Multi-Robot Perimeter Patrol in Adversarial...
Transcript of Multi-Robot Perimeter Patrol in Adversarial...
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Multi-Robot Perimeter Patrol in Adversarial Settings
Noa Agmon, Sarit Kraus and Gal A. Kaminka
Department of Computer Science Bar Ilan University, Israel
{segaln, sarit, galk}@cs.biu.ac.il
Presenter: Solomon Ayalew
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Introduction • Multi robot patrol in a closed area with the
existence of an adversary
• Traditional approach is Visit the area frequently
• If robots move in a deterministic way: Penetration is easy
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Introduction cont.
This paper:- Non deterministic Algorithm for a team of Homogenous patrol robots
Divide the perimeter in to segments i robot monitors 1 segment i per unit time cycle robot @ segment i have 3 choices Go to segment i-1 or i+1 or stay there (i)
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Movement models
3 movement models 1. DZCP : Directional Zero Cost Patrol 2. BMP : Bidirectional Movement Patrol 3. DCP : Directional Costly-Turn Patrol
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Adversarial model
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Adversarial model The adversary is strong (has full knowledge of the
system) Know the patrol scheme
1. # of robots, distance between them, their current position 2. Movement model of robots & characterization of their
movement
Can be learned by observing for sufficiently long time Assume worst case scenario
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Goal
Robots are responsible for detection not handling Multiple penetration is the some as single penetration
Adversary tries to penetrate @ the weakest spot in the cycle
Main goal: Find a patrol algorithm that maximizes penetration detection
in the weakest spot
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Algorithm
Algorithm is characterized by a probability p p could be 1 => deterministic So 0 <= p <= 1
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Border Penetration Detection (BPD) problem
Given Circular fence of length l divided in to N segments K robots uniformly distributed with d distance
d = N/k
Assume : it takes t time units for the adversary to penetrate
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cont.
let fi(p) =ppdi , 1 ≤ i ≤ d − 1 ppdi : probability of penetration detection Probability that a segment will be visited at least ones
during t time units
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Cont.
find optimal Popt such that the minimal ppd throughout the perimeter is maximized
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Cont.
Lemma 1: given p, func ppdi (Ra) for const t & Ra @ segment s0 is montoic decreasing func.
As distance b/n a robot & a segment probability of
arriving in it during t time units decrease
Lemma 2: if distance between two consecutive robots is smaller, the ppd in each segment is higher & vice versa
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Cont.
Lemma 3: team of k mobile robots in mission maximizes minimal ppd if: a. The time distance b/n every two consecutive robot is
equal b. The robots are coordinated: Move in the some dxn All change dxn @ the some time
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Algorithm to find popt
1st find the detection probability in each segment
2nd manipulate these equations to find popt (maxmin
point)
Complexity of algorithm is in polynomial time
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Finding the equation
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Cont.
• p of reaching a certain state in time r is the sum of probabilities of reaching in state sj multiplied by p of being in state sj @ time r-1
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Cont.
.
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Cont.
• Time complexity: FindFunc is d.(2d+2).(t+1). Since t is bounded by d-1 &
d=N/k complexity is O((N/k)3)
Next find maxmin point Is the value that lies inside the intersection of the all
integrals of fi
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Algorithm 2
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Result
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Cont.
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Cont.
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Conclusion and future work
Non- deterministic algorithm under strong adversary Polynomial time complexity
Continuous case rather than discrete model More realistic movement models With arbitrary tuning time
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Cont.
Other adversarial models Case of unknown adversary similar to Bayesian
games Adopt this algorithm in other domains e.g. Area patrol
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.
?
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