Download presentation

Presentation is loading. Please wait.

Published byJaqueline Beall Modified over 3 years ago

1
Coverage, Connectivity and Mobility in Wireless Mobile Sensor Robots Youn-Hee Han yhhan@kut.ac.kr Korea University of Technology and Education Laboratory of Intelligent Networks http://link.kut.ac.kr

2
Introduction 2/76

3
Review: Sensor Node Architecture System architecture of a typical wireless sensor node i) a computing subsystem consisting of a microprocessor or microcontroller ii) a communication subsystem consisting of a short range radio for wireless communication iii) a sensing subsystem that links the node to the physical world and consists of a group of sensors and actuators iv) a power supply subsystem, which houses the battery and the dc-dc converter, and powers the rest of the node.

4
4/76 Mobile Sensors Mobile Sensor Capabilities [1,2] Sensing Sensing Communication Communication Computation Computation Locomotion Locomotion Self-deploy function Self-deploy function Mobile Robots with Sensors [Eight Legged Robot of LEGO mindstorm] [www.thinkbotics.com] Static Sensor Capabilities [Similar to a Tank]

5
5/76 Mobile Sensor Robots : Distributed Multi-Robots with Sensing Capability Single Sensor vs. Distributed Multiple Sensors Single Robot vs. Distributed Multi-Robots

6
Issues in Distributed Multi-Robots [3] Biological Inspirations Use of the local control rules of biological societies, such as ants, bees, and birds to the development of similar behaviors in multi- robot systems. behavior-based robotics robot architectures are built on activity-generating building blocks rather than on centralized representations and deductive logic. Communication Network robotics and Inter-robot interaction How to handle non-deterministic time delays in communications and achieve robust performance in faulty communication environment E.g., the remote tele-operation of space exploration robots Connectivity Issues What Issues in Mobile Robots? 6/76

7
Issues in Distributed Multi-Robots [3] Localization, Mapping, and Exploration Enables robot team members to track positions of autonomously moving objects Navigate between places of interest in an initially unknown environment Motion Coordination Multi-robot path planning, formation generation Reconfigurable Robotics Architecture, Task Allocation, and Control Object Transport and Manipulation What Issues in Mobile Robots? 7/76

8
Then, what issues in Mobile Sensor Robots ? Environmental Robotics the deployment of distributed sensors and supported mobile sensor robots to observe, monitor, and assess the state of complex environmental processes. It involves many different types of distributed sensing in land, sea, and air, and the coordination of mobile sensors through adaptive redeployment and adaptive sampling of environmental phenomena. Coverage Issues What Issues in Mobile Sensor Robots? 8/76 [2004 WTEC ROBOTICS WORKSHOP]

9
Mobile Sensor Robots 9/76 [ 2008-09-22] ' ' · … ' (swarm of robots)'. 16~18, ' ' ' ' BBC. 11 3 ' '. ' (Mindsheet)', ' (Locust)', 8 ' (Owls)'. ' ' ' '. 8. 1 4 1... 8,. ' '. " "., ' (MAST)' 1. MAST ( ) ' '.

10
10/50 Change of Research Issues in Sensor Networks Hardware (2000) CPU, memory, sensors, etc. Protocols (2002) MAC layers Routing and transport protocols Applications (2004) Localization and positioning applications Management (2005) Coverage and connectivity problems Coverage and connectivity problems Power management Power management Etc. Etc. From Dr. Yu-Chee Tseng (Associate Dean), College of Computer Science, National Chiao- Tung University

11
Coverage Problem In general, determine how well the sensing field is monitored or tracked by sensors. Objectives of the problem Determine the coverage hole (or targets) Minimize the number of sensors deployed Make the whole area covered by three or more sensors Location determination by Triangulation Maximize the network lifetime [Def.] Sensor Network Lifetime The time interval that all points (or targets) in the given area is covered by at least one sensor node. Etc. Study of Coverage Problem 11/50

12
Review: Art Gallery Problem Victor Klee (1973) Place the minimum number of cameras such that every point in the art gallery is monitored by at least one camera Chvátal's art gallery theorem (1975) guards (cameras) are always sufficient and sometimes necessary to guard a simple polygon with vertices 42 vertices upper bound: 12/50

