Pursuit Evasion

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A Robotic Sensor Network (RSN) is a network of devices equipped with sensing, communication, actuation (e.g.: mobility) and computation capabilities. Many RSN automation tasks, such as surveillance and tracking, can be modeled as pursuit-evasion games. In a pursuit-evasion game, one or more pursuers try to capture an evader who, in turn, tries to avoid capture. This project will develop a theory of pursuit-evasion games taking place in complex environments among complex systems.


Motivation

Pursuit strategies to be developed as a part of this project will provide robust solutions for a number of tasks in emergency response, search and rescue, energy and environmental monitoring, and health care automation. In particular, their utility will be demonstrated on a prototype system for monitoring the elderly. More broadly, the results of this project will participate in the formation of the next generation of automation technologies by advancing the state-of-the-art in distributed sensing and decision making.


Goals

Pursuit-evasion games among complex systems are computationally hard in their most general form. Hence, we focus on instances that model RSN automation tasks. Specifically, this project involves

  1. the investigation of the effect of information available to the players on the outcome of pursuit-evasion games,
  2. the development of distributed pursuit strategies which efficiently reason about various forms of uncertainty, and
  3. the adaptation of these results to solve two ubiquitous sensor-actuator network automation tasks (tracking and surveillance) in a robust fashion.


Contributions

We have recently published a survey paper on search and pursuit-evasion in robotics and a toolkit based on our recent work. Our contributions so far can be summarized as follows:

  • We started with a game that takes place on a graph. The players have only local visibility. We show that two pursuers can capture the evader on any graph (with high probability). We also present an algorithm which recognizes graphs on which a single pursuer suffices. [1]
  • Next, we studied a version where the game takes place in a simply-connected polygon. The pursuers have only line-of-sight visibility. We showed that a single pursuer can locate the evader (which can be arbitrarily faster than the pursuer) in any simply connected polygon with high probability. This game is known as the "visibility based pursuit-evasion game". If the pursuers are as fast as the evader, we show that they can in fact capture the evader. [2] (An applet that demonstrates this strategy)
  • We are currently working on designing pursuit-evasion strategies for more general systems. Recently, we have extended the pursuit strategy for finding the evader in a polygon to the case where the pursuer's motion is subject to polyhedral kinematic constraints. [3]
  • We have also studied a pursuit-evasion game where the players' motions are restricted to a roadmap. [4]

Our recent contributions can be summarized as follows:

  • Robotic Routers - The task of a network of robotic routers maintaining the connectivity of a mobile user with a base station is formulated as a pursuit-evasion game, in which the user is an adversary trying to break connection. The resulting robotic router strategy guarantees connectivity to any user (adversarial or otherwise) for the maximum duration of time possible.
  • O. Tekdas, W. Yang, and V. Isler. Robotic Routers: Algorithms and Implementation. Int. Journal of Robotics Research, 2009. Note: Accepted.
pdf bibTeX
  • Lion and Man game - In the original Lion-and-Man game, a lion tries to catch a man (with equal maximum speed) while the man simultaneously tries to avoid capture. We study variants of this game relevant to applications where mobile robots have limited sensing capabilities.
  • First, we showed that the lion's pursuit strategy applies to simply-connected polygonal environments.
V. Isler, S. Kannan, and S. Khanna. Randomized Pursuit-Evasion in a Polygonal Environment. IEEE Transactions on Robotics, 5(21):864--875, 2005.
pdf bibTeX
  • Then, we restricted the lion (pursuer) to have bearing-only sensing information about the man (evader) and presented a pursuit strategy that takes the lion to within a step-size distance of the man. It appears that exact capture is unlikely.
N. Karnad and V. Isler. Bearing-Only Pursuit. In Proc. IEEE Int. Conf. on Robotics and Automation, 2008. Note: To appear.
pdf bibTeX
  • Next, we introduced a circular obstacle into the lion-and-man game played in a simply-connected polygon. The game was formulated as an optimal control problem, where the obstacle is expressed as a terminal condition. We derived optimal trajectories for the lion and the man, and, presented a decision algorithm that takes any initial condition as input and declares which player wins as the output (along with the winning strategy).
N. Karnad and V. Isler. Lion and Man Game in the Presence of a Circular Obstacle. In IEEE International Conference on Intelligent Robots and Systems (IROS), 2009. Note: To Appear.
pdf bibTeX
  • Our most recent result shows that three pursuers can capture the evader in any polygon (possibly with holes) if they can see it at all times.
pdfbib. The remaining question is then: when do two pursuers suffice? Here is a sufficient condition.
  • We also studied the effect of reducing the pursuer's sensing range for a pursuit-evasion game played on a graph.
V. Isler and N. Karnad. The Role of Information in the Cop-Robber Game. Theoretical Computer Science, 3(399):179--190, 2008. Note: Accepted to the Special Issue on Graph Searching.
pdf bibTeX

Videos

  • The role of information in pursuit evasion: Graph theoretic models, Applied Algebraic Topology Seminar, IMA, June 2009. Video available through IMA
  • Pursuit-Evasion outreach: demonstration of a greedy pursuit strategy in an educational setting.
  • Turn-based pursuit evasion with localization: mobile robots query a vision system to obtain their coordinates.

