to the base staton to relay data from the senor clusters; when ths happens the remanng UAV automatcally re-plans ts operatons If a sensor cluster s lost the UAVs cooperatvely reconfgure

16 Motvatng Example Four Landslde Detecton/Predcton Network of communcaton sensor such as geophones Changes n relatve locatons used to detect onset of landslde Alarm Analyss Staton Before Dstrbuted Sensor Node Wreless Communcaton Lnk After

17 Motvatng Example Fve Center Pvot Irrgator Control Assume can bury a sensor at some prescrbed depth at regular ntervals Adjust water applcaton rate based on the sensor readngs between cycles Sensor

18 Outlne Introductory Comments Dynamc Resource Networks DSN) General Ideas Motvatng Examples A Framework for Dffuson Problems A Coordnated Optmzaton Approach Consensus Varables and Extensons Example Decentralzed, cooperatve adaptve schedulng Hgher-order Consensus Example Flockng-lke behavor n coordnated moton Dstrbuted Computaton Global Optmzaton va Coordnaton Example Data exfltraton problem

19 Mote-Based Dstrbuted Robots Prototype plume-trackng testbed $ nd Place Prze n 2005 Crossbow Smart-Dust Challenge

20 MAS-DIFF Smulator Developed at USU Prof. YangQuan Chen)

21 Outlne Introductory Comments Dynamc Resource Networks DSN) General Ideas Motvatng Examples A Framework for Dffuson Problems A Coordnated Optmzaton Approach Consensus Varables and Extensons Example Decentralzed, cooperatve adaptve schedulng Hgher-order Consensus Example Flockng-lke behavor n coordnated moton Dstrbuted Computaton Global Optmzaton va Coordnaton Example Data exfltraton problem

22 An Algorthmc Approach for Cooperaton Bgger pcture s coordnaton and control of multple, cooperatng, heterogeneous enttes: Our techncal approach, a generalzaton of potental feld approaches, s based on so-called consensus varables and has connectons to problems n: Coupled-oscllator synchronzaton Neural 2 1 networks

23 Consensus Varable Perspectve Asserton: Mult-agent coordnaton requres that some nformaton must be shared The dea: Identfy the essental nformaton, call t the coordnaton or consensus varable. Encode ths varable n a dstrbuted dynamcal system and come to consensus about ts value Examples: Headng angles Phase of a perodc sgnal Msson tmngs In the followng we buld on work by Randy Beard, We Ren, et al., at BYU, to use consensus varables to solve global problems n a dstrbuted fashon

24 Consensus Varables Suppose we have N agents wth a shared global consensus varable Each agent has a local value of the varable gven as Each agent updates ther local value based on the values of the agents that they can communcate wth k G where j are gans and j defnes the communcaton topology graph of the system of agents Key result from lterature: If the graph has a spannng tree then for all

25 Consensus Varables Specfcally, let so that If C satsfes Then: 1. C has one egnenvalue at zero and the others are stable occurs ff the assocated graph has a spannng tree) 2. s a stochastc matrx postve, wth row sum equal one) 3. e Ct = c T 1, 1,..., N ) cj > 0, j cj = 0, j < 0 & = 1 Ct e [ ] M v1 K vn, v = 1 1 C

26 Example: Sngle Consensus Varable

27 Extenson 1 - Forced Consensus Forced Consensus Sometmes we may lke to force all the nodes to follow a hard constrant Ths can be done by njectng an nput nto a node as follows Then we use a feedback controller as gven n the followng

28 Example Forced Consensus

29 Extenson 2 Multple, Constraned Consensus Often we wll have multple consensus varables n a gven problem It can be useful to enforce constrants between these varables, specfcally, to have = j + Δj Agan we can gve a feedback control strategy to acheve ths type of constraned consensus between groups of agents

30

31 Example Multple, Constraned Consensus

32 Outlne Introductory Comments Dynamc Resource Networks DSN) General Ideas Motvatng Examples A Framework for Dffuson Problems A Coordnated Optmzaton Approach Consensus Varables and Extensons Example Decentralzed, cooperatve adaptve schedulng Hgher-order Consensus Example Flockng-lke behavor n coordnated moton Dstrbuted Computaton Global Optmzaton va Coordnaton Example Data exfltraton problem

