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Multi-Vehicle Exploration and Routing in Adversarial Environments. Eric Feron Farmey Joseph Jerome le Ny Program Review Meeting The Stata Center at MIT June 22, 2005. Exploration for UAVs. Ambush-aware Routing. Exploration with stochastic agents.
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Jerome le Ny
Program Review Meeting
The Stata Center at MIT
June 22, 2005
Exploration with stochastic agents
Multi-Vehicle Exploration and Routing in Adversarial Environments
Military Police drive from base each day to school or hospital to provide security
Humanitarian convoy leaves supply base each day to deliver food, medicines, etc. to aid dispersal site
Ambassador makes daily trip from home to embassy
Must randomize the routing so as to minimize the probability of being ambushed by hostile forces?
Determine an optimal mixed strategy for choosing among possible routes between origin and destinationRouting
edges » usable roads
nodes » road intersections
Player 1 (VIP) chooses a path from origin node to destination node
Player 2 (hostile forces) simultaneously chooses k nodes as ambush locations
k typically small, dependent on enemy resources
If P1 is ambushed at node i, game outcome is ai > 0.
ai» level of exposure of node i to an ambush
If P1’s path avoids all ambush nodes, game outcome is 0.The VIP Transport Game
flow along an edge = probability of traversing that edge
for k-ambush problem: minimize the max flow (weighted by ai) into any set of k nodes
s.t. Dp – 1z·0
Ap = b
p ¸ 0
Solve for Player 1’s optimal strategy (p*) and the expected value of the game outcome (z*)
autonomous vehicles, engineered mobility (UAVs, cars…). Reliable, few agents involved.
carried by environment + limited control of mobility. Cheap (batch fabrication, ex MEMS), unreliable individually, but use redundancy.
(ref: Talwar et al., Nature 417, 2002)
Some exploration scenarios in 1-D
N agents dropped at x1,…,xN. Minimize sum of the distances traveled to completely explore the line. How to choose respective exploration segments, i.e. R1,…,RN?
optimal # of agents:
(ex: naturally mobile sensors.)
Continuous model: speed is uncertain
control u(t) Є [-1;1]
Go right (p>q):
Goal: explore the line with 1 prob. agent
Equivalent results, easier with BM
until 1st success
cost for increasing
(Savla, Frazzoli and Bullo, 2005)
of the optimum