I explaining transition in 1 email is not easy, but paparazzi is probably the most flexible open-source autopilot with direct support for a multitude of sensors, boards and airframes.
At this point there are 2 choices concerning transitioned flight:
-manual flight transition: in this setup transition is a 90 degree rotation of the setpoint with coordinated turn dynamics for the turns (roll -> yawrate). You only need gain-sheduling for the attitude loop. [
http://www.youtube.com/watch?v=IK_-yTrwNtU]
-fully autonomous transition: this setup also requires gain-sheduled innerloops, but on top of that has several outerloop controllers, each with their own gains and activated by the lift allocation controller. [
http://www.youtube.com/watch?v=B14mZXjOhCQ]