I am currently working on a 2D platformer game and i was hoping to have AI that could follow the player instead of mindlessly moving side to side in the map. I looked into astar pathfinding and i managed to make a simple pathfinding system for an overhead game. The thing i am having trouble with is getting the AI to follow the path in a 2D platformer. I can make simple AI follow paths on overhead games, but i have no idea how to do this in 2D. how do i make the pathfinding itself calculate gravity, jumpheight, pitfalls and all of the other 2D obstacles? also how would i make the AI even follow a path like this? i would like to make an AI like the one in this video

Remember that A* is a graph-based function. It only follows connections between nodes. It doesn't matter if those nodes are regular, odd, evenly spaced, top-down, or from the side. The best bet is to pre-calculate all possible jumps (up and down) and plot how those would look in space. Then, as you prepare your level, you mark up the places where the nodes connect -- obviously next to each other, but also where there are potential jump paths as well. Then, the AI just analyzes those nodes and the connections available to find the best possible route to the goal.

Now all of that assumes A*. If you are just using a local steering function, that is actually (believe it or not) slightly more complicated in this manner. If you were to simply scan the squares in an area around you (say a 3x3 grid centered on the agent), you can identify places you could possibly go next. Either by moving 1 square left or right (normal movement), a square up or down and also left right (e.g. your 4th-6th columns in the video above), etc. If you can't go directly to a square in the direction you want to move, you also scan 2 squares over and see if there is something available to jump to. That way, if a direct path is not available, it might elect to jump a gap (e.g. the middle-right area of your video). That's more of a clunky rule-based brute force way of doing it, though.

Thank you for the reply, but im still confused about how i would implement the search algorithm. First of all how would i make the search algorithm take into account gravity and jumping. also how would i make the algorithm go from one solid node to another and take into account the gaps in between and the distances for jumping. lastly would i implement a search algorithm in the AI itself or just a generic search algorithm that anything can use. thanks for the help so far and sorry i couldnt grasp how i would implement it.

IADaveMark basically just told you the answer you're looking for.

You have to remember that A* is just a search algorithm that goes through different states and pruning out those states that aren't desirable so you can find the path you're looking for. It doesn't care about the exact details of how you get to each location in the state graph. It just matters that you can get from one state to another in some way that reflects the cost of that transition.

If you properly set up the graph, the graph itself retains the information about where you can jump to or drop to. The A* search simply tells you to get from A to B to F to G, where there might be a drop from B to F. It is up to your agent to realize that you need to drop down from B to F when you reach B.

Alright thanks for the help guys.