Automatic Differentiation of Non-holonomic Fast Marching for Computing Most Threatening Trajectories Under Sensors Surveillance

We consider a two player game, where a first player has to install a surveillance system within an admissible region. The second player needs to enter the monitored area, visit a target region, and then leave the area, while minimizing his overall probability of detection. Both players know the target region, and the second player knows the surveillance installation details. Optimal trajectories for the second player are computed using a recently developed variant of the fast marching algorithm, which takes into account curvature constraints modeling the second player vehicle maneuverability. The surveillance system optimization leverages a reverse-mode semi-automatic differentiation procedure, estimating the gradient of the value function related to the sensor location in time \({\mathcal O}(N \ln N)\).

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