I want to design a neural network / ConvNet to generate a set of points on a given map, which correspond to possible positions of a robot. The map contains a lot of empty space for walls, and the robots can't be in those positions. Therefore, the network should take in the map, and generate pairs of numbers (x, y) corresponding to places on the map that is not wall. What would be an appropriate choice of neural network structure to implement this task?

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The approach you might have to take will depend upon whether you wish to generalize to new unseen maps and be able to segment the map in to feasible(available for robot navigation) and infeasible (wall/other ojects/obstacles). Please be aware that you need to generate these maps dynamically if your environment will change over time(like moving obstacles/other robots/objects). For this if you have a good amount of annotated training data with maps with wall regions marked(segmented out), you could use a standard neural network based segmentation algorithm like Mask-RCNN (https://github.com/matterport/Mask_RCNN) on your dataset. Alternatively, if do not have a lot of annotated data and you just want a general purpose path planning algorithm, that can plan on a path from point A to B with out running in to obstacles you could use a MPC based obstacle avoidance algorithms as ones described in https://arxiv.org/abs/1805.09633 / https://www.tandfonline.com/doi/full/10.1080/00423114.2018.1492141