This is a very interesting video that debunks some common theories of how the bicycle balancing works, and also proposes some extra insights (although no definitive theory yet)

https://m.youtube.com/watch?v=NcZCzr9ExKk

Also see this one for extra footage of the Gyroless, "trail-less" TMS bicycle that still manages to balance itslef

https://m.youtube.com/watch?v=LbeENKn5kZU