Overview. Basic Setup [9] Motivation and Tasks. Modularization 2008/2/20 IMPROVED COVERAGE CONTROL USING ONLY LOCAL INFORMATION

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1 Overvew 2 IMPROVED COVERAGE CONTROL USING ONLY LOCAL INFORMATION Introducton Mult- Smulator MASIM Theoretcal Work and Smulaton Results Concluson Jay Wagenpfel, Adran Trachte Motvaton and Tasks Basc Setup [9] 3 Mult- System (MAS): Number of autonomous agents sensng and nteractng wth other agents and the envronment. Cooperatve tasks: Rendezvous [1] [2] [3]: all agents rendezvous at an arbtrary pont Deployment [1] [4]: acheve maxmum deployment of agents n envronment Coverage [1] [4] [5]: acheve maxmum coverage of regons of nterest Flockng [6] [7] [8] moton coordnaton n a synchronzed manner and obstacle avodance [6] [1] Ln Martnéz et al - et Local - Moton control Coordnaton strateges for wth groups Dstrbuted of moble Informaton autonomous agents [7] [2] [4] Jang Ln Cortés et -al An et - al The mproved - Spatally-dstrbuted mult-agent algorthm rendezvous for coverage coordnaton problem optmzaton -control 2003 of and mult-agent control wth system lmted-range based on r-lmted nteractons vorono parttons [8] [3] [5] Tanner Cortés Schwager et al al et --al Robust Flockng - Dstrbuted rendezvous agents Coverage wth for varyng moble Control nterconnecton autonomous wth Sensory agents Feedback topology va proxmty -for 2004 Networked graphsrobots Basc Setup: Coverage of Regons of Interest: s can sense nformaton gven by the envronment, e.g. temperature gradents. : A s ntroduced as a central unt whch processes the nformaton obtaned by the agents. Communcaton: Communcaton cost s ntroduced. s act as a relay to transfer the nformaton obtaned by other agents to the base. Goal: Gan coverage of the areas wth hgh nformaton densty whle keepng the power consumpton low. [9] L et al Dstrbuted Cooperatve Coverage Control of Sensor Networks Modularzaton 5 Dvde For dfferent agent n control certan tasks functonable t s necessary parts to lke have n standard dfferent control trajectory theory: plannng, dfferent controllers or even a dfferent Dynamcs sensor behavour. Envronment detector Task Manager Trajectory Computaton Controller Mult- Smulator MASIM Class Overvew General Structure Modularzaton example: 1

2 Mult- Smulator MASIM Class Overvew 7 8 Need for a tool to smulate mult-agent behavor wthout restrctons Self-programmed Framework MASIM MAS Mathematcs Geometry TaskManager Control Trajectory Planner Implemented n JAVA Modular desgn usng OO-programmng technques d on MASON [10] Mult-agent smulaton core lbrary Provdes basc vsualzaton Free avalablty MAE Arena MAS_UI Smple Functon2D Spatally Dscretzed Functon2D Precalculated Functon2D TM_Exploraton Coverage Feedback TP_Rlm VoronoCell TP_L_ComCost _Extended [10] Package Overvew: MASIM Package Overvew: Mathematcs 9 10 Class MAS Intalzaton, Schedulng Class MAE Encapsules the envronment, densty functon, msson space, etc Class Arena Geometry of the msson space Class MAS_UI Vsualzaton, GUI MASIM MAS MAE Arena MAS_UI Package for mathematc computatons Sub-Package Geometry: Classes for geometrc computatons, e.g. r-lmted vorono cells Class Functon2D Encapsules functons f : R²->R Subclasses mplement functonalty for spatally dscretzed grds, precalculated functon values and other specal types of functons Mathematcs Geometry Functon2D Spatally Dscretzed Functon2D Precalculated Functon2D Package Overvew: Package Overvew: Control Class Implements basc functonalty Sub-classes: Smple: Smple Dynamcs : Specalzed agent Sub-package : Non control-related modules Class Class Smple Control-related modules of the agent: Class TaskManager Class TrajectoryPlanner Class Feedback Subclasses mplement specalzed functonalty TaskManager TM_Exploraton Coverage Control Trajectory Planner TP_Rlm VoronoCell TP_L_ComCost _Extended Feedback 2

