Combine the sugar and pineapple in a medium saucepan over medium heat, and cook until sugar dissolves, stirring occasionally. Remove from heat, and cool slightly. Chill.

Combine pineapple mixture, yogurt, and vanilla in a large bowl. Pour the mixture into the freezer can of an ice-cream freezer, and freeze according to manufacturer's instructions. Spoon yogurt into a freezer-safe container; cover and freeze 1 hour or until firm.