Publications on pursuit-evasion games

2016
23U. Ruiz, V. Isler
Capturing an Omnidirectional Evader in Convex Environments Using a Differential Drive Robot
IEEE Robotics and Automation Letters, 1(2): 1007-1013, 2016.
22N. Noori, A. Renzaglia, J. V. Hook, V. Isler
Constrained Probabilistic Search for a One-Dimensional Random Walker
IEEE Transactions on Robotics, 32(2): 261-274, 2016.
21N. Noori, A. Beveridge, V. Isler
Pursuit-Evasion: A Toolkit to Make Applications More Accessible Tutorial
IEEE Robotics Automation Magazine, PP(99): 1-1, 2016.
2015
20Ubaldo Ruiz, Volkan Isler
Capturing an Omnidirectional Evader in Convex Environments using a Differential Drive Robot
CoRR, abs/1508.06333, 2015.
2014
19N. Noori, V. Isler
Lion and Man Game on Polyhedral Surfaces with Boundary
In IEEE Conference on Intelligent Robots and Systems (IROS), 2014.
pdf,.bib
18J. Vander Hook, V. Isler
Pursuit and Evasion with Uncertain Bearing Measurements
In Proc. 2014 Canadian Conference on Computational Geometry, 2014.
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17N. Noori, V. Isler
Lion and Man Game on Convex Terrains
In Workshop on the Algorithmic Foundations of Robotics (WAFR), 2014.
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2012
16D. Bhadauria, K. Klein, V. Isler, S. Suri
Capturing an Evader in Polygonal Environments with Obstacles: The Full Visibility Case
International Journal of Robotics Research, 2012.
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15N. Noori, V. Isler
Lion and Man with Visibility in Monotone Polygons
In Workshop on the Algorithmic Foundations of Robotics (WAFR), 2012.
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2011
14T. Chung, G. Hollinger, V. Isler
Search and pursuit-evasion in mobile robotics
Autonomous Robots(3), 2011.
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13D. Bhadauria, V. Isler
Capturing an Evader in a Polygonal Environment with Obstacles
In 22nd International Joint Conference on Artificial Intelligence, 2011.
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2010
12O. Tekdas, W. Yang, V. Isler
Robotic Routers: Algorithms and Implementation
Int. Journal of Robotics Research, 29(1), 2010.
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2009
11N. Karnad, V. Isler
Lion and Man Game in the Presence of a Circular Obstacle
In IEEE International Conference on Intelligent Robots and Systems (IROS), 2009.
pdf,.bib
2008
10V. Isler, N. Karnad
The Role of Information in the Cop-Robber Game
Theoretical Computer Science, 3(399): 179--190, 2008.
pdf,.bib
9N. Karnad, V. Isler
Bearing-Only Pursuit
In Proc. IEEE Int. Conf. on Robotics and Automation, 2008.
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2006
8V. Isler, S. Kannan, S. Khanna
Randomized Pursuit-Evasion with Local Visibility
SIAM Journal on Discrete Mathematics, 1(20): 26--41, 2006.
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2005
7C. Belta, V. Isler, G. J. Pappas
Discrete Abstractions for Robot Motion Planning and Control in Polygonal Environments
IEEE Transactions on Robotics, 5(21): 864--875, 2005.
pdf,.bib
6V. Isler, S. Kannan, S. Khanna
Randomized Pursuit-Evasion in a Polygonal Environment
IEEE Transactions on Robotics, 5(21): 864--875, 2005.
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5V. Isler, D. Sun, S. Sastry
Roadmap Based Pursuit-Evasion and Collision Avoidance
In Robotics: Science and Systems, 2005.
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2004
4V. Isler, S. Kannan, S. Khanna
Randomized Pursuit-Evasion with Limited Visibility
In ACM-SIAM Symposium on Discrete Algorithms, 2004.
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3V. Isler, K. Daniilidis, G.J. Pappas, C. Belta
Hybrid Control for Visibility-Based Pursuit-Evasion Games
In IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004.
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2V. Isler, S. Kannan, S. Khanna
Locating and Capturing an Evader in a Polygonal Environment
In Sixth International Workshop on the Algorithmic Foundations of Robotics, 2004.
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1V. Isler
Algorithms for Distributed and Mobile Sensing
PhD Thesis, Department of Computer and Information Science, University of Pennsylvania, 2004.
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This work is supported by the NSF grant Pursuit-Evasion Games with Complex Systems in Complex Environments