3 Functonalty of the Smulaton 14 Mult-agent smulator MASIM Class Overvew General Structure Modularzaton example: So far herarchcal relaton of classes. But, how does the smulaton work? How s the smulaton bult from these classes? Functonal relaton between classes. Address the ssue n two steps: General structure of the smulator: Whch classes are requred to buld a smulaton envronment for the agents? Modular structure of the agents: Whch classes model the functonalty of the agents? General Structure of the Smulator Modular Structure of the s Densty functon Arena From before: s functonalty s dvded nto modules. Ths can as well be seen n the software mplementaton Class : Very basc functonalty Contaner for modules Subclasses extend functonalty beyond modularzaton Modular Structure of the s 17 Communcaton Interagent communcaton Mult-agent smulator MASIM Detector Trajectory plannng Dfferent moton behavors. Feedback control Task managng Select proper modules to acheve desred tasks Task Manager Trajectory Planer Feedback Detector Controller s dynamcs & propertes Class Overvew General Structure Modularzaton example: 3

4 Example Module: Example Module: Basc Propertes Owned by agent Communcaton range Basc Methods Constructors Important Propertes Neghbors n com-range Communcaton Costs To Amount of data to be transferred Data of agent s detector Data to be relayed Cost Functon Example Module: Example Module: Important methods Compute communcaton cost to neghbors and base Update communcaton neghbors Fnd shortest path to base Depends on neghbors communcaton cost to base Loop avodng Important Propertes Valdaton flags Important Methods Search path to base Improved robustness aganst lnk falures Enables to fnd a com-path to base after loss of com-neghbor 23 Example Module: Algorthm: 1. Connecton to base va relayng neghbor s checked. 2. If connecton s lost, agent s nvald and sets all com. neghbors to nvald as well. 3. Invald agents search for a new connecton to the base by searchng for vald agents. 4. If a new connecton to the base s found, all connected neghbors are set vald agan. Theoretcal Work and Smulaton Results Problem Formulaton Keep-together functon Exploraton Combnng Tasks 4

5 Msson Space and Sensor Model Coverage Control Msson Space: 2-D plane: Event densty Functon: poston: 2 R( x), x s and s ( s,, s ) N Goal s to maxmze the expected event detecton probablty over the msson space P( x, s) 1 [1 p ( x)] N 1 Probablty that an event s detected. Detector Model: the probablty to detect an event depends on: Dstance to poston, where event takes place, as sgnal strength declnes. x s p ( x) p e 0 F( s) R( x) P( x, s) dx max Fs ( ) s1,..., s N Value functon Communcaton Communcaton Cost 27 Communcaton between agents: A functon descrbng the communcaton cost to receve and forward data, ncreases monotoncally wth ncreasng dstance to target agent. e( d) d 1 2 Communcaton to base: Computng the shortest path to the base va a routng protocol. n Energy for transmttng one bt data over a dstance d 28 Goal s to mnmze the communcaton cost c 3 Overall power consumpton to transfer one bt of data from agent to the base. ( s ) R( x) p ( x) dx Data rate orgnated by the th agent. Downstream neghbor: s the next agent n the shortest path to the base h N G( s) c ( s ) 1 Communcaton Cost Functon U Upstream neghbors: s a set of neghbors, whch use agent to communcate wth the base mn Gs ( ) s1,..., s N Solvng the Optmzaton Problem Summary 29 Maxmze F(s) and mnmze G(s) max J( s) wth J( s) 1F ( s) 2G( s) s1,..., s N Optmzaton va partal dervatves F G r 1 2 : v s s J s reference trajectory 30 Formulated coverage control problem va value functon F(s) Introduced communcaton cost va cost functon G(s) Optmzaton of J(s) va partal dervatves Certan assumptons Under certan assumptons t s possble to approxmate these dervatves wth only local nformaton. [9] movement wth only local nformaton [9] L et al Dstrbuted Cooperatve Coverage Control of Sensor Networks

6 Keep Together Functon: Motvaton Theoretcal Work and Smulaton Results Problem Formulaton Keep-together functon Exploraton Combnng Tasks 32 Lmted communcaton range Wreless communcaton s restrcted to certan dstances wthn whch a relable communcaton s possble. Communcaton from agents to base s necessary To transmt the sensed nformaton to the base t s necessary that every agent stays connected to ts neghbors Artfcal potental functon to keep the agents connected 33 Keep Together Functon: Propertes Potental functon n dependence of dstance d d a b Dstance from pont a to pont b Propertes of functon f: f( d) s contnous and monotoncally ncreasng f (0) 0 lm f ( d ) dr Example: d f( d) ( R d) n R= 5 n=2 34 Applcaton of Keep Together Functon It s necessary to stay n contact wth the downstream neghbor and all upstream neghbors. Dstances to down- and upstream neghbors have to be smaller than R Notaton d s s h f ( d ) f Dstance from agent to ts downstream neghbor h Functon f whch depends of d s denoted as f 35 Applcaton of Keep Together Functon Formulaton of gradents to keep agents together T f s T f j ju s KT-gradent to downstream neghbor KT-gradent to upstream neghbors Reference Trajectory T T f f j r v s ju s 36 Desgnng the Keep Together Functon Choose Communcaton Range R Keep Together Functon should not overrde other gradents f neghbors are suffcently close Desgn functon f close to zero for d < R and f for dr R= 5 n=20 6

