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  1. B.Tech. Project Presentation Intercepting a Moving Target in Road Networks by Prateek Khatri Under the guidance of Prof. N. L. Sarda

  2. The Problem • Given a road-network, n number of pursuers and one evader, devise a strategy to coordinate all pursuers to capture the evader. • Assumptions: • Speed of pursuer and evader not bounded • Pursuer receiving regular updates about evader position • Pursuer knows the initial position of the evader

  3. Introduction • Devising the strategy: Here the aim is to develop a strategy for pursuers considering the constraints of a road network. Presently a simple shortest path strategy is implemented. Developing an intelligent strategy for evader can help check the efficiency of the pursuer strategy. • Simulation: Here the aim is to develop a web based interface for simulation and analysis of the strategies. The interface will allow the user to select the simulation parameters like starting nodes for pursuer and evader, no. of pursuers and no. of evaders, etc.

  4. Previous Works • The work by Parsons and Motwani have focussed on the visibility based pursuit-evasion in graphs • Some others have advocated the use of randomized solutions as the probability of pursuer catching evader increases • Most of the works have focussed on polygonal environments • None of the work encountered have focussed on road networks specifically • Randomized strategy as given in [2] using RRTs focusses on polygonal regions but can be adapted for graphs as well

  5. Limitations of earlier works • Road networks are very different from the robotic environments. • Dynamic constraints on fuel, roads,traffic conditions, number of vehicles available • Implicit assumptions: • Bounded and polygonal environment • No constraints on paths • No constraints on number of pursuers

  6. Strategies • Possible pursuer strategies: • Shortest path to evader at every update (Implemented) • Dividing the area into n parts for n pursuers • Randomized Strategy • Heuristic based strategies: roadblocks, toll booths, etc. • Possible evader strategies: • Random (Implemented) • Moving away from the initial point • Heuristic based strategies: crowded roads, narrow roads, hiding place, etc • Capture Conditions: • Pursuer within some small distance of evader (Implemented) • Pursuer can see evader (in case of line of sight)

  7. Simulation • Discrete-event simulation has been implemented to test and analyse the strategies. • The problem is simulated with one pursuer and one evader with following strategies: • Pursuer – Shortest path at every update • Evader – Random run and moving far away from the initial position • Capture condition – evader within some distance of pursuer • Assumptions • Pursuer needs random updates to follow evader • Total number of events in the simulation can not be more than 1000 • Simulation is over if it one of the two conditions are satisfied: • Evader is caught • Total number of events become more than 1000

  8. Implementing Simulation

  9. Implementing Simulation

  10. Visualization • A web-based visualization software is developed to monitor and analyze the process • User can set the simulation parameters, can select the initial nodes for pursuer and evader. • Developed using JSP, Servlets and OpenLayers

  11. DEMO

  12. Visualization workflow

  13. Manual Tasks

  14. Display Layer displays the map network Shows the path Layer displays nodes in the map Shows the starting positions Shows the current positions

  15. Results: capture time vs. number of pursuers • Map used: Hyderabad Road Network • Difficulty of taking into account all the factors responsible in chase is avoided by measuring the simulation time over 10 and 20 simulation runs and averaging the results

  16. Result: measured over 10 simulation runs

  17. Results: measured over 20 simulation runs

  18. Future Work • Developing heuristic based strategies for both pursuer and evader • Incorporating the road constraints • Automating all the tasks in required in the preprocessing for visualization • Use of Raster layers instead of vector layers for displaying map will speed up the process

  19. References • [1] Theory and Applications of Graphs, chapter Pursuit-evasion in a graph. Springer Berlin / Heidelberg, 1978. • [2] A. AlDahak and A. Elnagar. A practical pursuit-evasion algorithm: Detection and tracking. In Robotics and Automation, 2007 IEEE International Conference on, pages 343 - 348, April 2007. • [3] W. Herbert and F. Mili. Route guidance: State of the art vs. state of the practice. In Intelligent Vehicles Symposium, 2008 IEEE, pages 11671174, June 2008. • [4] L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. A visibility-based pursuit-evasion problem. In Intl. J. of Computational Geometry Applications, volume 9, pages 471 - 493, 1999.