A Mixed-Integer Linear Programming Model for Generating Single-Track Gray Codes

In this article, the problem of constructing the single-track gray code (STGC) encoders is considered. STGCs are very useful in absolute position encoding for angular sensors which are used in a wide range of applications such as photographic lenses, weapons, rotating radar platforms, etc. A mixed-integer linear programming (MILP) model is proposed to search for optimal period-
$p$
STGCs, for any arbitrary integer
$p\ge 2$
. Various objective functions and various side constraints can be included in the proposed model in order to generate STGCs with private features which can be very useful in cost reduction, production complexity reduction, etc. The use of such a mathematical programming formulation for the STGC construction problem enables us to take advantage of the powerful mathematical optimization methods and lead to finding STGCs in a reasonable amount of time. The proposed model is applied to find several STGCs of different types.