Maxim A. Batalin, Gaurav S. Sukhatme Presented by:Shawn Kristek

 A robot has networked sensor nodes that it can deploy. These static nodes then suggest the least recent direction taken when visited. i.e. An intelligent breadcrumb trail for robots

 Problem Definition  Algorithm  Analysis  Simulations  Implementation  Conclusions

 Problem Definition  Algorithm  Analysis  Simulations  Implementation  Conclusions

Quick Facts  Goals  Coverage  Exploration  Based on the deployment of static, communication-enabled, sensor nodes  No localization or maps  Unlimited active nodes assumed

The Nodes  Heart of this work  Simple computation  Sensing  Small Processor  Simple communication  Limited range radio  Forms a sensor network / support infrastructure – the breadcrumb trail

The robot  Uses the nodes to solve the coverage problem  Only uses local data from closest node  Goal is to visit least recently visited (LRV) node Robot visiting/dropping node Forward moving robot

 Problem Definition  Algorithm  Analysis  Simulations  Implementation  Conclusions

R = receive NODE_INFO messages from nodes in vicinity if out of SHORT communication range with n then (n closest, d closest ) = node and corresponding direction in R with largest signal strength if n ≠ NULL then Send(UPDATE_DIR, n closest, d closest ) Send(UPDATE_DIR, n closest, Opposite(d closest )) else deploy sensor node n ' with suggested direction d ' (n closest, d closest ) = (n ‘, d ‘) if no obstacles detected in direction d closest (n,d ) = (n closest, d closest ) else Send(UPDATE_DIR, n closest, d closest ) Wait for response, repeat the check if moving and obstacle detected ≤ OBSTACLE_AVOIDANCE_RANGE then if obstacle is large and no nodes in vicinity deploy sensor node n‘ with suggested direction d ‘ (n,d ) = (n ‘, d ‘) if obstacles detected in direction d then Send(UPDATE_DIR, n, d ) Wait for response, repeat the check else avoid the obstacle if d = NULL then Move in direction d n, d – current node and suggested direction R – set containing data received from nodes in robot’s vicinity (node id, signal strength, suggested direction); SHORT – communication range threshold used to determine when to deploy new nodes; Opposite(d) – function returning direction opposite to d Robot

Repeat: if received UPDATE_DIR message from robot with direction d update then W (d update ) = W (d update ) +1 Send(NODE_INFO, n, ANY_OF(arg min ∀ d Є D( i ) W (d )) ) n, d – current node and suggested direction D(i)– set of direction incident to node i, the possible directions W(d) – number of times direction d traversed from this node ANY_OF(G) – function returns member of set G according to arbitrary rule; ex. ordered, or random Node What it does: Waits for updates and sends directions, based on updates.

LRV in Action  Initially no nodes -Robot starts by deploying a node  Next nodes deployed are networked to at least one other node  This continues indefinitely or until no new nodes are required  The robot then continually covers the environment

 Problem Definition  Algorithm  Analysis  Simulations  Implementation  Conclusions

 Graphs  Trees  Lattice  Note: The algorithm uses none of these. This is for analysis only.

On Graphs  Treat nodes as the vertices of a graph even though no explicit adjacency lists are maintained at each node  Analyze the steady state n – current node the robot is at n’ – next node; the node the robot transitions to while Cover/Explored the graph = FALSE do n’ = ANY_OF(argmin ∀ j E(n) W(n, j )) W(n, n’ ) := W(n, n’ ) +1 n := n’

On Trees  Complete  The least weight edge is selected  Trees - graphs without cycles  Exploration time Θ(2|E|) or Θ(n)

On a Lattice  Special case graph  Why is this applicable? -Implementation utilizes compass with k bits and 2 k directions -Analyze case of several equal W(e)

What they found for a Square Lattice  LRV coverage O(V 1+Є )

More Comparison  LRV  1-LRTA*  DFS n – current node the robot is at n’ – next node; the node the robot transitions to while Cover/Explored the graph = FALSE do n’ = ANY_OF(argmin ∀ j E(n) W( j )) W(n) := W(n’) +1 n := n’

Convergence Speed  RW  LRV  1-LRTA*

Square Lattice Assumptions  DFS  All resources available -Nodes -Map -Localization -Perfect navigation  Limited number of simple nodes  1-LRTA*  Graph exploration algorithm  Not purely local

On a Cube Lattice

Cube/Square Lattice  Ordered selection instead of random  Tie breakers – optimal time more likely Circle Line Cross

Effects of Order Choices – Cover Time Maps Random Cross Line Circle Darker – more time

 Problem Definition  Algorithms  Analysis  Simulations  Implementation  Conclusions

 Follows Problem Definition  Player / Stage  Pioneer 2DX robots  1.5m,180 ˚ fov planar laser range finder  Wireless communication Differences:  Cover time – laser  Noise

 Problem Definition  Algorithms  Analysis  Simulations  Implementation  Conclusions

Nodes  Recommend direction  The four cardinal directions; i.e. 2 bit compass  Each direction - OPEN or EXPLORED  OPEN first T – binary state (OPENED, EXPLORED) C – counter for a direction E – possible additional information

Robot  Behavior-based decisions  Obstacles  Node locations  Node recommendations

 Problem Definition  Algorithm  Analysis  Simulations  Implementation  Conclusions

 Feasible applications  Network repair/maintenance  Questionable Comparisons  Graph algorithms???  Overall good results/ideas  Coverage times less than O(n ln n)  Self healing – dead nodes replaced  Simple