13
Review: Power Saving Make the sensor node sleep!!! [13] Modes * 2Mb/s IEEE 802.11 Wireless LAN Tx Rx Idle Sleep Energy Consumption Rockwells WINS Nodes TxRxIdleSleep 0.38 ~ 1 W0.75 W0.72 W0.4 W Medusa II Nodes TxRxIdleSleep 22 ~ 24 mW22 mW6 mW0.02 mW http://www.inf.ethz.ch/personal/kasten/research/bathtub/energy_consumption.html It is highly recommended to schedule the wireless sensor nodes to alternate between active (Tx, Rx, Idle) and sleep mode

14
Review: Power Saving Make the sensor node intelligent!!! [13] The ratio of the energy spent in sending one bit of information to the energy spent in executing one instruction. 1500~2700 for Rockwells WIN nodes 220~2900 for the MEDUSA II nodes 1400 for the WINS NG 2.0 So, local data processing, data fusion and data compression are highly desirable.

15
Algorithm Characteristics 1) Centralized 2) Distributed 3) Self-* Self-determination free choice of ones own acts without external compulsion Self-organization (Self-configuration) a process of evolution where the effect of the environment is minimal, i.e. where the development of new, complex structures takes place primarily in and through the system itself Self-healing For example, a mobile sensor can move to an area with a coverage hole or routing void and significantly improve network performance. Problem Design Methodology 15/50

16
Coverage 16/50

17
Sensor Deploy Method Deterministic (planned) vs. Random Coverage Types Area coverage vs. Target (Point) coverage Problem Design Criteria (1/2) 17/50 6 5 4 3 2 1 7 8 R S2S2 S1S1 S4S4 S3S3 t3t3 t1t1 t2t2

18
Coverage Modeling Binary Model vs. Probability Model Communication Range ( ) & Sensing Range ( ) vs. vs. Homogeneous vs. heterogeneous? Problem Design Criteria (2/2) 18/50 Binary, unit disc sensing model Probabilistic sensing model

19
Coverage Modeling Binary Model [1] Each sensors coverage area is modeled by a disk Any location within the disk is perfectly monitored by the sensor located at the center of the disk; otherwise, it is not monitored by the sensor. Probability Model [2] An event happening in the coverage of a sensor is either detected or not detected by the sensor depending on a probability distribution Hence even if an event is very close to a sensor, it may still by missed by the sensor. 19/50

20
Binary Model: K-coverage in 2-D K-coverage (only within Binary Model) [Definition] covered A location in an area is said to be covered by if it is within 's sensing range. [Definition] k-covered (location or area) A location in an area is said to be k-covered if it is within at least K sensors' sensing ranges. k is called coverage level Why K>1? Fault-tolerance in case of the dismissal of some sensors Power saving and enlarge network lifetime Triangulation: getting location of a targeted object Uplift the confidence level on gathering information 20/50

21
Binary Model: K-coverage in 2-D Problems about K-coverage [1] [Definition] k-NC problem Given a natural number k, the k-Non-unit-disk Coverage (k-NC) problem is a decision problem whose goal is to determine whether all points in an area are k-covered or not. [Definition] k-UC problem Given a natural number k, the k-Unit-disk Coverage (k-UC) Problem is a decision problem whose goal is to determine whether all points in an area are k-covered or not, subject to the constraint that r 1 = r 2 = · · · = r n. 21/50 k-NC (k=1) k-UC (k=1)

22
So this area is not 1-covered! 1-covered means that every point in this area is covered by at least 1 sensor 2-covered means that every point in this area is covered by at least 2 sensors This region is not covered by any sensor! Is this area 1-covered? This area is not only 1- covered, but also 2- covered! What is the coverage level of this area? Coverage level = k means that this area is k-covered Binary Model: K-coverage in 2-D 22/50

23
Binary Model: K-coverage in 2-D Algorithm to determine coverage level, k, in a given sensor network? [1] [Definition] k-perimeter-covered Consider any two sensors s i and s j. A point on the perimeter of s i is perimeter-covered by s j if this point is within the sensing range of s j [Theorem] An area A is k-covered iff each sensor in A is k-perimeter-covered. 2 1 Partially self-determination, but a central node determines the coverage level (k) finally. 23/50

24
Binary Model: Coverage Configuration in 2-D Coverage Configuration Protocol (CCP) [3] 1) a coverage level (k) is allocated to all sensors 2) all sensors are deployed randomly at the target area 3) Each sensor makes itself sleep or active to achieve the coverage level [Theorem] A given area is k-covered if the following conditions are satisfied 1) All intersection points between each pair of sensors are "k- covered" 2) All intersection points between each sensor and boundary of the area are "k-covered 24/50 Active nodes Intersection points

25
Binary Model: Coverage Configuration in 2-D Coverage Configuration Protocol (CCP) [3] A node becomes sleep if all intersection points inside its coverage is already K-covered by other active nodes in its neighborhood. A node becomes active if there exists an intersection point inside its sensing circle that is not K-covered by other active nodes. 25/50 Active nodes Sleeping nodes Intersection points active?

