
Gaspar's hint: "There's a task to be done in the Future, where machinery originated."
Robo's sidequest takes place in the future, in 2300 A.D. at the Geno Dome, which is to the southeast of the world map. You'll actually do some dungeon crawling and puzzle solving in this one, which is why you should put it late in the list. Head to the Geno Dome with Robo at the front of your party and he'll open up a path for you. He'll be a permanent fixture of your team throughout this next quest. You'll head down a conveyor belt and fight five or so waves of monsters. Equip the Gold Stud on someone and use the most powerful magic techs you have available. At this point, these enemies shouldn't be too difficult.

There's a blinking blue dot directly east of where you enter in the new room; don't interact with it unless you want to return to the beginning (to leave or redo the conveyor belt fights). Clear the room of monsters, and go into the middle room which is just west of the door you just came out of. Here, watch the robot charge himself up and follow him after getting Full Tonic from the chest nearby. He will open a door near where you entered by charging himself up and stepping into an alcove to open it. Head in that room for a quick fight and 2 more chests (Full Tonic, 50,000 G). Back where the charger bot came from, use the computer to get more info about the robots, dolls, conveyor belt, and sealed doors. What you'll want to do is charge up with energy from the room by the computer and step into an alcove to open its door. At the northwest, turn the center switch on and the others off to open the alcove and go in it with a charge to reach the first Poyozo Doll, picking up a Speed Tab where it used to sit as well. That's the easy part.

Head into the elevator in the southeast corner. Ignore the door for the moment, There will be a save point and a chest with a Lapis nearby. Fight a few groups of Laser Guards, Ignore the main door to the north (this is where you need the two dolls) and go down a ladder to the southwest. After grabbing 15,000 G from a chest, go through the door to witness a bunch of people being processed by the plant. A deadend with a chest (Full Ether) is on the other side of this room. Leave this room the way you came, go back up the ladder and to the east until you see the door blocked by red laser beams. Step back and have Robo run at the switch he can't reach and he'll leap at it to let you get a MegaElixir and a Magic Tab. Go back further and head through the ordinary door we ignored earlier (next to the elevator), picking up a Power Tab at the beginning of the long hallway, and fight another group of monsters to find another elevator going back to the previous area. Flip the switch to the bottom left to remove a laser so you can reach the conveyor belt. Next, go up and to the left of the door you entered the room. There is a switch up there to reverse the direction of the conveyor belt. There's also a Magic Tab in the secret passage you walk through to get to the switch, so pick it up as well. At the base of the conveyor belt to the right there is a room with some enemies and 2 chests with Elixir and Lapis.

Head back and around to where you get Robo charged up with electrical energy, you have to be very fast here. Have Robo race from the charger, down the hall and around to the conveyor belt, which is helping him move faster this time now that you reversed its direction, and go in to the alcove with the locked door to open up the passage to the security robot. Grab the 2 chests with Full Ether and HyperEther and have the robot slowly follow you back to the security robot in the southwest corner, keeping in mind that it can get stuck going around corners. The two robots will short each other out, and you'll grab a Vigil Hat and the last Poyozo Doll. Head back up the elevator to reach a sealed door where you can place both the Poyozo Dolls to clear a passage. On your way up there, you'll run into Robo's old girlfriend, Atropos.
Head to the east if you want to save and use a shelter, then head to the northwest to place the two dolls and visit the mastermind behind all of this.
Robo will get the Terra Arm and Crisis Arm, one of which is his best weapon, and one of which is a bit more unpredictable depending upon his HP. All the machines in the factory will shut down, and you'll be done with the sidequest.