Several times while playing through missions in Fallout 4 the companion/NPC that I am supposed to escort will stand still and not move any further (Specifically Deacon and Nick Valentine). Here are a few ways that might help you persuade them to get moving again. Remember, the best way to avoid these problems is to save often so you always have a previous save to return to (save at least every few minutes and not always to the same save file). If you are a veteran of playing Bethesda games then you already know that frequently saving is the best way to approach Fallout/Elder Scrolls as they are often very buggy due to the size and scope of the game.
Fast travel then return
If convenient, fast travel out of the area and return again. This will reload the area and hopefully cause your companion to find the will to move. This solved all my problems with Nick Valentine as it was an outside quest that allowed for easy fast travelling. If you are inside then, if it is convenient, go outside and try this.
Save and reload
Save the game in which the NPC is stuck, reload in and the NPC may load into a different location which will cause them to become unstuck. This is how I was able to get Deacon to move.
Try talking to them
Sometimes NPCs will not proceed any further until you initiate a conversation with them. This is most common when you are exploring an area with an NPC for a specific quest and not when you are freely exploring with your companion.
How to make Mama Murphy move?
Mama Murphy not moving is not a bug, she just doesn’t move from her initial location you set the chair in. You can move her by ringing a town bell in your settlement causing her to stand up and move to the bell’s location.
Any other methods that worked for you?
Comment below and let me know. Thanks for reading.