I'm trying to solve a problem about AI. I have a "robot" that should go from a point A to B much quickly and cheap as possible. This Rover can't climb heights higher than 10 units and the cost of his route is influenced by the kind of terrain. I need your help becouse I need to find a admissible heuristic for solving my problem. I already try the Euclidian distance but it's not enough. Can you help me?
I would recommend taking a look at this page for some ideas of heuristics. They will not all be applicable in your situation, since I don't believe you have a grid map? But you can at least have a look.
Furthermore, I'd recommend trying to take into account the various costs that are possible in different kinds of terrain. If, for example, you know that every single possible type of terrain has a minimum cost of 2, you can safely multiply your Euclidean distance by 2. If the most common type of terrain has a cost of 2, but there also are some types of terrain with a lower cost, you lose the guarantee of finding an optimal solution if you start multiplying by 2, but you may still find solutions more quickly in practice.
To me, the question sounds like a homework assignment (correct me if I'm wrong), which makes it difficult to give a single answer. I guess that the point of the homework assignment even is to research a bit and try some different things and see how they work (or don't work), which can improve your understanding of how the algorithm works. So, really, just try some things.