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This paper describes a neural implementation of the resistive grid technique for route finding. The resistive grid, or Laplacian planning technique, is not plagued by local minima problems and guaranties and existing route to be found. The neural network comprises 2 layers. In the upper layer, lateral connections between neurons communicate information on the potentials of neighbouring nodes in the grid. The lower layer represents a spatial memory in which information on the positions of obstacles an the target is stored. Each neuron in the upper layer receives a single input from a node in the lower layer corresponding to the same spatial location. This input is used to constrain the potentials in selected nodes in the resistive grid. The interplay between resistive grid and spatial memory results in a very flexible architecture easily adaptable to new environments. Its properties are demonstrated with a 2-dimensional path-planning problem for a mobile robot. The Dirichlet and Neumann boundary conditions are compared in terms of routes found and computational costs. Limitations and possible developments of the resistive grid technique are discussed.