Collaborative Robotics and Wireless Sensor Networks in Area-Coverage related Problems

John Stergiopoulos

Dept. Elect. & Comp. Eng.Univ. of Patras, Greecestergiopoulos@ece.upatras.gr

Anthony Tzes

Dept. of Elect. & Comp. Eng.Univ. of Patras, Greecetzes@ece.upatras.gr

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Presentation Layout

Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part I

Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part I: Problem Setup (1)

Coordinate the motion of the nodes in order to Coordinate the motion of the nodes in order to achieve optimum sensing coverage of a regionachieve optimum sensing coverage of a region

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part I: Problem Setup (2)

Mobile-network characteristics Homogeneous mobile nodes Uniform symmetric limited sensing patterns Discrete-time spatial evolution Bounded control inputs Communication capabilities

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part I: Problem Setup (3)

Optimization cost :

No analytic expression exists for the cost function

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part II

Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part II: Optimization Techniques (1)

Offline global optimization

Ω, n, r Optimal network configuration

Path planning needed for achieving optimal positioning

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part II: Optimization Techniques (2)

Computationally intensive (even for small n) Non-adaptive

change in the region of interest (Ω) network alteration (n, r)

Exhaustive search (…) “Genetic algorithms”-based strategies

… however …

re-perform optimization (!)

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part II: Optimization Techniques (3)

Online optimization strategies Each node self-organizes its action so that its motion

contributes to netwok coverage Decision taken is based on local information No path planning needed; the nodes will self-position

themselves accordingly through time

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part II: Optimization Techniques (4)

Gradient-based techniques Huge/infinite number of local extrema Convergence to locally-optimum positions

Adaptive by nature Applicable in real-time scenarios

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part III

Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part III: Voronoi Diagrams (1)

Why use Voronoi tessellation?

Local information – decentralized approach

Each node tries to optimize its “local” area-coverage contribution through its motion

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part III: Voronoi Diagrams (2)

Optimize “local” coverage contribution Motion of one node at a time is required

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part IV

Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part IV: Generalized Coverage Algorithm (1)

Main concept

One node moves at each time-step to ensure network’s area-coverage monotonicity, while avoiding oscillatory phenomena

Direction at which a node should move inside its Voronoi cell is defined according to “coverage-increase” criteria

Unless its motion contributes to coverage, the node does not move

Stability of the network’s motion is guaranteed

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part IV: Generalized Coverage Algorithm (2)

Communication issues

Each node has a communication range such that local information from Delaunay neighbors at step k and k+1 is obtained

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part IV: Generalized Coverage Algorithm (3)

Compute own Voronoi cell (local information – Delaunay neighbors)

Compute current “local” area-coverage Define the direction at which to move Predict area-coverage at step k+1, if motion is performed

at this direction Move only if coverage is to be increased

Node i is to move at step k

How is the selection of the node-to-move performed?

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part IV: Generalized Coverage Algorithm (4)

Centralized approach

step kstep k-1

Need for global supervision Communication issues arise

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part IV: Generalized Coverage Algorithm (5)

Decentralized approach

… or cyclic self-selection (based on the node’s ID)

Randomizers on each node’s processor (same seed)

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Motion of a node inside its Voronoi cell guarantees collision avoidance

Part V

Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part V: Coordination Schemes (1)

At each step, a node performs an optimization to define the direction to move towards

Optimal direction is the one that leads to maximum area-coverage contribution at the next step, considering its Delaunay neighbors

ε-maneuvers are performed, so that the Voronoi cell does not alter significantly

Steepest-descent scheme

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part V: Coordination Schemes (2)

CVT-based coordination strategies lead to optimization of some “symmetry” criterion

CVT-based schemes

If a node moves towards the centroid of its R-limited Voronoi cell, it tends to maximize the symmetry of the unexploited regions arounds itself

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part V: Coordination Schemes (3)

Since the unexploited regions of a node act as repulses, when the latter is moving towards , the algorithm is coverage-oriented

A node moves towards iff its coverage contribution will increase

One-step-ahead prediction ensures area-coverage monotonicity

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part VI

Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part VI: Simulation Studies (1)

Steepest-descent scheme

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part VI: Simulation Studies (2)

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part VI: Simulation Studies (3)

CVT-based scheme

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part VI: Simulation Studies (4)

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Part VI: Simulation Studies (5)

In both cases, the pecentage area-coverage is a monotonically increasing function of time

In the “deepest-descent” case, maximum coverage is obtained faster than in the CVT-based scenario (rational, considering the nature of the algorithm)

The network tends to keep itself more cohesive via the CVT-based scheme (“move towards ”), while μicro-maneuvers are performed by the nodes when the network’s state is near-to-optimal

Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

Thank youFor more information please refer to:

stergiopoulos@ece.upatras.grtzes@ece.upatras.gr