I am in the process of making a FPS in c++ / openGL / Qt

I needed a way to define levels for the game. I recently wrote a renderer for collada dae files. I was thinking if I could design a level in software like sketchup and use that in my game. The renderer can render the dae model, but my concern is about the collision detection. That is, I don't want the player to walk through walls etc. All that I get from the collada file is a bunch of primitives, such as Triangles / Polygons etc.

How do I handle collision detection? I am not sure how to approach this problem or if it is even feasible or not ? I am very new to this, but I was thinking if someone had done this, they could point me in the right direction.

I'd appreciate any help!