I've written a collision system which detects/resolves collisions between a rectangular player and a convex polygon world using the Separating Axis Theorem. This scheme works fine when the player is colliding with a single polygon, but when I try to create a level made up of combinations of these shapes, the player gets "stuck" between shapes when trying to move from one polygon to the other.

The reason for this seems to be that collisions are detected after the player has been pushed through the shape by its movement or gravity. When the system resolves the collision, it resolves them in an order that doesn't make sense (for example, when the player is moving from one flat rectangle to another, gravity pushes them below the ground, but the collision with the left hand side of the second block is resolved before the collision with the top of the block, meaning the player is pushed back left before being pushed back up).

Other similar posts have resolved this problem by having a strict rule on which axes to resolve first. For example, always resolve the collision on the y axis, then if the object is still colliding with things, resolve on the x axis. This solution only works in the case of a completely axis oriented box world, and doesn't solve the problem if the player is stuck moving along a series of angled shapes or sliding down a wall.

Does any one have any ideas of how I could alter my collision system to prevent these situations from happening?