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Exploring an Environment with Bounded Visibility

This Master's thesis proposal presents a comprehensive exploration of environments with bounded visibility. It defines preliminary problems related to optimal pathfinding and exploration by a robotic agent in constrained environments. The study focuses on practical applications in robot navigation, particularly in human-rescuer robots and autonomous driving. Key factors such as the robot's shape, sensory capabilities, motion restrictions, and optimization criteria are examined to derive optimal strategies in bounded regions. Literature on online algorithms is reviewed to assess competitiveness and efficiency in robotic applications.

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Exploring an Environment with Bounded Visibility

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  1. Exploring an Environment with Bounded Visibility کاوش محیط توسط ربوت با محدودیت در دید Master of Science Proposal in field of Computer science Hossein Moarefi Supervisors : MansoorDavoodiMonfared BahramSadeghiBigham October 2013

  2. Overview • Definition of Preliminary Problem • Application in Real World • Practical Aspect in Robotic • Optimality and Competitiveness in Online Algorithms • Literature Review & Thesis Bibliography • Problem Definition

  3. Definition of Preliminary Problem : Exploration: The robot ability to make an Optimal Tour (or map) by starting from S , and observing every point of environment. Searching : The robot ability to make a Optimal Path to reach a target point t , from its starting point s. Note : Optimization Criteria proposed in Online Fashion

  4. Background : Dependence to the Length of Input Analysis base on WORST_CASE - Complexity of Time - Complexity of Memory • Information arrives during a period of Time • Analysis base on competitiveness • Complexity of Memory • -Fault Tolerance Behavior • -Independent to the Input String Offline Algorithm : Online Algorithm :

  5. Application In Real World . Human-Rescuer Robots

  6. Application In Real World . Generating Topological Map of Environment . Path Planning for Autonomous Driving and …

  7. Real World Computable World Objectives : • ROBOT • Shape of Body • (point , Circle , Polygon , … ) • Sensors • ( touch , vision ) • Motion Restriction • Computational Abilities • Environment • Bounded Region Vs. Unbounded Region • Rectangular , Orthogonal , Polygonal and etc. • Graph , Cellular , Grid and etc. • Obstacle-Free vs. In presence of Obstacles • COST • Minimum Number of View Points • Minimum number of Turns or links • Path Length Metric • ( Euclidian metric , … ) • Dimension of Space

  8. Practical aspect in ROBOTIC : Constraints on Robot models Visibility Constraints : -Bounded visibility -Continuous Visibility -Discrete visibility

  9. Optimality and Competitiveness of Algorithms : Competitive ratio : efficiency of online algorithms for searching and exploration algorithms is generally measured using their competitive ratios. Cost of Online Algorithms Competitive ratio = Cost of optimal Offline Algorithm Search Ratio : For specific case of geometric searches in an unknown environment for a target of unknown position this ratio introduced. In this case , the optimal offline algorithm although knows the Environment map , but it fails to know the location of target.

  10. Definition of Problem : • Exploring an Environment Q • Point Robot ( P ) with Bounded Visibility with range ( R ) • Known Starting Point : S Creating the Shortest Tour inside Q which all points of Q could be seen by P.

  11. Previous Related Works : • Robbie Shade , PhD Thesis , Oxford University 2011 – Choosing Where To Go: Mobile Robot Exploration • J. Chalopin, Sh. Das, Y. Disser, M. Mihalak, and P. Widmayer. • Telling convex from reflex allows to map a polygon. In Proceedings of the 28th STACS , 2011 • S. k. Ghosha , R. Klein [ Survey ] -Online algorithms for searching and exploration in the plane - Computer Science Review 4 – (2010) • Tom Kamphans , PhD Thesis , university of Bonn,Germany 2006 – • Models and Algorithms for Online Exploration and Search • Ch. Icking , R. Klein , E. Langetepe , S. Schuierer , I. Semrau – • An Optimal Strategy for Walking In Streets- SIAM journal of Computing 33 , 2004 • Frank Hoffmann, Christian Icking, Rolf Klein, and Klaus Kriegel. • The polygon exploration problem. SIAM Journal on Computing, 31:577–600, 2002

  12. Thanks for your attention ! … I Kept Looking for sweet Home

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