Upon entering the application, Robert is presented with something that looks like a To-Do list:
To add a task to the list Robert presses the plus button, which brings him to the Add Task screen:
Here Robert can add a picture of the task as well.
When Joffrey opens the app, he'll see the list of tasks to be done:
And if he checks something off, he's presented with the complete task dialog:
This allows the user (in this case Joffrey) to tell the app that it was he who completed the dishes, and allows him to take a picture of the completed task.
Completed tasks are shown in the list as checked off tasks, and the image of their completer is shown next to the task.