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This is quite possible, but not just only with opencv. I started similar project with sensors, and gave up because of cost factor. I'm trying out the approach of using opencv. At high level, following are the critical steps in my solution.

1. Use opencv to analyze the frames in the video, so that you can build PGN or FEN string
2. Pass PGN/FEN to an opensource chess engine like StockFish. Stockfish provides an API
3. Manipulate the robotic arm moves, based on move suggested by stockfish. I'm using MeArm robot that has DOF as 3.

I'm trying out in Raspberry pi and I'll opensource once I finish it. Nevertheless, there are lot of complexities to work out in detail.