This page explains how to start and complete the Robbie's Research side quest.
How to Begin the Robbie's Research Side Quest
Read the Locked Mementos page and complete the steps through "Get New Sheikah Slate Features" to begin the Robbie's Research quest.
How to Complete the Robbie's Research Side Quest
First, you need to meet Robbie. He is in Akkala Ancient Tech Lab, which is northeast of Katosa Aug Shrine.
In the Akkala Ancient Tech Lab, talk to Robbie. To prove that you are really Link, you will have to remove all your armor.
Robbie will ask you to bring the blue flame to light the furnace in front of the lab. Get a torch if you don't have one. Then look west from the lab to see the blue flame.
Make your way to the flame, but beware of the many Moblins, wolves, and other enemies in the area. Stealth equipment or masks from Kilton's shop or Expansion Pass "EX" quests are helpful here.
Be sure to look for stone lanterns along the path as you carry the blue flame. Light the lanterns with the blue flame as you go along so that if your torch gets extingished by rain or by running, etc., you won't have to go all the way back to the first blue flame.
After you light the furnace in front of the Akkala Ancient Tech Lab, the Robbie's Research quest will be complete.
Robbie's Research Quest Rewards
Talk to Robbie to get three Ancient Arrows, which always go in a straight line and are very effective against Ancient enemies and Lynels. After this, you can also purchase Ancient equipment from Cherry.