Does the robot have to start the match with a button on the brain?

Rule <PSC2> states “Teams must bring their Robot controller to the field with them, although drivers start the robot by pressing a button on the brain and may not engage the robot with the controller during the match.”

Can the robot start the match by touching a TouchLED instead of a button on the brain?

The kid’s robot uses light sensors to sense the lines on the table and the light sensors need to be calibrated for the table and the lighting conditions at the competition. Before the match begins, the robot is turned on, the program is selected and it does the calibrations. When the ref indicates the match will start, the kids just touch the TouchLED and the robot will begin running its program.

Is this legal?

Yes, this is legal.