26
Binary Model: K-coverage in 3-D K-coverage in 3-D [4] [Definition] k-BC Problem Given a natural number k, the k-Ball-Coverage (k-BC) Problem is a decision problem whose goal is to determine whether all points in a 3-D cuboid sensing area are k-covered or not. How to determine k? (3D 2D) Determine whether the sphere of a sensor is sufficiently covered (2D 1D) Determine whether the circle of each spherical cap of a sensor intersected by its neighboring sensors is covered 26/50

27
Probability Model Why Probability Coverage Model? [2] Quality of sensor surveillance may be much affected by sensing distances, signal propagation characteristics, obstacles, and environmental factors. Probability coverage model may be more realistic! Methodology Simple Model [5] Signal-strength-based Model [2] 27/50 ( ) ( ).

28
Probability Model Simple Model [5] : the probability that a sensor can sense a event happened at a location : the detection probability contributed by the sensors 28/50

29
Coverage and Scheduling 29/76

30
Scheduling Basic Policy Sensor should be active or sleep? Scheduling (related to the coverage issue) An interval: is active Another interval: is active So, the battery power can be saved 30/76

31
Scheduling Scheduling Type Centralized 1) All sensors send their location information to the centralized sink node. 2) The sink node performs its scheduling algorithm for the sensors 3) The sink node broadcasts the scheduling information to all sensor nodes 4) Each sensor becomes active or sleep according to the information Distributed Each sensor self-determies its scheduling time # of messages reduced 31/76

32
Centralized Scheduling MDSC (Maximum Disjoint Set Covers) [9] 32/76 [Definition] Maximum Disjoint Set Covers Problem

33
Centralized Scheduling MDSC (Maximum Disjoint Set Covers) [9] For example, C={S 1, S 2, S 3, S 4 }, TARGETS={t 1, t 2, t 3 } A sensors battery lifetime: 1 Network Lifetime without any scheduling: 1 By MDSC Scheduling Two Set Covers, C 1 and C 2 C 1 ={S 1, S 2 } with active time=1 C 1 ={S 3, S 4 } with active time=1 So that, network lifetime: 2 33/76 s2s2 s1s1 s4s4 s3s3 t3t3 t1t1 t2t2 s1s1 s2s2 s3s3 s4s4 t3t3 t2t2 t1t1

34
Centralized Scheduling MSC (Maximum Set Covers) [10] MDSC MSC MDSC problem is a special case of MSC problem.! 34/76 [Definition] Maximum Set Covers Problem removed!

35
Centralized Scheduling MSC (Maximum Set Covers) [10] For Example, By MSC Scheduling Network Lifetime: 2.5 35/76 active time=0.5 active time=1 s2s2 s1s1 s4s4 s3s3 t3t3 t1t1 t2t2

36
Centralized Scheduling MSC (Maximum Set Covers) [10, 11] Existing Algorithms Linear Programming [10] Greedy [10] (Complexity: ) Branch-and-Bound [11] i: # of set covers, m: # of targets, n: # of sensors 36/76

37
Centralized Scheduling MSC (Maximum Set Covers) [10, 11] Existing Algorithms Linear Programming [10] Greedy [10] (Complexity: ) Branch-and-Bound [11] 37/76 i: # of set covers, m: # of targets, n: # of sensors

38
Distributed Scheduling 1-Coverage Preserving Scheduling (1-CP) [12] For Example The set of intersection points within s area The set of sensors covering the target p T rnd =20 Ref 1 =2, Ref 2 =9, Ref 3 =11 Init Phase: 1) Each sensor exchange its location and Ref. value 2) Each sensor get its schedule (active) time 38/76

39
Distributed Scheduling 1-Coverage Preserving Scheduling (1-CP) [12] 2 9 11 5.5 16.5 39/76

40
Connectivity 40/76

41
Connectivity Why Connectivity? Any sensing data should be sent to gateway (sink, base station) node Multi-hop routing Base Station Sink 41/76

