Andrew Howard, Maja J Matari´c, and Gaurav S Sukhatme Speaker : Lee Heon-Jong

1. Mobile Sensor Network Deployment Using Potential Fields: A Distributed, Scalable Solution to the Area Coverage Problem Andrew Howard, Maja J Matari´c, and Gaurav S Sukhatme Speaker : Lee Heon-Jong Advanced Ubiquitous Computing

2. Contents • Introduction • Related Work • Potential Fields • Equation of Motion and Control Law • Static Equilibrium • Experiments • Conclusion and Further Work Advanced Ubiquitous Computing

3. Introduction • A mobile sensor networkis composed of mobilesensor nodes. • Mobile sensor node has communication, sensing, computation, and locomotion capabilities. • Locomotion facilitates a number of useful network, including the self-deploy ability. Advanced Ubiquitous Computing

4. 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. Advanced Ubiquitous Computing

5. Introduction • This paper describe 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. Advanced Ubiquitous Computing

6. Related Work • Coverage type of many-robot system [5] : *[5] D. W. Gate. Command control for many-robot system. • 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. Advanced Ubiquitous Computing

7. Related Work • Related problems • Potential field techniques for local navigation and obstacle avoidance problem [10] *[10] O. Khatib. Real-time obstacle 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 cooperative 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

8. Potential Fields • Each node is subject to force F from potential field U. F = - ▽U • Divide potential field into two component • Uo due to obstacle • Un due to sensor node U = Uo + UnF = Fo + Fn Advanced Ubiquitous Computing

9. Potential Fields • Potential due to obstacles • i : obstacle seen by the node • ko : constant strength of the field • ri : Euclidean distance between the node and obstacle iri = | xi – x |, xdenote the position of node, xi denote the position of obstacle i. Advanced Ubiquitous Computing

10. 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 sensor data. Advanced Ubiquitous Computing

11. Potential Fields Advanced Ubiquitous Computing

12. Potential Fields • Total force due to other nodes • kn : constant strength of the nodes field Advanced Ubiquitous Computing

13. Equation of Motion • Equation of motion • : the acceleration of the node • : the velocity of the node • m : The mass of the node • v : viscous coefficient • This viscous friction term “ ” is used to ensure that the node will come to a standstill in the absence of external forces. Advanced Ubiquitous Computing

14. 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. Advanced Ubiquitous Computing

15. Control Law • Change of commanded velocity is determined by using piecewise-constant approximation. Where is largest allowable change in velocity. • The commanded velocity is determined: Where is maximum allowed velocity. Advanced Ubiquitous Computing

16. Control Law • Two regimes in which the correspondence will fall. • For small velocity, the viscous friction term will tend to produce oscillation rather than asymptotic convergence to zero velocities. • typical behavior of discrete control system. • Can be eliminated by a velocity ‘dead-band’. • Large acceleration and velocities will be clipped, in which case the deviation may become large. • It increases time taken to reach equilibrium. • Impact must be determined empirically. Advanced Ubiquitous Computing

17. Static Equilibrium • The network will reach a static equilibrium • System energy is composed of potential and kinetic energy. • Total energy is determined by summing these energies for all nodes. • Viscous friction term of motion equation has the effect of removing energy. The system is dissipative The network must asymptotically approach static equilibrium Advanced Ubiquitous Computing

18. 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. Advanced Ubiquitous Computing

19. 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. Advanced Ubiquitous Computing

20. Experiments Fig.2. A proto-typical deployment experiment for a 100-node network. (a) Initial network configuration. Advanced Ubiquitous Computing

21. Experiments (b) Final configuration after 300 seconds. (c) Occupancy grid generated for the final configuration;visible space is marked in black (occupied) or white (free);unseen space is marked in gray Advanced Ubiquitous Computing *http://robitics.usc.edu/~ahoward/movies.html

22. Experiments Advanced Ubiquitous Computing

23. Experiments • Feature of the deployment is the evenness of the node spacing(1.6±0.4m) • No gaps or breaks in the coverage. • Rate of coverage decrease with time. • Final configuration(500m2) is 10-fold improvement over the initial configuration(50m2). • Average velocity of boundary nodes in the early phase is higher. Advanced Ubiquitous Computing

24. Conclusion • Potential field approach can be used to deploy mobile sensor network. • It is a distributed and scalable approach. • It has provable convergence characteristics. Advanced Ubiquitous Computing

25. 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. Advanced Ubiquitous Computing