Control of UAVs

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Control of UAVs

• Raja Sengupta (sengupta_at_ce.berkeley.edu)
• Assistant Professor
• Civil and Environmental Engineering Systems
• UC Berkeley
• Joint Work with the C3UV team

2
Challenge of Flying Low

• Helicopter pilots fly low
• FAA requires see and avoid
• Find the freeway and follow it

3
Used Sectionals to build a Manhattan model at 300
feet (approx.)

• Simulation testing of Control

4
Flying Low Strategy

• Helicopter pilots fly low
• Find the freeway or waterway and follow it
• Avoid few remaining obstacles

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Cal Freeway Detection on MLB Video(No Control)

• Generic corridor
• detection by one-
• dimensional
• learning
• Roads
• Aqueducts
• Perimeters
• Pipelines
• Power Lines

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Road FollowingClosed Loop Control, August 2003
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Generalization Vision Based Following of Locally
Linear Structures(Closed Loop on the California
Aqueduct, June 2005)
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Obstacle Avoidance
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Tailored to..

• For most UAV applications (gt50 m), the obstacles
  of concern will be large objects such as towers,
  buildings or large trees
• For these cases, the problem of obstacle
  detection is different from that of ground
  vehicles in environments cluttered with many
  obstacles.

VS
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Flight Demonstration

• Experiment flown on a Sig Rascal airframe with a
  Piccolo avionics package and vision processing on
  an onboard PC104.
• An 8.5 foot diameter balloon was used as the
  obstacle (distance currently calculated using
  GPS).

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Flight Demonstration
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Flight Demonstration
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Distributed Information Management for
Collaboration
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Objective Distribute the data objects shared by
the team across the members of the team

Operation decomposer
Team Level
Resource allocation/scheduling
Operation monitor
Dispatcher
Formation Navigation
UCB Rathinam 2004
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Scalable Information Management

• Geographic Data Management Network

Sengupta AINS 2003
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Scalable Information Management
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Distributed Implementation in Action
Movie of our Implementation 4 agents on 4
laptops over a wireless LAN
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End
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Detailed Slides
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Results Tracking the California Aqueduct

• The average error of the position of the vehicle
  from the curve was 10 meters over a length of 700
  meters of the canal.

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Results Canal Following

• The road detection algorithm runs at 5 Hz (takes
  lt 200 ms) or faster on the PC104 (700 MHz, Intel
  Pentium III).
• No visible error was found from video sequences
  of over 100 frames containing the canal

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Flying Low

• Helicopter pilots fly low
• Find the freeway and follow it
• FAA requires see and avoid
• obstacles and aircraft

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Obstacle Avoidance is a Constraint Not a
MissionApproach Safe Set-theoretic

• Assume capabilities of the airplane
• Compute an unsafe set
• When in the safe set, execute the mission
• On the boundary execute the obstacle avoidance
  control
• Assume obstacles are
• Sparse
• Stationary
• Rectangular

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As the UAV avoids an obstacle it slides on the
boundary of the unsafe set
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Analytical Solution
Pl
Cr_ns
Cr
Oa
Ocusp
y (m)
Ona
BRS
Cl
Pr
x (m)

• The analytical solution can be calculated in 5 ms

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Cal UAV Target CapabilitiesObstacle Avoidance

• Simulation testing of Control
• Flight through Manhattan model (300 feet)

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Related Work

• Vision-based obstacle avoidance has been studied
  primarily in the context of mobile ground robots.
• Lenser 03, Ohya 00, Lorigo 97,
• Vision based navigation of UAVs
• Saripalli 02, Shakernia 02, Furst 98 Landing
  with known markings
• Sinopoli 01, Doherty 00 Visual landmark
  navigation (terrain avoidance) for helicopter
• Ettinger 02, Pipitone 01, Kim 03 Pose
  estimation for aircraft
• Obstacle/Collision Avoidance for UAVs
• Mitchell 01 Aircraft avoiding known aircraft
• Sigurd 03 Aircraft with magnetic sensors
• Sastry 03 Helicopters avoiding known
  helicopters/obstacles
• How 02 MILP for Obstacle Avoidance
• Vision based obstacle avoidance
• Barrows 03 Biomimetic reactive control

