1 Mobile Sensor Network Deployment using Potential Fields : A Distributed, Scalable Solution to the Area Coverage Problem Andrew Howard, Maja J Mataric´,

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Mobile Sensor Network Deployment using Potential

Fields : A Distributed, Scalable Solution to the Area Coverage

ProblemAndrew Howard, Maja J Mataric´ , and Gaurav S Sukhatme

Robitics Research Laboratories, Dept. of Computer Science, University of Southern California, Los Angeles.

International Symposium on Dustributed Autonomous Robotics Systems (DARS02)

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Outline

Introduction Related Work Potential Fields Equation of Motion and Control Law Static Equilibrium Experiments Conclusion and further work

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Introduction

A mobile sensor network is composed of mobile sensor nodes.

Mobile sensor node has communication sensing, computation, and locomotion capabilities.

Locomotion facilitates a number of useful network, including the self-deploy ability.

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Introduction

Deployment environment may be hostile and dynamic. Ex: Damaged building

Target environment gives two constraints :

Model of environment are either incomplete, inaccurate or unavailable.

Sensor nodes may be lost or destroyed.

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Introduction

This paper describes a potential-field-based approach to deployment.

The only assumption is each sensor node can determine the range and bearing of nearby nodes and obstacles.

The approach does not require model of environment or centralized control.

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Related Work Coverage type of many-robot system [5] :

Blanket coverage: reach a static arrangement of nodes that maximize

the total detection area.

Barrier coverage: minimize the probability of undetected penetration

through the barrier.

Sweep coverage: more-or-less equivalent to a moving barrier.

* [5] D. W. Gate. Command control for many-robot system.

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Related Work

Related problems

Potential field techniques for local navigation and obstacle avoidance problem [10]* [10] O. Khatib. Real-time obstacles avoidance for manipulators and mobile robots.

Multi-robot exploration and mapping problem [3, 4, 14, 15]* [3] W. Burgard, M. Moors, D. Fox, R. Simmons, and S. Thrun. Collaborative multi-robot exploration.

* [4] G. Dedeoglu and G. S. Sukhatme. Landmark-based matching algorithms for cooperation mapping by autonomous robots.

* [14] R. Simmons, D. Apfelbaum, W. Burgard, D. Fox, M. Moors, S. Thrun, and H. Younes. Coordination for multi-robot exploration and mapping.

* [15] S. Thrun, W. Burgard, and D. Fox. A real-time algorithm for mobile robot mapping with applications to multi-robot and 3d mapping.

Traditional art gallery problem [12] * [12] J. O’Rourke. Art Gallery Theorems and Algorithms.

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Potential Fields

Each node is subject to force F from potential field U.

Divide potential field into two component due to obstacles due to sensor nodes

nUoU

UF

no UUU no FFF

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Potential Fields

Potential due to obstacles

: obstacles seen by the node : constant strength of the field : Euclidean distance between the node and obstacle i;

, denote the position of node, denote the position of obstacle i.

i i

oo rkU

1

ok

irxxr ii x ix

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Potential Fields

Total force due to obstacles

The force is expressed entirely in terms of the relative position of obstacles, it allows us compute directly from sensed data.

ii i

oi

i

oooo rr

kdx

dr

dr

dU

dx

dUUF ir 2

1

xxi ir 1irirxxi ir ,

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Potential Fields

Fig.1. (a) Potential field generated byA simple environment; the contoursshow the lines of equal potential.

Fig. 1. (b) Force field generated by The potential field; arrows indicatethe direction (but not magnitude) of the force.

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Potential Fields

Total force due to other nodes

: constant strength of the nodes field

ii i

nn rrkF ir 2

1

i i

nn rkU

1

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Equation of Motion

Equation of motion

: the acceleration of the node : the velocity of the node : the mass of the node : viscous coefficient

This viscous friction term “ “ is used to ensure that the node will come to a standstill in the absence of external forces.

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Control Law

Use control law to map virtual physical system to real system.

Real nodes have both kinematic and dynamic constraints.

Assuming the nodes have holonomic drive mechanisms to ignore kinematic constraint.

Dynamic constraint can’t be ignored. Nodes have both maximum velocity and maximum

acceleration. Control law should capture dynamic constraint.

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Control Law

Change of commanded velocity is determined by using piecewise-constant approximation.

is the largest allowable change in velocity.

The commanded velocity is determined:

is the maximum allowable velocity.

with

with

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Control Law

Two regimes in which the correspondence will fail.

For small velocity, the viscous friction term will tend to produce oscillation to zero velocities. Typical behavior of discrete control system.

Can be eliminated by a velocity ‘dead-band’.

Large acceleration and velocities will be clipped. It increases time taken to reach equilibrium.

Impact must be determined empirically.

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Static Equilibrium

The network will reach a static equilibrium

System energy is composed of potential and kinetic energy.

Total energy is determined by initialization.

Viscous friction term of motion equation has the effect of removing energy.

The system is dissipative

The network must asymptotically approach static equilibrium

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Static Equilibrium

Above argument rests on the assumption that the environment is static.

The network may not reach equilibrium in continually changing environment.

The network will reach static equilibrium in periodically or intermittently environment, but the equilibrium may be different after change.

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Experiments

Experiment environment

100 sensor nodes with scanning laser.

Laser range is 4m and 360 degree field-of-view.

Maximum velocity is 0.5 m/s

Simulated by using Player robot server[7] and the Stage[17,6] multi-agent simulator.

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Experiments

Fig. 2. (a) Initial network configuration.

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Experiments

Fig. 2. (b) Final configuration after 300 seconds.

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Experiments

Fig. 2. (c) Occupancy grid generated for the final configuration;visible space is marked in black (occupied) or white (free);unseen space is marked in gray.

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Experiments

Fig. 3. Network coverage area and average node separationas function of time for a 100-node deployment experiment. The coverage and separation are plotted on different scales.

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Experiments

The node spacing is even (about 1.6±0.4m).

No gaps or breaks in the coverage.

Rate of coverage decreases with time.

Final configuration (500m2) is 10-fold improvement over the initial configuration (50 m2).

Average velocity of boundary nodes in the early phase is higher.

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Conclusion

Potential field approach can be used to deploy mobile sensor network.

It is a distributed and scalable approach.

It has provable convergence characteristics.

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Future Works

More experiments with different factors

Internal factors: environment, initial condition…

External factors: strength of fields, node mass, viscosity coefficient…

Apply approach to coverage problems in which line-of-sight connectivity is important.