Intelligent Patrolling

1. Intelligent Patrolling Sarit Kraus Department of Computer Science Bar-Ilan University Collaborators: Noa Agmon, Gal Kaminka, Efrat Sless

2. Physical Security with Bounded Resources • Limited security resources prevent full security coverage at all times; allows adversaries to observe and exploit patterns in selective patrolling or monitoring. • Randomized patrolling or monitoring is necessary.

3. Randomized Checkpoints

4. Multi-Robot Adversarial Patrol • Motivation: • High security facilities • Large military bases • Neighborhood watch

5. Protecting a Parade: route is announced

6. Protecting a Moving Target: randomizing the route

7. Why Do We Need Automated Methods for Randomization? • People are not good at randomization • The randomized strategy should depend on: • the adversary and the defenders’ utilities • the environment parameters • the defender’s resources.

8. Multi-Robot Adversarial Patrol: The Environment • Perimeter • Divided into segments • Uniform time-distance • Robot travels through one segment per time unit • Adversary • Tries to penetrate through the perimeter • Takes t>0 time units to penetrate

9. Robotic Model • k homogenous robots • Robotic movement model: • Robots’ movement is directed • Turning around “costs” τ time units

10. Algorithm Framework • Patrol algorithm: • Continue straight with probability p • Turn around with probability 1-p • PPD: Probability of Penetration Detection • p depends on the distance between robots and on the penetration time.

11. Robot Movement • Optimal: Robots are uniformly placed around the perimeter • Coordinated • If decide to turn around they do it simultaneously • Preserve uniform distance

12. Robot Movement • Optimal: Robots are uniformly placed around the perimeter • Coordinated • If decide to turn around they do it simultaneously • Preserve uniform distance

13. Robot Movement • Optimal: Robots are uniformly placed around the perimeter • Coordinated • If decide to turn around they do it simultaneously • Preserve uniform distance

14. Robot Movement • Optimal: Robots are uniformly placed around the perimeter • Coordinated • If decide to turn around they do it simultaneously • Preserve uniform distance

15. Handling Events What if a robot needs to inspect the penetration? • Once a penetration is detected, one robot is extracted from the team to inspect it • Coordinated attacks are beneficial to the adversary

16. What Happens If Penetration Detected?

17. What Happens If Penetration Detected? • Robot that detected the penetration will inspect it • Other k-1 robots will spread uniformly • To achieve optimal behavior for k-1 robots Phase 1: k robots (before event), steady state Phase 2: Reorganization Phase 3: k-1 robots (after event), steady state Optimal patrol known

18. Naïve Approach • Deterministic:Each robot goes straight to its final position

19. Randomized Reorganization • Challenges: • each robot needs to move differently • How much time to spend on the reorganization? • We randomized over possible paths • Finding the strategy is complex, in theory, but we used heuristics to find it in reasonable time

20. Physical Security with Bounded Resources: Summary • Randomized patrolling or monitoring is necessary. • Automated randomization is important • Interesting problems? sarit@cs.biu.ac.il