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In our previous project we did something very similar and we used laser_line_extraction package to get straight lines from the scans. It will give you the polar parametrizations of the line and the starting and ending points, so it shouldn't be difficult to get a goal pose and control the vehicle towards it.
This is actually how the Fetch and Freight do it (mobile manipulator and mobile platform from Fetch Robotics, respectively). Their code is open source, take a look here. I think they're making use of the shape of the dock to help: it's trapezoidal-shaped, and they know its dimensions, so I think they're keying onto that (but I don't know for sure, I haven't checked).