Study On The Strategies To Search In Position-Independent Polygons

Path planning is one of the fundamental problems in autonomous systems; the aim for this problem is to generate a path between the starting point and the target position where the target located. The search for a target in an environment can be considered as an online problem if the environment is unknown before the robot starts to search. The performance of a competitive strategy can be measured by comparing the distance traversed by the robot with the length of the shortest path from the starting point to the target location. The worst case ratio of the distance traversed by the robot to the optimal distance from starting point to target point is called the competitive ratio of the search strategy.If the competitive ratio is a constant which is independent of the information, such as the edge or concave (convex) vertex of the polygons, then the search strategy is called a constant competitive ratio searching strategy. Moreover, if the constant competitive ratio is independent of the starting position or the target position, then this searching strategy is called as position-independent constant competitive ration search strategy. There are only the streets and the star-shaped polygons in the classes of the polygons that admit position-independent constant competitive ratios, so they belong to the classes of position-independent polygons. Particularly, the classes of star-shaped polygons are considered firstly as the position-independent polygons.Firstly, the more competitive strategy for searching in star-shaped polygons is presented by using the modified-curve as the trvavling path of robot, which based the analysis of star-shaped polygons environment and the old strategy. And the new strategy achieves the competitive ratio of 11.18. The correctness of the result is guaranteed by using the rigor deduction.Secondly, for the search in streets, the strategies achieve the ratios of 25.68 by modifying the back path and computing the distance traveled by robot when the start point of robot is restricted. If the start point is free, then the streets will divided into two parts by the middle chord, and the robot will search in each part by using the similar strategy. And the strategy achieves a competitive ratio of 47.334, which also is a better result than the old one.The strategies achieved above, especially the ones for the streets greatly improve the performance of searching strategies for position-independent polygons, and theyare the best results until now.In the end, the conclusion is given and the further research direction for online-searching strategies is pointed out.