Kinematic Movement Collisions

I’m having a hard time finding any good reading material for this. I’m working on a runtime and physics engine. I’ve got the physics engine to have stable world space with dynamic objects interacting with each other, static, and kinematic objects.

The problem I’m running into right now is creating an api for moving a kinematic character controller. Intersecting GJK + EPA were good enough for discrete dynamic collision detection and response for dynamic objects, but i know that Distance GJK sweeps with conservative advanced continuous collision detection offers some of the best results for kinematic character controllers.

I’ve been scanning through the PhysX, Cute and other source codes, but I’m feeling I need a bit deeper of an explanation.

Would anyone happen to know of good papers, books, articles or otherwise on the topic?