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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,

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Coordination Algorithms for Motion-Enabled Sensor Networks

CDC Workshop Point-Stabilization, Trajectory-Tracking, Path-Following, and Formation Control of Autonomous Vehicles San Diego, Dec 12, 2006 Francesco Bullo Center for Control, Dynamical Systems and Computation 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

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Outline

(i) state of the art (ii) research directions (iii) fundamental challenges (iv) technical approaches: models and scenarios for motion-enabled sensor networks (v) current open problems

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Incomplete state of the art

AeroVironment Inc, “Raven” small unmanned aerial vehicle iRobot Inc, “PackBot” unmanned ground vehicle Distributed algorithms automata-theoretic: “Distributed Algorithms” by Lynch numerical: “Parallel and Distributed Computation” by by Bertsekas and Tsitsiklis Cooperative control “rendezvous” by Morse and Anderson “flocking” by Olfati-Saber, Jadbabaie

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Incomplete state of the art: cont’d

Behavior-based robotics learning algorithms by Mataric, architectures by Parker, heuristics Operations research, geometric optimization “facility location” by Robert and Toussaint “illumination problems” by Urrutia “approximation and interpolation theory” by Gruber “vehicle routing problems” by Bertsimas and van Ryzin

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Research directions

Build: distributed systems embedded actuator/sensors networks Develop distributed disciplines: (i) sensor fusion (ii) communications (iii) coordinated control (iv) task allocation and scheduling Challenges (i) scalability (ii) performance (iii) robustness (iv) models

Environmental monitoring Building monitoring and evac Security systems

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Technical approach

(i) models and application scenarios (ii) orchestration of control, communication, sensing, computing

1. Feedback

rather than open-loop computation for known/static setup

2. Information flow who knows what, when, why, how
3. Optimization

design efficient algorithms

Wildebeest herd in the Serengeti Geese flying in formation Atlantis aquarium, CDC 2004

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Models of robotic networks

A uniform/anonymous robotic network S is (i) I = {1, . . . , N}; set of unique identifiers (UIDs) (ii) A = {Ai}i∈I, with Ai = (X, U, f) is a set of physical agents (iii) interaction graph

disk graph visibility graph Delaunay graph

geometric or state-dependent message random geometric packet/bits

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Control and communication protocols

(i) communication schedule T = {tℓ}ℓ∈N0 (ii) communication alphabet L including the null message (iii) set of values for logic variables W (iv) message-generation function msg: X × W × I → L (v) state-transition functions stf: W × LN → W (vi) control function ctrl: X × W × LN → U

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Task and complexity

Coordination tasks (i) Logic-based: synchronize, elect leader, form teams (ii) Motion: deploy, rendezvous, flock (iii) Sensor-based: search, estimate, identify, track, map Complexity

control effort, time, communication packets, computational cost
algorithm and task
worst case and expected
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Scenario 1: Deployment algorithms

Assumptions: 1st order agents (p1, . . . , pn), unspecified comm graph Objective: achieve optimal coverage Expected environment coverage

let φ be distribution density function
let f be a performance/penalty function

f(q − pi) is price for pi to service q

define multi-center function

HC(p1, . . . , pn) = Eφ

f(q − pi)

=
i
Vi(p1,...,pn)

f(q − pi)φ(q)dq

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Scenario 1: Distributed gradient result

If f : R≥0 → R has finite discontinuities at R1 < · · · < Rm, then ∂HC ∂pi (p1, . . . , pn) =

∂ ∂pi f(q − pi)dφ +

∆fα(Rα)

arci,k(2Rα)

nkdφ

= integral over Vi

+integral along arcs inside Vi Gradient depends on information contained in Vi

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Scenario 1: Dispersion laws for deployment

Dispersion laws At each comm round:

1: acquire neighbors’ positions 2: compute own dominance region 3: move towards incenter /

circumcenter / centroid of

wn dominance region

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Scalability/performance/robustness analysis

(i) distributed over Delaunay graph (ii) convergence to local minima of HC; performance monotonic with n (iii) time complexity: worst case O(n3 log(n)) in 1d (iv) robust to: agent arrival/departure (v) robust to: small delays and asynchronicity (vi) robust to: sensor noise

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Scenario 2: Boundary estimation

Assumption: local sensing and tracking, interpolation via waypoints Objective: estimate/interpolate moving boundary

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Scenario 3: Visually-based deployment

Assumptions: Sensing and communication within line-of-sight Objective: complete visibility of nonconvex environment Approach: optimal partition, incremental exploration, information flow

s Q s Q s Q k_2 s Q Q s

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Scenario 3: complexity and robustness

Depth-first deployment Breadth-first connected deployment

scalability/performance/robustness analysis (i) time complexity: worst-case O(n), balanced-case O(log(n)) (ii) required # agents: worst-case ⌊n/2⌋, locally greedy (optimum is NP hard) (iii) robust to: arbitrary finite delays and packet losses (iv) robust to: sensor noise, agent arrival/departure, environment changes

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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