42
K-Connectivity Connected Graph of Sensor Networks Vertex: each sensor nodes Edge: direct communication path for pairs of sensors there exists an edge between two vertices iff the distance between them is less or equal to the transmission range r. 42/76

43
K-Connectivity [Definition] k-connectivity The network will remain connected after removing any arbitrary k-1 sensors from network. It is also called vertex k-connectivity (not edge k-connectivity) k-connected: any pair of nodes are connected by k indep. paths Independent paths: 43/76

44
K-Connectivity Examples 44/76 2-connected 4-connected

45
K-Edge-Connectivity [Definition] k-edge-connectivity The network will remain connected after removing any arbitrary k-1 edges from network. k-edge-connected: any pair of nodes are connected by k disjoint paths disjoint paths: 45/76

46
Min-Power Connectivity Problem Connectivity & Transmission Power Nodes in the network correspond to transmitters More power larger transmission range More Edges More Connectivity transmitting to distance r requires r power Battery operated power conservation critical [Definition] Min-Power Connectivity Problems Find min-power range assignment so that the resulting communication network satisfies prescribed properties (k- connectivity) 46/76

47
Min-Power Connectivity Problem 47/76 b a c d g f e a b d g f e c Range assignmentCommunication network

48
K-Connectivity & K-Coverage Relation between K-Coverage and K-Connectivity [3] Communication Range: Sensing Range: [Theorem] If the given region is continuous and, The region is k-covered means The region is k-connected For example, k=1 Assume that the requested coverage level, k, is one and If The sensors covers the whole region completely, then Any sensing data produced by a sensor can be delivered to the sink node. 48/76

49
Sensing and Communication Ranges Real Products Ranges [7] 49/76

50
Self-deployment I 50/76

51
Self-deploy using Potential Field [4] Problem Definition How to maximize the sensor coverage in a model-free environment Assumption each node is equipped with a sensor that allows it to determine the range and bearing of both nearby nodes and obstacles sensors can be constructed using scanning laser range-finder, supersonic or omni-camera. Procedure Summary Potential Field-based Strategy 51/76 Determine the virtual forces from nodes and obstacles convert the virtual forces into a control vector to be sent to its motors. Deploy the sensor nodes randomly

52
Potential Fields and Forces [4] Potential Fields generated by Obstacles and Boundary [5] Potential Field 52/76 The force vectors in the potential field generated by AvoidObstacle behavior

53
Force Vectors Force Vector due to obstacles : coordinate of the current sensor node : coordinate of obstacle : distance from obstacle and the node : constant describing the strength of the field Force Vector due to other sensors : coordinate of other sensor : distance from sensor and the node : constant describing the strength of the field The compound force vector by the two components Force Vectors from Potential Field 53/76

54
From Force Vectors to next location Next Acceleration : mass of the node : friction force ( ) : viscosity coefficient : current velocity of node Next Velocity : unit time Next Location : current location of the node How to determine the next position? 54/76

55
Example 55/76 (2,0) (9/2,0)

56
Performance Evaluation 56/76 Proto-typical deployment experiment for a 100-node network. (a)Initial network configuration. (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.

57
Performance Evaluation 57/76 Performance

58
Self-deployment II 58/76

59
Self-deploy using Coverage Hole [7] Problem Definition How to maximize the sensor coverage with minimal time and minimal movement distance in an obstacle-less model-free and finite environment Procedure Summary Coverage hole-based Strategy 59/76 Discover the coverage hole (the area not covered by any sensor) Calculate the target positions of the moving sensors Deploy the sensor nodes randomly

60
Voronoi Diagram Voronoi polygon : Voronoi polygon of sensor node O is the set of Voronoi vertices of O is the set of Voronoi edges of O : the set of Voronoi neighbors of O example All positions inside are closer to the node O than to any other nodes 60/76

61
Voronoi Diagram Why Voronoi diagram? All positions inside a Voronoi partition are closer to the generating node than to any other nodes So, each sensor is responsible for the sensing task only within its Voronoi partition One partition is small area to be monitored by one sensor Each sensor just examine the coverage hole locally 61/76

