Four teams, four people in each team, how to arrange the badminton match and how to draw lots when the players of the four teams don't touch each other?

You mean four players on the same team don't touch each other in the first round? Then they can draw lots like this: four players in each team draw lots from the four numbers 1, 2, 3 and 4, and the same number is drawn in the same division. Four players in the same division can draw lots to decide to be divided into two groups for elimination. This can ensure that players of the same team will not touch each other in the first two rounds.