7 Keep Together Functon 37 Now compare behavor: Optmzng only coverage and communcaton cost, no Keep-Together Functon Addtonally consderng Keep-Together functon 38 Densty Functon Gradent and Communcaton Cost Theoretcal Work and Smulaton Results Problem Formulaton Keep-together functon Exploraton Combnng Tasks 39 Wth Keep Together Functon Revew Coverage Control 41 Coverage control: Maxmzng the probablty of detectng events. Most mportant areas of the msson space are well covered. Problem: Areas of the msson space may be hdden from the agents. Not all mportant areas are covered. 42 Msson space wth hdden areas 7

8 Algorthm for Exploraton 43 Explorng the msson space: Use a deployment algorthm Maxmze the area covered by all agents. Algorthm uses r-lmted Vorono Cells Movng towards centrod of r-lmted Vorono Cell Radus s gven by communcaton range. Usng only local nformaton. 44 Exploraton usng r-lmted Vorono Cells Combnng Tasks: Motvaton 46 Theoretcal Work and Smulaton Results Problem Formulaton Keep-together functon Exploraton Combnng Tasks Now we have two tasks: Coverng the most mportant areas of the msson space to maxmze the probablty of detectng events. Explorng the complete msson space by maxmzng the area covered by all agents. Idea: Combne both tasks: Frst explore the msson space. Then cover the most mportant areas. Enables the agents to cover areas unreachable f only usng coverage control. Combnng Tasks: Motvaton Taskswtch va Consensus Extended Setup: Swtch task when the whole msson space has been explored. Problem: How does each agent know, that the whole msson space has been explored? s only possess local nformaton. Informaton about all agents / whole msson space s needed. Consensus s the state where all agents n the network acheve agreement. In ths case, agreement on swtchng the task. Ths s equvalent to agreement that the complete msson space s explored. Msson space s explored when all agents stop movng. Implement an agreement protocol based on movement of agents. 8

9 Taskswtch va Consensus Taskswtch va Consensus 49 Add two varables λ gves the state of agent λ = 0 means agent s movng λ = 1 means agent has stopped Λ s the consensus state of agent 1 j 1 N N N s the set of neghbors of agent N s the number of neghbors of agent 50 In every step: Frst update state λ. Then update Λ accordng to the gven formula. If the msson space has not completely been explored: There are movng agents wth state λ = 0 For the consensus varable holds Λ < 1. If all agents have stopped: 1 for each agent. Taskswtch va Consensus Consensus wth ε = If Λ > (1-ε), wth ε 1, then Set Λ = 1 Swtch to coverage task Ideally, all agents ht the threshold at the same tme. In realty, there s always a small delay between the frst and the last agent to ht the threshold. Add a dead-tme to each agent before t starts movng accordng to the coverage task. 52 λ 1 = 0 1 Λλ 1 = = ⅓/ 9 λ 1 = 0 Λ 1 = Λ0 1 = 0 λ 2 λ 2 = = 00 1 Λ Λ 2 = = ⅓/ 9 λ 2 = 0 Λ 2 = 0 Swtchng task Threshold ht (>0.9) λ 3 λ = 3 = Λ Λ 3 = 5 3 = ⅓/ 9 0⅓ Frst agent s consensus varable hts threshold 53 Smulaton Results 54 Smulaton Results 9

10 55 Smulaton Results 56 Smulaton Results Summary 58 Concluson Summary Outlook Extendable and versatle smulaton envronment for Mult- Systems Analyss of jont detecton probablty coverage algorthms and enhanced functonalty Keep-Together Functon Combnng dfferent control tasks for mproved behavor Realzng a consensus algorthm for task swtchng All Algorthms use only local nformaton Outlook Outlook 59 s Specalzed agents, e.g. communcaton agents Ansotropc Improved routng protocols Detector Ansotropc Detector Combnaton of dfferent detectors and sensng tasks Controller Dfferent controller technques Convergence for dscrete controller 60 Envronment A tme dependent densty functon for event probablty Non-rectangular arenas Smulator Asynchronty Theoretcal Work Proof the functonalty of the Keep-Together Functon 10

11 61 62 THE END Consensus mt agent falure Paper man, cortes Relay agent falure -> agents lost n space Dead-tme for task swtch Thank you for your attenton 11