I have a nearby neighbour that parks 2 or 3 heavy trucks (often including trailers the same size as the truck) on the nature strip just about every night. I see three trucks go past my place at specific times each morning, I don't know if it's a single person doing a round or there are employees that pick them up.
Anyway, short story is, you're not allowed to park any vehicles on the nature strip. The fact that they're heavy commercial vehicles in a residential neighbourhood is probably a double hit.
Time to go "Rochard" on them I think! :D