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Model S 2015 85D AP1 issue with centering in lane

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Hi all, I have a Model S 85D with AP1 and recently I have noticed that when I have autopilot engaged that even when I am on a straightaway on a full scale 8 lane highway when either I come up on another car in the lane to the right or left or if they come up on me that my car wants to pull closer to them versus staying centered. Has anyone had this issue as I consistently need to disengage from AP and take over steering, as its clear I am almost in the other cars lane. Not sure if this is a software issue or a sensor issue. I would love some feedback from the community. Thanks
 
About once in every 50 times I activate AP on one of my cars (12/2014 P85D) it will shoot immediately to the right edge of the lane I'm currently in. On the dash it even displays that it's on the right line so it's not like the system "thinks" it's centered. It does this regardless of if there's a car to the right of me or not and will hold this position for probably 15-20 seconds. Then it will center itself and everything will be fine. If there's a car there and I take control, center and try again it will repeat this behavior. There have been times when, in traffic, it's repeated this half a dozen times or more. It's almost like when it gets in this mode I have to let it work things out. Our other cars haven't displayed this behavior once.
 
Thanks for all the replies. I brought my Model S into the service center and did a test drive, but they do not believe their is an issue. I am not sure what other remedy I have to the issue if they do not see it and for them its too minor to figure out if its a software or a sensor issue. Any ideas on how to handle with the service team at Tesla?
 
Mine always stays towards the right as well. It's the one thing I hate about autopilot.

I wish it would do: right lane, stay slightly right. If in the left lane, stay slightly left. But I'd definitely settle for dead center!