A Hybrid Routing Approach Using Two Searching Layers

– This paper considers SUB_GOALs by using basic A* algorithm and Subgoal Graphs in a hybrid approach to execute optimal route. SUB_GOALs identified with pre-searching from basic A* at break points and Subgoal Graphs at corners of obstacles are added to SUB_TABLE to expedite the final searching in the hybrid approach. Map to work on is divided to subregions with decision-making process by using line-of-sight to avoid redundant searching. In the final searching layer, all feasible SUB_GOALs gained from decision-making process in the same subregion are connected to find final solutions of routes. Solutions achieved in the divided subregions are evaluated and combined to discover the final optimal route. The proposed hybrid approach is applied to three different scenarios in various dimensions of maps. In these three scenarios, the shortest route without hitting obstacles is calculated as 46.67, 57.76 and 124.7 units, respectively, and compared with other search algorithms. Simulation results of route planning are demonstrated to exhibit the effectiveness of the proposed hybrid approach.


I. INTRODUCTION
In mobile robot research, route planning is one of the key factors for implementation of autonomous mobility of robots. Various solutions can be suggested by different characteristics of planning as performance improvements, different escape plans according to the risks, collision avoidance especially for mobile obstacles. Most of the studies dedicated to the planning of the optimum route indicate obtaining the effective route from starting point S to final point F avoiding obstacles or collisions in complicated environment. Route planning algorithms focus on different approaches as grid-based searching, interval-based searching, geometric algorithms, sample-based algorithms, and remarkable points algorithms. These approaches can be used to solve various structures of different problems with advantages and disadvantages.
In recent years, grid-based search algorithms have been used to find the optimum route in many application areas (such as maps, games). Photographers in the Indonesian city of Bandar Lampung have used one of the grid-based searching algorithms, the A* algorithm, to find the optimum route to the photo points [1]. In another study in Indonesia, the A star algorithm has been used to find the shortest path distance between the Ministry of Pharmacy Polytechnic and Medan Health Polytechnic [2]. A* Algorithm has been used in a game involving a guard and a thief to choose the shortest route that can be taken by the guard to catch the thief [3].
Grid-based searching divides the operation field into grids and the robot is moved from the grid where it is located to neighbour grids according to the searching algorithm (such as A*, Dijkstra, etc.) in order to create a route from point S to point F [4]. Interval-based searching algorithms originated from a similar approach of grid-based searching algorithms but the interval searching algorithm is operated with configuration space which uses each coordinate as a degree of freedom of the object instead of grids [5]. Sample-based algorithms use sample configurations in the configuration space. A*, D* and etc. algorithms keep in a list remarkable points to find the shortest route from S to F. A* Algorithm is an admissible heuristic shortest route finding algorithm which uses the function f(n) = g(n) + h(n) to calculate the distance. g(n) is the cost of coming from starting point S to current point R, h(n) is also estimated cost to reach final point F from current point R and as will be noted, the reason why f(n) is heuristic is that it has a heuristic function h(n) which is based on the prediction of the cost from R to F [6]. D* is also Dynamic A* Algorithm which is one of the improved version of it. In this algorithm, the cost parameters change during the operation of the problem as the name of algorithm implies with Dynamic A* [8]. More A* based algorithms are developed and used for different applications with the improvements in the A* Algorithm to obtain good enough route planning for mobile navigation of autonomous robots [9].
On the other hand, various intelligent optimization methods as Fuzzy controller, Genetic Algorithm, Ant Colony Algorithm, Taboo Search Algorithm, Bee Colony Algorithm and etc. are used to ensure optimum route for different robots [7], [10]. Liu et al. [11] proposed a bat algorithm (IDBA) developed to solve the multipoint shortest path planning problem. Masehian et al. [12] also proposed robot route planning with Particle Swarm Electrical, Control and Communication Engineering ________________________________________________________________________________________2021, vol. 17, no. 1 60 Optimization based algorithm for the shortest and smooth route. Elkhateeb et al. [13], with the Bee Colony Algorithm, provided the control of 2 free-degree robotic arm manipulators.

