How does Voxel grid works?

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More details than what? It's a 3D grid: A collection of aligned boxes: .

It can be "implemented" using a 3D array in memory, but for voxel maps one usually uses an octree.

If you want to know more about voxel mapping see the page of the octomap library, where you will also find visualizations of voxel grids/maps.

You can also use meshes to query the closest point between two meshes (one is your robot model, the other part of the environment). But as far as I know, performance-wise these are limited to low amounts of polygons, i.e., not well suitable for meshes generated from sensor data.