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    Re: Cook's Incremental Reckoning
    From: Brad Morris
    Date: 2010 Apr 4, 07:11 -0700

    Hi Frank

    The robotic error is quite simple really. Robots do not keep track of position by inches, millimeters or any other rational number. They use encoders, in which the unit is a "count". It is always an integer, like 17458 counts, but not 2.5 counts. When you specify to robotic piece of equipment to position itself to 4.5 inches, there is a translation between inches and counts and at the lower levels, the servo mechanism moves to the count location which was specified. So if you specify a position that is between two counts, the robotic positioning equipment will choose (typically) the closest one. This is all quite fine when you are dealing with absolute positions. The trouble lies with incremental positioning. Each time the delta move is specified, this 'round off' error comes into play. Add enough round off errors and there is a problem.

    I distinctly recall a laser interferometric positioning robot. It's job was to position itself within an X-Y cartesian plane. The resolution of the equipment was five nanometers. That means, one count was five nanometers. Pretty small increment (about 1/5 of a millionth of an inch). The client had it incrementally position itself, even with our cautions. Eventually, it walked its way into error. A common occurence for incremental positioning.

    Now put that into navigation terms. My DR position today is based upon yesterday's increment. I will sail in a NW direction at 7 knots. Using my traverse tables, I find that I have a new DR position. Without reference, the accumulation of error in DR position can occur. Even if the traverse table was deadly accurate, the DR is not recorded to the precise real world position you are at, rather, it is to the resolution of the table. The navigator records to the nearest 1' of longitude, but really, it could be to some odd number of seconds as well. Round up, round down, but eventually, this minor error accumulates into a significant problem. Of course, once a longitude method was possible, these DR positions can be corrected (referenced).

    In this discussion, it was made clear that this error was not a predominant error. I agreed with that assessment.

    Best Regards
    Brad

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