II. LITERATURE REVIEW
In the shortest route planning approaches, the studies for finding the shortest route with less computationally intensive algorithms have gained speed by using basic methods or hierarchical structures, including approximations of simple methods. Uras et al. [14] developed a method to create Subgoal Graps (SGs) by using neighbour grids. Subgoals are defined as the corners of obstacles which supply the shortest route in the field without obstacles by using the route from current point R to the other corner point closer to final point F. Uras et al. [15] proposed a subgoal graph algorithm for different levels to generate optimal route planning in grid based areas. They tried to achieve generalization of partitioning process in order to abbreviate the graph. Nussbaum et al. [16] suggested a new algorithm for Moving Target Search with SGs to find a solution to dynamic robotics applications. This algorithm is established for segregation of the field and SGs are implemented to increase the speed of searches. Xu et al. [17] investigated finding the way by using the subgoal graph algorithm to reduce a large area to a certain extent in large area scans.
Zuo et al. [18] proposed a two-level structured hierarchical algorithm based on basic A* and least-squares policy iteration to create a smooth route with robot kinematics. The simulation results are also obtained for the moving obstacles. In the next work, they will ensure these performances in real robotic application. Peng et al. [19] developed a new solution to store data in OPEN and CLOSED tables (OPEN_TABLE, CLOSED_TABLE) in order to shorten the operation time of A* algorithm. The operation efficiency was tried to be improved by using a new storing approach and more than 40 % gain was obtained in this study. Duchon et al. [20] suggested some modifications of A* algorithm to provide route optimality and less operation time. There are some assessments related to modified A* algorithms for various scenarios of optimal route planning.

III. MOTIVATION
In this study, some significant notions are represented as below.
• A new method is proposed in order to obtain optimal route considering SUB_GOALs by using basic A* algorithm and SGs in a hybrid approach. • The operation area is divided into subregions with decision-making process to prevent unnecessary searching. • SUB_GOALs determined with pre-searching from basic A* at break points and SGs at corners of obstacles are added to SUB_TABLE to speed up the final searching in the hybrid approach. • In the divided subregions by blocking unnecessary searching with decision-making process and by using lineof-sight (LOS), all feasible SUB_GOALs from SUB_TABLE in the same subregion are connected to find solutions of routes. • Solutions are evaluated and combined with the decisionmaking process to find the final optimal route. The paper is organised as follows: In Section 1, the content of the subject is introduced. The literature review about related works is presented in Section 2. Motivation of the study is specified in Section 3. All algorithms used in this study are given in Section 4. The proposed method is represented in Section 5. Results for different scenarios are illustrated in Section 6 and finally conclusion is presented in Section 7.

IV. OBJECTS
In this study, a hybrid algorithm is developed with basic approaches of two basic algorithms called A* algorithm and SGs. A guidance for the final search is created by using determined SUB_GOALs from basic algorithms. Thus, the shortest route is guaranteed with final search. The map is also divided into subregions to make searching as a very simple procedure. Algorithms used in the hybrid method are introduced as below.

Algorithm_1
A* algorithm is the most preferred option for route finding in various applications, since it can be used in a wide range of contexts with its flexibility [21]. In the basic terminology of A* algorithm, the function f(n) is used for calculating distance as mentioned before and n defines each point of the operation area divided into grids. The first term of f(n) is given in Eq. (1): and the heuristic function is presented in Eq. (2) according to Manhattan function [18]: Here, descriptions of the terms in Eqs. (1) and (2) can be given with Eq. (3): Here k χ is the horizontal distance and yk is the vertical distance.
Pseudocode of basic A* algorithm process indicated by Algorithm_1 is represented in Table I. SUB_GOALs obtained from basic A* algorithm are determined as break points and saved in SUB_TABLE to generate final searching.

