2,704 research outputs found
Pursuit on a Graph Using Partial Information
The optimal control of a "blind" pursuer searching for an evader moving on a
road network and heading at a known speed toward a set of goal vertices is
considered. To aid the "blind" pursuer, certain roads in the network have been
instrumented with Unattended Ground Sensors (UGSs) that detect the evader's
passage. When the pursuer arrives at an instrumented node, the UGS therein
informs the pursuer if and when the evader visited the node. The pursuer's
motion is not restricted to the road network. In addition, the pursuer can
choose to wait/loiter for an arbitrary time at any UGS location/node. At time
0, the evader passes by an entry node on his way towards one of the exit nodes.
The pursuer also arrives at this entry node after some delay and is thus
informed about the presence of the intruder/evader in the network, whereupon
the chase is on - the pursuer is tasked with capturing the evader. Because the
pursuer is "blind", capture entails the pursuer and evader being collocated at
an UGS location. If this happens, the UGS is triggered and this information is
instantaneously relayed to the pursuer, thereby enabling capture. On the other
hand, if the evader reaches one of the exit nodes without being captured, he is
deemed to have escaped. We provide an algorithm that computes the maximum
initial delay at the entry node for which capture is guaranteed. The algorithm
also returns the corresponding optimal pursuit policy
Cooperative Pursuit with Multi-Pursuer and One Faster Free-moving Evader
This paper addresses a multi-pursuer single-evader pursuit-evasion game where
the free-moving evader moves faster than the pursuers. Most of the existing
works impose constraints on the faster evader such as limited moving area and
moving direction. When the faster evader is allowed to move freely without any
constraint, the main issues are how to form an encirclement to trap the evader
into the capture domain, how to balance between forming an encirclement and
approaching the faster evader, and what conditions make the capture possible.
In this paper, a distributed pursuit algorithm is proposed to enable pursuers
to form an encirclement and approach the faster evader. An algorithm that
balances between forming an encirclement and approaching the faster evader is
proposed. Moreover, sufficient capture conditions are derived based on the
initial spatial distribution and the speed ratios of the pursuers and the
evader. Simulation and experimental results on ground robots validate the
effectiveness and practicability of the proposed method
Optimal Interdiction of Unreactive Markovian Evaders
The interdiction problem arises in a variety of areas including military
logistics, infectious disease control, and counter-terrorism. In the typical
formulation of network interdiction, the task of the interdictor is to find a
set of edges in a weighted network such that the removal of those edges would
maximally increase the cost to an evader of traveling on a path through the
network.
Our work is motivated by cases in which the evader has incomplete information
about the network or lacks planning time or computational power, e.g. when
authorities set up roadblocks to catch bank robbers, the criminals do not know
all the roadblock locations or the best path to use for their escape.
We introduce a model of network interdiction in which the motion of one or
more evaders is described by Markov processes and the evaders are assumed not
to react to interdiction decisions. The interdiction objective is to find an
edge set of size B, that maximizes the probability of capturing the evaders.
We prove that similar to the standard least-cost formulation for
deterministic motion this interdiction problem is also NP-hard. But unlike that
problem our interdiction problem is submodular and the optimal solution can be
approximated within 1-1/e using a greedy algorithm. Additionally, we exploit
submodularity through a priority evaluation strategy that eliminates the linear
complexity scaling in the number of network edges and speeds up the solution by
orders of magnitude. Taken together the results bring closer the goal of
finding realistic solutions to the interdiction problem on global-scale
networks.Comment: Accepted at the Sixth International Conference on integration of AI
and OR Techniques in Constraint Programming for Combinatorial Optimization
Problems (CPAIOR 2009
Optimal strategies for driving a mobile agent in a guidance by repulsion model
We present a guidance by repulsion model based on a driver-evader interaction
where the driver, assumed to be faster than the evader, follows the evader but
cannot be arbitrarily close to it, and the evader tries to move away from the
driver beyond a short distance. The key ingredient allowing the driver to guide
the evader is that the driver is able to display a circumvention maneuver
around the evader, in such a way that the trajectory of the evader is modified
in the direction of the repulsion that the driver exerts on the evader. The
evader can thus be driven towards any given target or along a sufficiently
smooth path by controlling a single discrete parameter acting on driver's
behavior. The control parameter serves both to activate/deactivate the
circumvention mode and to select the clockwise/counterclockwise direction of
the circumvention maneuver. Assuming that the circumvention mode is more
expensive than the pursuit mode, and that the activation of the circumvention
mode has a high cost, we formulate an optimal control problem for the optimal
strategy to drive the evader to a given target. By means of numerical shooting
methods, we find the optimal open-loop control which reduces the number of
activations of the circumvention mode to one and which minimizes the time spent
in the active~mode. Our numerical simulations show that the system is highly
sensitive to small variations of the control function, and that the cost
function has a nonlinear regime which contributes to the complexity of the
behavior of the system, so that a general open-loop control would not be of
practical interest. We then propose a feedback control law that corrects from
deviations while preventing from an excesive use of the circumvention mode,
finding numerically that the feedback law significantly reduces the cost
obtained with the open-loop control
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