“…Due to one dimensional search problem and the 1-1 bijective property to ordered trees, our approach is potential to sample other combinatorial objects such as legal sequences of n pairs of parentheses, triangulated n-gons, and other combinatorial objects based on catalan numbers. In future work, we aim at studying the smoothness considerations in paths [19], [37], the integration with trajectory tracking [38], the online adaptation and integration with other intelligent schemes such as Fuzzy Logic [39], the performance for very large n and their further applications in combinatorial optimization in Robotics Fig. 11: Lower bound of the convergence of the evaluated algorithms over 20 independent runs.…”