V. THE PROPOSED HYBRID METHOD
Hybrid method is combined from two searching layers by using basic A* and SGs algorithms. In order to determine the final route as mentioned in Fig. 1, SUB_GOALs are assigned to create SUB_TABLE at the pre-searching layer.
A* algorithm is utilised to obtain break points to be used in SUB_GOAL mission and it also shows the orientation from starting SUB_GOAL to final SUB_GOAL of each divided subregion.
Let us find the other new joint SUB_GOAL which has the same (i∨j) with joint SUB_GOAL. Then let us choose joint SUB_GOAL=new joint SUB_GOAL. Let us find the number of (joint SUB_GOAL) →t which is also the number of divided subregion. In the light of these descriptions, the Map_1 divided into sub-regions for the first scenario is given in Fig. 2.
If one uses all SUB_GOAL combination to find the shortest path, it may take long time. In this approach, LOS defined with the pseudocode given in Table III is used to see direct h-reachable SUB_GOALs from one to other as shown in Fig. 3 for the first region of the map with the first scenario .    Let us find joint SUB_GOAL (1) for the first region which has the location of (x = 15 ∧ y = 2). S(sub region(1))=location of (x = 25 ∧ y = 17) and direction of slope→{−x, −y}. Thus, the decision-making process finds the location of (x = 23 ∧ y = 11) into all points visible from S as the suitable visible point illustrated in Fig. 3a and this suitable SUB_GOAL is saved to generate the final route.

Remark:
If all visible SUB_GOALs have the same (i∨j) then it is necessary to choose the one that has 〖(min(j)∨min(i)〗in the orientation of the first region, which has the direction of slope as {−x, −y}, which means {i→i_min∧j→j_min}. Visible SUB_GOALs from S seen in Fig. 3a Here, visible SUB_GOAL (4)   In Fig. 6 In the proposed method, simple SGs is implied for presearching in order to procure SUB_GOALs in an easy way. Nevertheless, N-level SGs is applied to show effectiveness of the proposed method in a fair manner. Each map is divided into the number of t sub-region by using the decision-making process, which benefits from Eq. (6).
There are 4, 7 and 9 subregions from S to F for three maps given in Figs. 4-6, respectively. Definitions about the first scenario have been specified with Eqs. (6) and (7) in the previous section. In the second and third scenarios (Figs. 5 and 6, the direction of subregions can be defined by using Eqs. (8) and (9) Lengths of routes for three scenarios of maps with different dimensions are obtained as presented in Table IV. There are three methods: simple A* algorithm, SGs and the proposed hybrid method as shown in Figs. 4-6.  After the decision-making process, the obtained parts of routes for each subregion are combined to carry out final routes for each map. Lengths are obtained for final routes by using g(n) function as mentioned in Eq. (1). The shortest lengths of routes are obtained by using the proposed hybrid method as 46.67 for Map_1, 57.76 for Map_2 and 124.7 for Map_3 and, therefore, the proposed method may be preferred for an operation route that is long and complicated such as video games.

VII. CONCLUDING REMARKS
In this study, a hierarchical structure, including hybrid approximations of simple methods: A* algorithm and SGs, has been proposed by using SUB_GOALs. Two layers have been included to organise pre-searching and final searching. The presearching layer consists of determining SUB_GOALs in order to save and apply at the final searching layer. Each map is divided into subregions by using the approach mentioned in Definition 1. The orientation of the route in each subregion is determined benefitting from the joint SUB_GOAL which is also needed to obtain division of subregions. Locations of visible SUB_GOALs obtained with LOS approach are effectual to discover joint SUB_GOALs. After, finding visible SUB_GOALs in the light of Definition 3, parts of the final route can be determined by combining visible SUB_GOALs which guarantee the shortest route. Three maps with different dimensions and scenarios are applied to show effectiveness of the proposed hybrid method. The shortest routes for three maps are obtained with the proposed method as compared with Electrical, Control and Communication Engineering ________________________________________________________________________________________2021, vol. 17, no. 1 66 A* algorithm and SGs. The future work is to improve the hybrid method by adding curves when a part of route is near to any obstacle to ensure the route planning for dynamic mobile robots.