When it comes to frameworks for ANN, each person will have their own preferences. I recently used Encog framework for implementing an image processing project and found it very easy to implement.
Now, coming to your problem statement, "a learning method that enables minesweepers to avoid colliding with mines" is a very wide scope. What is indeed going to be your input to the ANN? You will have to decide your input based on whether it is going to be implemented on a real robot or in a simulation environment.
It can be clearly inferred that an unsupervised learning can be ruled out if you are trying to implement something like the ALVIN.
In a simulation environment, the best option is if you can somehow form a grid map of the environment based on the simulated sensor data. Then the occupancy grid surrounding the robot can form a good input to the robot's ANN.
If you can't form a grid map (if the data is insufficient), then you should try to feed all the available and relevant sensor data to the ANN. However, they might have to be pre-processed, depending on the modelled sensor noise given by your simulation environment. If you have a camera feed (like the ALVIN model), then you may directly follow their footsteps and train your ANN likewise.
If this is a real robot, then the choices vary considerably, depending upon the robustness and accuracy requirements. I really hope you do not want to build a robust and field-ready minesweeper single-handedly. :) For a small, controlled environment, your options will be very similar to that of a simulated environment, however sensor noise would be nastier and you would have to figure in various special cases into your mission planner. Still, it would be advisable to fuse a few other sensors (LRF, ultrasound etc.) with vision sensors and use it as an input to your planner. If nothing else is available, copy paste the ALVIN system with only a front camera input.
The ANN training methodology will be similar (if using only vision). The output will be right/left/straight etc. Try with 5-7 hidden layer nodes first, since that is what ALVIN uses. Increase it up to 8-10 max. Should work. Use activation functions properly.