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Related Research

• Ground robots
• Fixed baseline stereo JPL, many others
• Monocular map construction Lenser (CMU), Kim
  (Berkeley)
• Cooperative stereo - CMU
• Optical Flow
• Helicopter ground following Srinivasan/Chahl
  (Australia)
• Corridor following - USC helicopter
• Micro UAV obstacle avoidance Centeye
• UAV depth map construction
• Lidar CMU Helicopter Project, Sastry (Berkeley
  Helicopter Project).
• Vision high precision IMU Bhanu (joint with
  Honeywell)
• Stereo Vision
• GT Helicopter

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Requires DepthTypically use Stereo Vision

• Given the image coordinates of a feature in one
  image
• if one can find the image coordinates of the
  feature in the other image (feature matching),
  and
• if one knows the rotation and translation of the
  two image planes then one knows the world
  coordinates of the feature (Ego-motion
  Estimation)

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Problem with Depth Estimation by Stereo Vision
Z
Z
Z-
0
z
Increased accuracy requires increased camera
separation
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Accurate Depth Estimation is a Problem

• Range error due to pixel errors is
  .

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Approach

• UAVs flying at low altitudes must autonomously
  avoid obstacles
• Strategy
• Segment the image into sky and non-sky
• Non-sky in the middle ? OBSTACLE
• Strategy 1
• Aim at the sky
• Strategy 2
• If it looms faster than a threshold and is in the
  middle ? AVOID
• Else do NOTHING

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Segmentation at Moffet Airfield

• Results for multiple regions found (only largest
  regions shown, dark blue represents all small
  regions)

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Sky Segmentation
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Vision Processing

• Classification balloon/horizon correctly found
  in 90 of images
• Time results 2Hz (120ms SVM, 200-600 ms
  horizon)

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Obstacle Avoidance Next Steps

• Loom 4 pixels/second asuming a 70deg FOV camera
  with 320 pixels, Speed 20 m/s
• turn radius 100 m, processing delay of 0.5 s,
  safe avoidance distance of 10 m, the minimum
  obstacle size is about 2.5 m

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Theoretical Work and Tool Development
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Resource Allocation Algorithms for Multi-vehicle
Systems with Nonholonomic Constraints
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Vehicle Target Path Planning Problem

• Vehicles V v1,v2,...vn, Targetst1,t2...tm,
  Angles of approach ?1, ?2... ?m
• Assign a cycle Pi for each vehicle starting and
  ending at vertex vi such that Ui PiV. A cycle
  Pi is a ordered sequence of vertices ti1,...tik
  for the vehicle i to visit
• Assign paths for each vehicle that satisfy the
  non-holonomy constraints for the given sequence.
• The objective is to minimize ?Cost(Pi)

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• Resource Allocation or Vehicle-Target Assignment
• Given a collection of targets that need to be
  serviced and a collection of vehicles, how do you
  assign vehicles to targets ?
• 1-1 Vehicle Target Assignment
• Vehicle-Target Path Planning
• More targets than vehicles

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1-1 Vehicle Target Assignment
Objective
Constraints

• Solution to the relaxed linear programming
  formulation is a feasible solution for the
  assignment problem
• Total unimodurality

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Vehicle Target Path Planning Problem