33 Outlne Introductory Comments Dynamc Resource Networks DSN) General Ideas Motvatng Examples A Framework for Dffuson Problems A Coordnated Optmzaton Approach Consensus Varables and Extensons Example Decentralzed, cooperatve adaptve schedulng Hgher-order Consensus Example Flockng-lke behavor n coordnated moton Dstrbuted Computaton Global Optmzaton va Coordnaton Example Data exfltraton problem

34 Extenson 3 Hgher-Order Consensus Can generalze to hgher-order as follows. Let & & M 1) 2) = 0 = 1 & l t) = N j= 1 k j t) G j t)[ l 1 k = 0 γ k k ) k ) j )] Then, f there s a spannng tree and system s stable) you wll get Stablty depends on the gans γ k l M l 1 l 2 l* t t 2 l 1 * for all l 2 * + γ for all + tγ + β for all

35 Extenson 3 Hgher-Order Consensus In more detal, we can show that the global dynamcs are gven by where and L s the communcaton topology matrx Turns out Γ has l zero egenvalues each of geometrcty 1)ff L has one one zero egenvalue ff there exsts a spannng node)

36 Extenson 3a Model-Reference Consensus As a fnal pont, suppose we are gven a reference model, defned by Let the consensus protocol be gven as Then t s possble to gve condtons for whch = = = + = = = 1 0 ) ) ) ) 1 2) 0 1) ) )] )[ ) ) l k r k r k k k N j l k k k j j l u t G t k t j γ η γ & M & &,k for all ) ) k r k

37 Extenson 3 Hgher-Order Consensus For example, consder a thrd-order consensus problem, appled to a formaton control problem wth fve vehcles, wth one vehcle havng an acceleraton setpont nput Enables formaton control Acceleraton Input

38 Extenson 3 Hgher-Order Consensus Suppose the leader node sees the followng acceleraton nput profle:

39 Extenson 3 Hgher-Order Consensus The resultng paths look lke:

40 Extenson 3 Hgher-Order Consensus The resultng x-axs trajectory shows the effect of the hgherorder consensus algorthm

41 Outlne Introductory Comments Dynamc Resource Networks DSN) General Ideas Motvatng Examples A Framework for Dffuson Problems A Coordnated Optmzaton Approach Consensus Varables and Extensons Example Decentralzed, cooperatve adaptve schedulng Hgher-order Consensus Example Flockng-lke behavor n coordnated moton Dstrbuted Computaton Global Optmzaton va Coordnaton Example Data exfltraton problem

42 Extenson 4 Dstrbuted Computaton Suppose we want to solve where we thnk of as a local varable on node Assumptons are that we do not have global knowledge of the complete vector v on every node nodes are connected wth a graph topology whereby every node s a spannng node N T N N N R v v v for v f v f v v = = ),, ) ) K M & M & v

43 Extenson 4 Dstrbuted Computaton Approach uses a multvarable extenson of the forced consensus deas presented above. * Let v be the soluton of v & = f v) Introduce a varable x at each node a local estmate of v ) Set up the followng system on each node x& b = x f, K, 1 & 1 M = & N v N j= 1 * k j N t) G = 0, K,0,1,0, K,0) ) for j t) t) t)) + b x T all Then f every node s a spannng node conjecture) j ) Inserts a setpont nto -th component of node

44 T b x b t t t k f x 0,0,0,1,0,0,0,0,0) ) )) ) ) ),, = + = = & M & K & T b x b t t t k t t t k f x 0,0,0,0,0,0,1,0,0) ) )) ) ) )) ) ) ),, = + = = & M & K & Extenson 4 Dstrbuted Computaton

45 Outlne Introductory Comments Dynamc Resource Networks DSN) General Ideas Motvatng Examples A Framework for Dffuson Problems A Coordnated Optmzaton Approach Consensus Varables and Extensons Example Decentralzed, cooperatve adaptve schedulng Hgher-order Consensus Example Flockng-lke behavor n coordnated moton Dstrbuted Computaton Global Optmzaton va Coordnaton Example Data exfltraton problem

46 Outlne Introductory Comments Dynamc Resource Networks DSN) General Ideas Motvatng Examples A Framework for Dffuson Problems A Coordnated Optmzaton Approach Consensus Varables and Extensons Example Decentralzed, cooperatve adaptve schedulng Hgher-order Consensus Example Flockng-lke behavor n coordnated moton Dstrbuted Computaton Global Optmzaton va Coordnaton Example Data exfltraton problem