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We address discrete-time pursuit-evasion games in the plane where every player has identical sensing and motion ranges restricted to closed discs of given sensing and stepping radii. A single evader is initially located inside a bounded subset of the environment and does not move until detected. We propose a Sweep-Pursuit-Capture pursuer strategy to capture… (More)

We address a pursuit-evasion problem involving an unbounded planar environment, a single evader and multiple pursuers moving along curves of bounded curvature. The problem amounts to a multi-agent version of the classic homicidal chauffeur problem; we identify parameter ranges in which a single pursuer is not sufficient to guarantee evader capture. We… (More)

We introduce a problem in which demands arrive stochastically on a line segment, and upon arrival, move with a fixed velocity perpendicular to the segment. We design a receding horizon service policy for a vehicle with speed greater than that of the demands, based on the translational minimum Hamiltonian path (TMHP). We consider Poisson demand arrivals,… (More)

— This paper addresses the solution of large zero-sum matrix games using randomized methods. We provide a procedure by which a player can compute mixed policies that, with high probability, are security policies against an adversary that is also using randomized methods to solve the game. The computational savings result from solving subgames that are much… (More)

— We introduce a problem in which a service vehicle seeks to defend a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to… (More)

- Shaunak D Bopardikar, Francesco Bullo, João Hespanha
- 2006

— We address the discrete-time Lion and Man problem in a bounded, convex, planar environment in which both players have identical sensing ranges, restricted to closed discs about their current locations. The evader is randomly located inside the environment and moves only when detected. The players can step inside identical closed discs, centered at their… (More)

—We consider the problem of dynamic vehicle routing under exact time constraints on servicing demands. Demands for service are generated in an environment as follows: uniformly randomly in space and Poisson in time. Every demand needs to be serviced exactly after a fixed, finite interval of time after it is generated. We design routing policies for a… (More)

— In the companion paper we introduced a vehicle routing problem in which demands arrive via a temporal Poisson process, and uniformly distributed along a line segment. Upon arrival, the demands move perpendicular to the line with a fixed speed. A service vehicle, with speed greater than that of the demands, seeks to provide service by reaching the location… (More)

— We introduce a dynamic vehicle routing problem in which demands arrive via a temporal Poisson process with a certain arrival rate, and uniformly distributed along a line segment. Upon arrival, the demands move in a fixed direction perpendicular to the line with a fixed speed. A service vehicle, modeled as a first-order integrator with speed greater than… (More)

— We address a discrete-time pursuit-evasion problem involving multiple pursuers and a single evader in an unbounded, planar environment in which each player has limited-range sensing. The evader appears at a random location in a bounded region and moves only when sensed. We propose a sweep-pursuit-capture strategy for a group of at least three pursuers and… (More)