Robotics and Sensor Networks: Coverage, Localization and Mobility

1. Robotics and Sensor Networks: Coverage, Localization and Mobility Kostas Bekris March 29, 2005 COMPASS project meeting

2. What is the relation? • Robotics and Sensor Networks are typically • considered two unrelated fields. • But: • Robots can provide mobility to Sensor Networks. • Sensor Networks can provide rich sensing • information to Robots. • and most importantly • The two fields are facing many similar challenges.

3. Robots for Sensor Networks • Mobile nodes can be used to: • Re-deploy and calibrate sensors, • React to sensor failures and • Deliver power. [Corke, Hrabar, Peterson, Rus, Saripalli, Sukhatme, 2004]

4. Sensor Networks for Robots A network offers detailed sensing information to a robot that is not possible to acquire otherwise. Distributed computation over the network. Robots can form mobile sensor networks. [Batalin, Sukhatme, Hattig, 2004]

5. Similar challenges • Many of the problems are the same: • Decision inference based on multiple sensing inputs • Sensor fusion • Location awareness • Coordination • Task allocation • Workspace or sensor field coverage • Compression of data • Uncertainty • Mobility

6. Topics to cover • I. Coverage • Art-Gallery Problems • (Computational Geometry) • II. Localization • Distributed Markov and Monte Carlo • (Machine Learning) • III. Mobility • Artificial Potential Functions & • Formation Control • (Control Theory)

7. I. Coverage

8. Coverage in Sensor Networks • Very important for deployment: • Under-deployment might result in communication • failures or failures in the sensing task • Over-deployment can significantly increase the cost • Typical Measure in • Sensor Networks: • Path Exposure [Meguerdichian, Koushanfar, Potkonjiak, Srivastava 2001]

9. Art-Gallery Problem The original art gallery problem: Find the smallest number of point guards g(n) necessary to cover any polygon of n vertices. According to the art gallery theorem the necessary number is: g(n) = n/3 Finding minimum set of guards: NP-hard [Conversation between Klee and Chvatal 1972] [Chvatal 1975] [Aggarwal 1984]

10. Heuristic Solution • Greedy approach for map building in robotics: • Place the first guard at the point of • maximum visibility • Next guard is placed where it sees the maximum • area not visible to the first and so on • The sub-problem of finding the next guard of • maximum visibility is called: • the Next-Best-View problem

11. Various approaches Randomized algorithms compute the optimal location up to a constant factor approximation. Sampling-based techniques can be used for the most realistic case of sensors with limited-range. Decomposition methods compute cells that can be observed by limited range guards. [Cheong, Efrat, Har-Peled 2004] [Gonzalez-Banos, Latombe 2002] [Kazazakis, Argyros 2002]

12. Robotic SN Deployment Incremental approach: select a node at a time to be deployed in a new location, a second nodes replaces it Build a centralized representation while maximizing network coverage and retaining line-of-sight communication. [Howard, Mataric, Sukhatme 2002]

13. II. Localization

14. Data for SN self-localization • Received Signal Strength: for known transmission • power, the propagation loss is measured to estimate • the distance based on a propagation model. • Time-of-arrival or time-difference-of-arrival: The • propagation time can be directly translated into • distance based on signal propagation speed. • Angle-of-arrival: Systems estimate the angle at • which signals are received.

15. Localization Approaches Assume a subset of the nodes can self-localize (e.g. GPS) localize the rest relative to the beacons. Trilateration Triangulation MLE [Bergamo, Mazzini 2002] [Niculescu, Nath 2003] [Savvides, Han, Srivastava 2002] [Nasipuri, Li 2002]

16. Uncertainty in Robotics Robots, like nodes of sensor networks, have to be aware of their location. Typical sensors in robotics: sonar, laser, cameras. Problem: inherent uncertainty in sensor measurements Probabilistic/bayesian techniques proven successful in dealing with uncertainty and providing robustness. [Fox, Burgard, Kruppa, Thrun: A probabilistic approach to collaborative multi-robot localization, 2000]

17. Markov Localization • Each robot maintains a belief for its position at time t • Belt(L) • where L is the robot’s configuration (e.g. {x,y,}). • Initially, Bel0(L) follows a uniform distribution. • Each robot collects data dt: • Odometry: at • Sensing observations: ot • Detections of other robots: rt

