This paper proposes an Evolutionary Programming (EP) approach to solve the polygonal approximation of digital curves. The solution provided by the method consists of a sequence of straight line segments to be applied as Advance and Rotate motion primitives of a 2D Cartesian robot. The proposed approach finds automatically the number of segments and the startingand ending points of each of them. We have tested our approach on a test set of digital curves that exhibits two main qualitative features: openess and straightness, in different degrees. We show that our method obtains good results for approximating the curves in the test set. We present both quantitative and qualitative results of these test.