• Traveling salesman problem if number of vehicles
  1 and no kinematic constraints
• Asymmetry, that is dij ? dji but satisfies
  triangular inequality
• c-Approximation algorithm cost of the solution
  is atmost c times the optimal value
• Approximation algorithms for asymmetric TSP
• Based on the number of points visited 0.99log(n)
  - Markus Blaser (2002)
• Based on the ratio of the distances dmax/dmin -
  Kumar and Li (2002)
• Single vehicle problem with non-holonomy - Bullo
  et al, 2005
• Multi vehicle problem with heuristics Zhijun et
  al, 2005
• Asymmetry with kinematic constraints can be
  bounded if the euclidean distance between the
  points are reasonably apart, d 2R
• Sensor footprints are at least of the order of
  the minimum turning radius.
• Basic idea
• Solve the problem assuming the distances are
  Euclidean
• Using the sequence for each vehicle, assign paths
  that satisfy kinematic constraints

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Motion Planning

• Find the minimal distance path joining ( x1,y1
  ,?1 ) and ( x2,y2,?2 ) subject to kinematic
  constraints

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Algorithm for Vehicle Target Path Planning Problem
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Algorithm for Vehicle Target Path Planning Problem
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Algorithm for Vehicle Target Path Planning Problem
Find the Eulerian walk for each subtree and
reduce it to a TSP tour for each vehicle 2
approximation algorithm because the cost of the
multigraph is 2Cost(MST)
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Algorithm for Vehicle Target Path Planning Problem
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Algorithm for Vehicle Target Path Planning Problem

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Algorithm for Vehicle Target Path Planning Problem

• Theorem The approximation algorithm has a bound
  of 2ddubins/deuclidean 6
• Further the distance between the points, better
  the bound is
• At best it could be 2
• Angles of approach for the targets were given

A
B
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Conclusions

• Addressed the problem of resource allocation in
  the context of unmanned aerial vehicles
• Algorithms for multiple vehicles satisfying
  kinematic and fuel constraints.
• Tighter bounds for the algorithms
• Future work could address vehicles with fuel
  constraints, targets with precedence constraints
  etc.

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Embedded Software Tools for Collaborative Control
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With the advent of Digital Computing Control
linked to the Synchronous Model of Computation
Caspi P. Embedded Control From Asynchrony to
Synchrony and Back, EMSOFT 2001
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SIMULINK F14 Control System
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F14 aircraft model
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Analog Autopilot
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Digital autopilot
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Extend Control Design Tools to Networked
Environments?
Develop code for swarm of UAVs for collaborative
control. The code is developed on the same
high-level, easy to use tools used to develop the
F14 control. The code is automatically
distributed across the different UAVs and it
behaves as expected.
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Distributing the Synchronous Model
Cascade Composition
Berry 91
yf(u)
ug(y)
Feedback Composition Fixpoint Semantics

• Both order and timing would have to be enforced
  across networks

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The Logical Order can be enforced Without
Scheduling! Zennaro, Sengupta EMSOFT05

• Implementation problem given a map ? from RA to
  STS traces we want an implementation map ? such
  that, for all STS s and RA r the following
  holds
• (r ?(s) ? r?t) ? s ? ?(t)
• Modularity preservation we seek a composition
  operator xRA with respect to which ? is a
  monomorphism between (STS, xSTS) and (RA, xRA).
  We want this operator to be implementable across
  a network

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What is currently available

• Simulink / RealTime Workshop currently does NOT
  support distributed implementation
• It has been proved that some modular synchronous
  systems can be compiled while preserving
  modularity in a distributed environment
• Benvenieste, Caillaud, Le Guernic
  Compositionality in dataflow synchronous
  languages specification and distributed code
  generation, Information and Computation, col.
  163, Nov 2000, Academic press
• Non finite system representation theoretical
  settings
• Tools for the automatic distribution of Simulink
  programs over TTA networks
• P. Caspi, A. Curic, A. Maignan, C. Sofronis, S.
  Tripakis and P. Niebert. From Simulink to
  SCADE/Lustre to TTA a layered approach for
  distributed embedded applications, ACM-SIGPLAN
  (LCTES'03), 2003
• Cannot be ported to non-TDMA networks

