In this investigation, we study the problem of bi-objective path planning problem among polygonal obstacles with the objectives minimizing the length and maximizing the clearance of the path, that is, maximizing the minimum distance between the path and the obstacles. The goal is computing Pareto optimal solutions, that is, the paths which cannot be shortened unless their clearance is minimized. In the first part of our study, we considered the case that the first objective is measured using the Manhattan metric and the second one using the Euclidean metric. We proposed an O(n3 log n) time algorithm, where n is the total number of vertices of the obstacles. The results are presented at TTCS 2020 conference and are published as a book chapter in LNCS Springer. The next phase of our study, consists of proposing an approximation algorithm for the case that both objectives are measured using the Euclidean metric. We aim to achieve our desired results by June 2021.