I sent the robot to the Rexford but it's lost somewhere in between for a week. I how to get this is complete.

This quest is known for it's many bugs and glitches. I hope you are on pc so you can use the console command to end the quest. Just google the console command

I wish since I chose to keep the robot, that the quest would end. Its just stuck incomplete now.

Not sure it's necessarily a bug, because the robot follows a very dangerous path back to Goodneighbor. I walked along with him, and even with me there he was killed two or three times so I had to go back to a previous save. Gunners and Mirelurks, IIRC.

well I sent the thing to GN, but he decided to go back to his basemant home at the brewery. he will accept my instructions to leave, but takes 2 steps and turns around back to his pod.

I gave up. he is still there!

Why would you send a robot who brews you free ice cold beer away?

I did that on my first play through and was super annoyed with the whole quest. Got him there eventually though...

My second time through, I sent him but didn't exit the bar you find him in. Instead, I found a seat and waited a few hours. He got there on his own. Much easier.

The quest NEVER ends if you keep him- some have reported killing the quest giver ends it with a failure and removes it from your list, but yeah, I walked with him for the first couple of blocks and saw how much his health was going down going through those firefights, so I saved the game and just fast-travelled away.

If you've not done it yet - It takes him forever to get to wherever you send him, but he'll eventually make it if you're not there in person to draw all the trouble like a magnet to him.

I just learned in another thread he can ice-down Nuka Colas too- KEEP THAT GUY!