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What is currently available

• Tools for the automatic distribution of
  synchronous systems
• A. Girault, C. Menier, Automatic production of
  Globally Asynchronous Locally Synchronous
  Systems, EMSOFT 2002
• ESTERELLE / Lustre
• Modularity is not preserved
• Techniques for distributing synchronous systems
• J.Romberg, A. Bauer. Loose synchronization of
  event-triggered networks for distribution of
  synchronous programs, EMSOFT 2004
• Focus on timing constraints
• Modularity is not preserved

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What is currently available (Our work)

• Tools for the automatic distribution of
  synchronous systems
• M. Zennaro, R. Sengupta, Distributing Synchronous
  Systems with Modular Structure, CDC 2004
• M. Zennaro, R. Sengupta, Distributing Synchronous
  Programs Using Bounded Queues, EMSOFT 2005 (to
  appear)
• M. Zennaro, R. Sengupta, Distributing Synchronous
  Programs Using Bounded Queues, a coordinated
  traffic signal application, Research Report,
  UCB-ITS-RR-2005-4
• Simulink (single rate, fixed-time discrete
  solver)
• Modularity is preserved

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BDSP library contd
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Relevant Papers

• S. Rathinam, R. Sengupta, S. Darbha, A Resource
  Allocation Algorithm for Multi-vehicle Systems
  with Non-Holonomic Contraints, Submitted to the
  IEEE Transactions of Automation Science, June
  2005.
• S. Rathinam, Z. Kim, A. Soghaikan, R. Sengupta,
  Vision Based Following of Locally Linear
  Structures, Submitted to the 44th IEEE conference
  on Decision and Control 2005, Spain.
• M. Zennaro, R. Sengupta. Distributing Synchronous
  Programs Using Bounded Queues. To appear in the
  Proceedings of EMSOFT 2005, Jersey City, USA.
• McGee T., Sengupta R., Hedrick J.K. Obstacle
  Detection for Small Autonomous Aircraft Using Sky
  Segmentation. In proceedings of the International
  Conference on Robotics and Automation, April
  2005, Barcelona, Spain.
• Frew E., Sengupta R. Obstacle Avoidance with
  Sensor Uncertainty for Small Unmanned Aircraft.
  In proceedings 43rd IEEE Conference on Decision
  and Control, December 2004, Paradise Island,
  Bahamas.
• Rathinam S., Sengupta R. UAV Navigation in an
  Unknown Environment, 43rd IEEE Conference on
  Decision and Control, December 2004, Paradise
  Island, Bahamas.
• Zennaro M., Sengupta R. Distributing Synchronous
  Systems with Modular Structure. In Proc. of the
  43rd IEEE Conference on Decision and Control,
  December 2004, Paradise Island, Bahamas.
• Frew E., Spry S., Mcgee T., Xiao X., Sengupta R.,
  Hedrick J. K. Flight Demonstrations of
  Self-Directed Collaborative Navigation of Small
  Unmanned Aircraft. To appear at AIAA 3rd Unmanned
  Unlimited Technical Conference, Workshop,
  Exhibit, Chicago, IL, September 2004.
• Rathinam S., Zennaro M., Mak T., Sengupta R. An
  Architecture for UAV Team Control. 5th IFAC
  Symposium on Intelligent Autonomous Vehicles,
  Lisbon, Portugal, July 2004