18. Updating the distribution • The belief represents the posterior up to time t: • Belt(L) = Pr(Lt|dt) • Perception model: • Pr(ot|L) • Motion Model: • Pr(L|at,L’) • Updates after: • Sensing: Belt(L) =   Pr(ot|L)  Belt-1(L) • Action: Belt(L) = Pr(L|at,L’)  Belt-1(L’)  dL’

19. Multi-Robot Case Independence assumption: Pr(L1, …, Ln|dt) = Pr(L1|dt)  … Pr(Ln|dt) Detections used to add additional constraints. Assume robot m detects robot n: Beltn(L) = Belt-1n(L)  Pr(Ln=L|rtm,Lm=L’)  Belt-1m(L’)  dL’

20. Monte-Carlo Localization Representation issue with the storage of distributions Monte Carlo approach: A distribution is a set of K weighted “particles”: S = { (Li,pi) | i=(1,…,K) } where: Li is a candidate position and pi is a discrete probability pi=1 Sensing leads to re-weighting the set of samples so as to agree with the measurements.

21. More on Localization • An equivalent approach is to distribute the • computation of a centralized Kalman filter to • separate Kalman filters. • More difficult problem: SLAM (Simultaneous • Localization and Mapping) • Incrementally generate a maximum likelihood • map • Probabilistically estimate the robots’ position [Roumeliotis, Bekey 2002]

22. Localization for RSN • Providing location aware services in buildings that • are equipped with wireless infrastructure • Build radio signal strength maps with multiple robots: • For a pair of locations return the expected • signal strength • Sample the environment and build the map for the • samples [Ladd, Bekris, Rudys, Marceau, Kavraki, Wallach 2002] [Haeberlen, Flannery, Ladd, Rudys, Wallach, Kavraki 2004] [Hsieh, Kumar, Taylor 2004]

23. III. Mobility

24. Why mobility? • Synoptic sensing implies either over-deployment • (impractical – you cannot have sensor everywhere) • or mobility • Mobility allows the system to focus sensing where • it is needed, when it is needed • The initial deployment of static nodes cannot deal • with all possible changes in the environment

25. Energy Considerations Example Mobile Platform: Robomote [Dantu, Rahimi, Shah, Babel, Dhariwal, Sukhatme 2004]

26. Goal of navigation approaches Navigational strategies for SN should not have extensive sensing and computational requirements. They should take advantage of the distributed nature of such networks. Computationally or memory expensive approaches are also not appropriate.

27. Navigation Functions Many distributed navigation approaches are based on “navigation functions”. Construct a real-valued map: V: Cf R with unique minimum at the goal and is maximal over Cfboundary. [Rimon, Koditschek 1992]

28. Navigation Functions Then the robot at position p can move according to: where d is an arbitrary dissipative vector-field. Under additional requirements NFs guide the robot to the goal without hitting local minima. In the multi-robot case, each robot can act as an obstacle in the potential function of other robots. (p,p’) = -V(p) + d(p,p’) [Dimarogonas, Zavlanos, Loizou, Kyriakopoulos 2003]

29. Source Gradient Climbing A mechanism in the environment may be inducing an environmental gradient field (light, sound source). APFs are used for locating the source with multiple robots. If a robot measures the gradient only in the direction of motion then it can only find minima along a line. An APF enforces the team to stay close and eventually the source will be found. [Ogren, Fiorelli, Leonard 2004]

30. Formation Control Another possibly desirable behavior with a team of mobile systems is to move the entire team in formation. Alternatives such as (l-) or (l-l) control have been considered as basic motion primitives for formations. [Desai, Ostrowski, Kumar 2001]

31. Conclusion

32. Our interest Interested in networks that have the ability to adapt the location of their nodes - not necessarily with autonomous mobility – to solve problems that might require node relocation Do not assume mobility is easily available and inexpensive as it is typically considered in robotics Take into account the cost of mobility and apply it only when it is necessary for the application

33. Sampling-Based Motion Planners An improvement over potential functions in typical robotic applications. They sample the configuration space of robots and construct lower-dimensional representations (e.g. graph structures). They solve path planning problems on the graph structures.

34. Issues to consider • Can we apply the SBMP framework to deal with • adaptive sensor network problems? • Can we have distributed SBMP? • Can SBMP plan not just for motion but for other tasks, • such as sensing and communication? • Can we take into consideration the fact that different • tasks have different energy costs?

35. Questions?? THE END