62
Coverage hole How to find the coverage hole? After constructing the Voronoi polygons, each sensor intersects it with the sensing circle of the containing sensor. If it is found, next? If any coverage hole exists in its Voronoi partition, the generating sensor decide where to move to eliminate it or reduce its size. 62/76

63
Movement protocols Three movement protocols VEC (VECtor-based) pushes sensors away from a densely covered area VOR (VORonoi-based) pulls sensors to the sparsely covered area Minimax moves sensors to their local center area Features Distributed Self-deployment protocols 63/76

64
VEC (VECtor-based) Strategy To find the overall virtual force as the vector summation of virtual forces from the boundary and all Voronoi neighbors. The virtual force will push sensors from the densely covered area to the sparsely covered area. Terms : the distance between two sensors (, ) : the distance between a sensor and boundary : the average distance between two sensors when the sensors are evenly distributed in the target area It should be calculated beforehand Final goal Initial Deployment 64/76

65
VEC (VECtor-based) E.g.) Vector Summation of the sensor s 1 s1 s2 Voronoi Partition Cover s3 Voronoi Partition Cover s3 s1 Boundary Boundary s1. 65/76

66
VEC (VECtor-based) The execution of VEC 35 sensors / 50m x 50m / random deployment Coverage : 75.7% -> 92.2% -> 94.7% 66/76

67
VOR (VORonoi-based) Strategy Pull sensors to their local maximum coverage holes Sensors move toward its farthest Voronoi vertex ( ) In the above figure, Sensor s i s target location is B is equal to the sensing range It is a greedy algorithm 67/76

68
VOR (VORonoi-based) The execution of VOR Coverage : 75.7% -> 89.2% -> 95.6% 68/76

69
Minimax Strategy Choose the target location as the point inside the Voronoi polygon whose distance to the farthest Voronoi vertex ( ) is minimized The target location is called Minimax point ( ) It reduces the variance of the distances to the Voronoi vertices, resulting in a more regular shaped Voronoi polygon It considers distances to all the Voronoi vertices, rather than only to the farthest vertex. VOR Minimax Circumcircle of 3 Voronoi vertices 69/76

70
Minimax VOR vs. Minimax Minimax point. So, how to find it? 70/76

71
Minimax Terms : Minimax point (target point) : Minimax circle centered at the minimax point, with radius : Circumcircle of three points Algorithm 1) Find all the circumcircles of any 2 and any 3 Voronoi vertices. 2) Among these circles, select the one having the minimum radius and covers all the vertices as the Minimax circle for that polygon. 3) The center of the selected circle is the Minimax point 71/76

72
Minimax The execution of Minimax Coverage : 75.7% -> 92.7% -> 96.5% 72/76

73
Performance Evaluation Coverage Minimax performs best, VEC the worst. Minimax fully utilizes the Voronoi polygon VEC does not consider holes nor Voronoi polygon structure when choosing target location Minimax better than VOR since it considers more information. 73/76

74
Performance Evaluation Coverage vs. Communication Range Performance is reduced when communication range is reduced. This is because most sensors do not know all the neighbors, thus construct inaccurate Voronoi polygons. Consequently get incorrect coverage holes and target locations. VEC is least affected, since it does not use the Voronoi polygon to determine target location. 74/76

75
Performance Evaluation Moving Distance Minimax moves longer distance than VOR, since not only fixes holes but tries to reach more regular shaped polygons. For VEC, moving distance is similar under different sensor densities. 75/76

76
Innercenter vs. Circumcenter vs. Centroid [Centroid vs. Center of Gravity] - (Centroid) (Center of Gravity). -,. - (homogeneous),. 76/76

77
References 1. C.-F. Huang and Y.-C. Tseng, The Coverage Problem in a Wireless Sensor Network, In ACM International Workshop on Wireless Sensor Networks and Applications (WSNA), pp. 115–121, 2003. 2. N. Ahmed, S. S. Kanhere and S. Jha, Probabilistic Coverage in Wireless Sensor Networks, in Proceedings of the IEEE Workshop on Wireless Local Networks (WLN, in conjunction with LCN 2005), Sydney, Australia, pp. 672-679, November 2005. 3. X. Wang, G. Xing, Y. Zhang, C. Lu, R. Pless, and C. Gill, Integrated coverage and connectivity configuration in wireless sensor networks, In ACM International Conf. on Embedded Networked Sensor Systems (SenSys), pp. 28–39, 2003. 4. C.-F. Huang, Y.-C. Tseng, and L.-C. Lo, The Coverage Problem in Three-Dimensional Wireless Sensor Networks, Journal of Interconnection Networks, Vol. 8, No. 3, pp. 209-227. Sep. 2007. 5. Y. Zou and K. Chakrabarty, "Sensor deployment and target localization based on virtual forces," in Proceedings of INFOCOM 2003, March 2003. 6. S.-P. Kuo, Y.-C. Tseng, F.-J. Wu, and C.-Y. Lin, A Probabilistic Signal-Strength-Based Evaluation Methodology for Sensor Network Deployment, International Journal of Ad Hoc and Ubiquitous Computing, Vol. 1, No. 1-2, pp. 3-12, 2005 77/76

