Constraint Programming for Path Planning with Uncertainty

Bounding an Optimal Search Path with a Game of Cop and Robber on Graphs

“…We show, in the third part, how the bounds perform when paired with the total detection (TD) heuristic used as a value-selection heuristic [10]. The TD heuristic is on many account similar to the bound derived in this paper which gives its theoretical justification.…”

“…In this paper, we present bounding techniques for a constraint programming (CP) model of the OSP problem introduced in [10]. We discuss, in Section 2, the DMEAN bound which has never been implemented in CP.…”

“…This bound, we call the Copwin bound, is obtained by relaxing the OSP into a game of cop and robber [11][12][13][14] which pertains to a well-studied game from graph theory (see Section 3). In Section 4, we show the benefits of using our novel Copwin bound by providing experimental results obtained on an existing CP model of the problem [10]. We conclude in Section 5.…”

Exact Solution for Search-and-Rescue Path Planning

“…In the proposed open-loop SAR model, the probability to successfully detect the target resulting from an agent path solution execution on the grid is defined as the sum over cells of the product of the probability of detection reflected from cell visits and target cell occupancy belief dictated by the cognitive map (grid) [5], [24]. Cumulative probability of success (CPOS) for a path solution (sequence of cell visits) over a time horizon T can then be expressed as follows:…”

“…Occupancy belief are assumed to be independent of past search visits as reported in [24]- [26], [5] for the optimal searcher path problem. Accordingly, based on the completion of a projected visit in cell c during time interval t, the posterior probability of cell containment p c' t+1 for any cell c' is given by:…”