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

2. 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. 3 Randomized Checkpoints

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

5. Protecting a Parade: route is announced 5

6. Protecting a Moving Target: randomizing the route 6

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

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

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

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

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

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

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

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

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 15

16. What Happens If Penetration Detected? 16

17. What Happens If Penetration Detected? Robot that detected the penetration will inspect it Other k-1 robots will spread uniformly o 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 17

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

19. Randomized Reorganization Challenges: o each robot needs to move differently o 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 19

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