“…In the past, an exact method based on the HPFs were applied in many area of researches including ship navigation [5], trajectory control [6], space robot path planning [7], navigation of snake-like robot [8], UAV motion planning [9], marine vessel path planning [10], 3D motion planning for UAV [11,12], space exploration [13], etc. In robot navigation problem, the HPFs were successfully applied in various types of environments [14][15][16][17][18][19][20]. As an exact method, the approach based on HPFs posses the advantage of complete algorithm property to guarantee that the solutions can be found if they exist, or otherwise the algorithm can detect when no solution exists.…”