Coordination Algorithms Outline for Motion-Enabled Sensor Networks CDC Workshop Point-Stabilization, Trajectory-Tracking, Path-Following, and (i) state of the art Formation Control of Autonomous Vehicles (ii) research directions San Diego, Dec 12, 2006 (iii) fundamental challenges Francesco Bullo (iv) technical approaches: models and scenarios for motion-enabled sensor networks Center for Control, Dynamical Systems and Computation (v) current open problems University of California at Santa Barbara http:/ /motion.mee.ucsb.edu Ack: Anurag Ganguli, Sara Susca, Ketan Savla Jorge Cort´ es (UCSC), Emilio Frazzoli (UCLA), Sonia Mart´ ınez (UCSD) Ack: ARO, ONR YIP, NSF Sensors • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit Incomplete state of the art Incomplete state of the art: cont’d Behavior-based robotics learning algorithms by Mataric, architectures by Parker, heuristics AeroVironment Inc, “Raven” iRobot Inc, “PackBot” unmanned small unmanned aerial vehicle ground vehicle Operations research, geometric optimization “facility location” by Robert and Toussaint “illumination problems” by Urrutia Distributed algorithms automata-theoretic: “Distributed Algorithms” by Lynch “approximation and interpolation theory” by Gruber “vehicle routing problems” by Bertsimas and van Ryzin numerical: “Parallel and Distributed Computation” by by Bertsekas and Tsitsiklis Cooperative control “rendezvous” by Morse and Anderson “flocking” by Olfati-Saber, Jadbabaie • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit
Research directions Technical approach Build: distributed systems Challenges embedded actuator/sensors networks (i) scalability (i) models and application scenarios (ii) performance (ii) orchestration of control, communication, sensing, computing Develop distributed disciplines: (iii) robustness 1. Feedback rather than open-loop computation for (i) sensor fusion known/static setup (iv) models (ii) communications 2. Information flow who knows what, when, why, how 3. Optimization design efficient algorithms (iii) coordinated control (iv) task allocation and scheduling Wildebeest herd in the Serengeti Geese flying in formation Atlantis aquarium, CDC 2004 Environmental monitoring Building monitoring and evac Security systems • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit Control and communication protocols Models of robotic networks (i) communication schedule T = { t ℓ } ℓ ∈ N 0 A uniform/anonymous robotic network S is (ii) communication alphabet L including the null message (i) I = { 1 , . . . , N } ; set of unique identifiers (UIDs) (iii) set of values for logic variables W (ii) A = { A i } i ∈ I , with A i = ( X, U, f ) is a set of physical agents (iii) interaction graph (iv) message-generation function msg : X × W × I → L stf : W × L N → W (v) state-transition functions ctrl : X × W × L N → U (vi) control function disk graph visibility graph Delaunay graph message geometric or state-dependent random geometric packet/bits • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit
Task and complexity Scenario 1: Deployment algorithms Assumptions: 1st order agents ( p 1 , . . . , p n ) , unspecified comm graph Objective: achieve optimal coverage Coordination tasks (i) Logic-based: synchronize, elect leader, form teams (ii) Motion: deploy, rendezvous, flock Expected environment coverage (iii) Sensor-based: search, estimate, identify, track, map • let φ be distribution density function • let f be a performance/penalty function f ( � q − p i � ) is price for p i to service q Complexity • control effort, time, communication packets, computational cost • define multi-center function • algorithm and task � � H C ( p 1 , . . . , p n ) = E φ min f ( � q − p i � ) • worst case and expected i � � = f ( � q − p i � ) φ ( q ) dq V i ( p 1 ,...,p n ) i • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit Scenario 1: Distributed gradient result Scenario 1: Dispersion laws for deployment Dispersion laws At each comm round: If f : R ≥ 0 → R has finite discontinuities at R 1 < · · · < R m , then 1: acquire neighbors’ positions 2: compute own dominance region ∂ H C ( p 1 , . . . , p n ) 3: move towards incenter / ∂p i circumcenter / centroid of � ∂ � � � � � own dominance region = f ( � q − p i � ) dφ + ∆ f α ( R α ) n k dφ ∂p i V i arc i,k (2 R α ) α k = integral over V i + integral along arcs inside V i Gradient depends on information contained in V i • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit
Scalability/performance/robustness analysis Scenario 2: Boundary estimation Assumption: local sensing and tracking, interpolation via waypoints Objective: estimate/interpolate moving boundary (i) distributed over Delaunay graph (ii) convergence to local minima of H C ; performance monotonic with n (iii) time complexity: worst case O ( n 3 log( n )) in 1d (iv) robust to: agent arrival/departure (v) robust to: small delays and asynchronicity (vi) robust to: sensor noise • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit Scenario 3: Visually-based deployment Scenario 3: complexity and robustness Assumptions: Sensing and communication within line-of-sight Objective: complete visibility of nonconvex environment Approach: optimal partition, incremental exploration, information flow Depth-first deployment Breadth-first connected deployment s s s s s scalability/performance/robustness analysis (i) time complexity: worst-case O ( n ) , balanced-case O (log( n )) k_2 (ii) required # agents: worst-case ⌊ n/ 2 ⌋ , locally greedy (optimum is NP hard) (iii) robust to: arbitrary finite delays and packet losses Q Q Q Q Q (iv) robust to: sensor noise, agent arrival/departure, environment changes • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit
Emerging discipline: motion-enabled networks • network modeling network, ctrl+comm algorithm, task, complexity • coordination algorithm deployment, task allocation, boundary estimation Open problems (i) algorithmic design for motion-enabled sensor networks scalable, adaptive, asynchronous, agent arrival/departure tasks: search, exploration, identify and track (ii) integration between motion coordination, communication, and estimation tasks (iii) Very few results available on: (a) scalability analysis in motion coordination: communication/control/time (b) robotic networks over random geometric graphs (multipath, fading) (c) complex sensing/actuation scenarios = ⇒ temporal logic specifications • First • Prev • Next • Last • Go Back • Full Screen • Close • Quit
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