The Booming Blade cantrip's secondary effect states that "[the target] becomes sheathed in booming energy until the start of your next turn. If the target willingly moves before then, it immediately takes 1d8 thunder damage, and the spell ends". We can deduce, then:
- That the damage does not trigger when the target is dragged or pushed around via physical means (grappling, shoving, scenario effects, etc.)
- That the damage does not trigger when the target is dragged or pushed around via magical means (Gust, Eldritch Blast with Grasp of Hadar, Graviturgist's Gravity Well, etc.)
This seems pretty clear. However, what happens when the following cases arise?
- The target is ordered to move via the use of Command (assuming they don't know yet that the thunderous aura is damaging).
- The target is forced to move via the use of Compulsion.
- The target is invited to move via the use of Suggestion.
- The target is Turned.
- The target is Frightened and forced to run via Dissonant Whispers.
- The target has a Geas that prohibits them from ending a turn next to an enemy if they can avoid it.
- The target is threatened into leaving the area or else. This one seems "willingly", but are they truly willing if they are panicking because you are telling them you will cut their heads off if they don't run?
This tweet seems to suggest that forcing people to move via mind control spells doesn't count as willing. However, after the release of the 2019 Sage Advice Compendium, Jeremy Crawford's Twitter rulings are no longer considered official, so I was looking for something more solid to make a RAW judgement of this interaction.