5,015 research outputs found
Optimal patrol to uncover threats in time when detection is imperfect
Consider a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. An attack takes a random amount of time to complete. The patroller takes one time unit to move to and inspect an adjacent node, and will detect an ongoing attack with some probability. If an attack completes before it is detected, a cost is incurred. The attack time distribution, the cost due to a successful attack, and the detection probability all depend on the attack node. The patroller seeks a patrol policy that minimizes the expected cost incurred when, and if, an attack eventually happens. We consider two cases. A random attacker chooses where to attack according to predetermined probabilities, while a strategic attacker chooses where to attack to incur the maximal expected cost. In each case, computing the optimal solution, although possible, quickly becomes intractable for problems of practical sizes. Our main contribution is to develop efficient index policies—based on Lagrangian relaxation methodology, and also on approximate dynamic programming—which typically achieve within 1% of optimality with computation time orders of magnitude less than what is required to compute the optimal policy for problems of practical sizes
RoSSO: A High-Performance Python Package for Robotic Surveillance Strategy Optimization Using JAX
To enable the computation of effective randomized patrol routes for single-
or multi-robot teams, we present RoSSO, a Python package designed for solving
Markov chain optimization problems. We exploit machine-learning techniques such
as reverse-mode automatic differentiation and constraint parametrization to
achieve superior efficiency compared to general-purpose nonlinear programming
solvers. Additionally, we supplement a game-theoretic stochastic surveillance
formulation in the literature with a novel greedy algorithm and multi-robot
extension. We close with numerical results for a police district in downtown
San Francisco that demonstrate RoSSO's capabilities on our new formulations and
the prior work.Comment: 7 pages, 4 figures, 3 tables, submitted to the 2024 IEEE
International Conference on Robotics and Automation. See
https://github.com/conhugh/RoSSO for associated codebas
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