The main contribution of this article is the combination of set-membership methods with optimizing approach. Hence, a correct-by-construction algorithm is defined with the intrinsic properties to be robust to uncertainties as it relies on set-membership approach. Moreover, embedding the motion planning problem into a constraint satisfaction problem (CSP), and more precisely into a global optimiza- tion framework, the proposed algorithm produces an optimal free-collision path with respect to a given cost function which is minimized.