78
References 7. Honghai Zhang and Jennifer C. Hou, ``On deriving the upper bound of a-lifetime for large sensor networks,'' Proc. ACM Mobihoc 2004, June 2004 8. S. Megerian, F. Koushanfar, G. Qu, G. Veltri, M. Potkonjak. "Exposure In Wireless Sensor Networks: Theory And Practical Solutions," Journal of Wireless Networks, Vol. 8, No. 5, ACM Kluwer Academic Publishers, pp. 443-454, September 2002 9. M. Cardei and D.-Z. Du, "Improving Wireless Sensor Network Lifetime through Power Aware Organization," ACM Wireless Networks, Vol. 11, pp. 333-340, 2005. 10. M. Cardei, M. T. Thai, Y. Li, and W. Wu, "Energy-efficient Target Coverage in Wireless Sensor Networks," In IEEE Infocom 2005, vol. 3, pp. 1976-1984, 2005. 11.,,, "," 2008, 2008 10 12. C.-F. Huang, L.-C. Lo, Y.-C. Tseng, and W.-T. Chen Decentralized Energy-Conserving and Coverage-Preserving Protocols for Wireless Sensor Networks, ACM Trans. on Sensor Networks, Vol. 2, No. 2, pp. 182-187, 2006. 13. V. Raghunathan, C. Schurgers, S. Park, and M. B. Srivastava, Energy-Aware Wireless Microsensor Networks, IEEE Signal Processing Magazine, 19 (2002), pp 40-50. 78/76

79
References 14. A. Howard, M. J. Mataric, and G. S. Sukhatme, An incremental self-deployment algorithm for mobile sensor networks, Autonomous Robots, Special Issue on Intelligent Embedded Systems, vol. 13(2), pp. 113–126, Sep 2002. 15. A. Howard, M. J. Mataric, and G. S. Sukhatme, Mobile sensor network deployment using potential fields: A distributed, scalable solution to the area coverage problem, The 6th International Symposium on Distributed Autonomous Robotics Systems (DARS02), June 2002. 16. T. Arai, E. Pagello, L. E. Parker, Editorial: Advances in Multi-Robot systems, IEEE Transactions on Robotics and Automation, Vol. 18, No. 5, pp. 655- 661, Oct 2002. 17. Michael A. Goodrich, Potential Fields Tutorial, http://www.ee.byu.edu/ugrad/srprojects/robotsoccer/papers/goodrich_potential_fields.pdf 18. A. Howard, M. J. Mataric, and G. S. Sukhatme, Mobile sensor network deployment using potential fields:A distributed, scalable solution to the area coverage problem, The 6th International Symposium on Distributed Autonomous Robotics Systems (DARS02), June 2002. 19. S. Poduri and G. S. Sukhatme, Constrained coverage for mobile sensor networks, IEEE International Conference on Robotics and Automation, pp. 165–172, May 2004. 20. G. Wang, G. Cao and T. L. Porta, Movement-assisted Sensor Deployment, IEEE INFOCOM 2004, Vol. 4, pp. 2469-2479, March 2004. 79/76

Similar presentations

OK

University Paderborn 07 January 2009 RG Knowledge Based Systems Prof. Dr. Hans Kleine Büning Reinforcement Learning.

University Paderborn 07 January 2009 RG Knowledge Based Systems Prof. Dr. Hans Kleine Büning Reinforcement Learning.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on power line communication modem Ppt on drug addiction in india Ppt on cattle farming for class 9 Convert 2007 to 2003 ppt online Ppt on revolt of 1857 muslims Ppt on types of research methods and designs Ppt on statistics and probability formulas Ppt on machine translation service Ppt on marketing download Download ppt on turbo generators