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Relevant Papers

• Frew E., Kim Z., Howell A., McGee T., Rathinam
  S.,Xiao X, Zennaro M., Jackson S., Morimoto M.,
  Hedrick J. K., Sengupta R.. Stereo-Vision-Based
  Control of a Small Autonomous Aircraft Following
  a Road. Second Annual Swarming Conference,
  Crystal City, MD, June 2004.
• Frew E., McGee T., Kim, Z., Xiao X., Jackson S.,
  Morimoto, M., Rathinam R., Zennaro M. , Padial
  J., Sengupta R. Vision Based Road-Following Using
  a Small Autonomous Aircraft. IEEE Aerospace
  Conference, Big Sky, Montana, March 2004.
• Rathinam S., Sengupta R. A Safe Flight Algorithm
  for Unmanned Aerial Vehicles. IEEE Aerospace
  Conference, Big Sky, Montana, March 2004.
• Mahajan A., Ko J., Mak T., Sengupta R. GDMN An
  Information Management Network for Distributed
  Systems. 2nd IEEE Conference on Autonomous
  Intelligent Networked Systems, Menlo Park, CA,
  June 2003.
• Lee J., Huang R., Vaughn A., Xiao X., Hedrick
  J.K., Zennaro M., Sengupta R. Strategies of
  Path-Planning for a UAV to Track a Ground
  Vehicle. 2nd IEEE Conference on Autonomous
  Intelligent Networked Systems, Menlo Park, CA,
  June 2003.
• Mahajan A., Ko J., Sengupta R. Distributed
  Probabilistic Map Service. Proc. of the 41st IEEE
  Conference on Decision and Control, December
  2002.
• Ko J., Mahajan A., Sengupta R. A Network-Centric
  UAV Organization for Search and Pursuit
  Operations. Proc. of the 2002 IEEE Aerospace
  Conference, March 9-16, 2002.
• Zennaro M., Ko J., Sengupta R., Tripakis S. A
  Service Network Architecture for a Multi-Vehicle
  Search Mission. Proc. of the 40th IEEE
  Conference on Decision and Control, December 4-7,
  2001.

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Geographic Data Management
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Scalable Information ManagementTarget Map and
Risk Map

• Target distribution map
• P(A, N, t) probability of N targets of type t in
  area A
• Target distribution update
• Fuses measurements from different kinds of
  sensors (SAR and EO)
• Bayesian update
• Risk map computation
• Integral of threat model with respect to the
  measure P(A, N, t)
• Generates the value function for navigation

UCB Rathinam 2003
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Movie of Implementation

• 4 laptops over wireless
• One publisher per laptop
• Start with one publisher
• Three others come up
• Some die
• Data redistributes as publishers join and leave

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Movie of Implementation
Total data made of many data objects

• 4 laptops over wireless
• One publisher per laptop
• Start with one publisher
• Three others come up
• Some die
• Data redistributes as publishers join and leave

70
Movie of Implementation

• 4 laptops over wireless
• One publisher per laptop
• Start with one publisher
• Three others come up
• Some die
• Data redistributes as publishers join and leave

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Movie of Implementation

• 4 laptops over wireless
• One publisher per laptop
• Start with one publisher
• Three others come up
• Some die
• Data redistributes as publishers join and leave

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Movie of Implementation

• 4 laptops over wireless
• One publisher per laptop
• Start with one publisher
• Three others come up
• Some die
• Data redistributes as publishers join and leave

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Data Consistency in the PublisherInconsistent
copies are detected whp
Wrong location copy 1
Data Location
Wrong location copy 2
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Data Consistency in the PublisherDrift in a 2-D
Markov Process
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Geographic Data Management NetworkSurvivable
Information for UAV Swarms

• The server backbone dynamically tracks the client
  agent organization
• Servers move in and out while the information
  survives

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Tracking the Agent OrganizationDynamic GDMN
backbone Control

• Design a distributed control algorithm for the
  servers to partition the data and the clients to
  minimize the total bit-meters (Kumar etal.) of
  work done in the system and balance the load on
  the servers.
• Let the load generated in each client be bi. If
  the locations of the points are denoted by pi and
  the location of the servers are denoted by cj,
  then the total cost is
• ? bi ( min dist(pi, cj) )
• ? i ? j
• The control algorithm updates server positions to
  reduce this cost

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Simulation

• This example involves 100 clients and 6 servers

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Control algorithm

• In each sampling interval, each server
• Measures the positions and the traffic generated
  by its clients
• GDML routing protocols make the client set the
  Voronoi cell
• Calculates the weighted centroid of all the
  clients it serves
• Moves towards its weighted centroid
• Works well if the servers travel faster than the
  clients
• The algorithm is based on the k-means algorithm
  (MacQueen ,1967 )