Journal of Electrical and Computer Engineering

Volume 2016, Article ID 3620895, 10 pages

http://dx.doi.org/10.1155/2016/3620895

## Disordered and Multiple Destinations Path Planning Methods for Mobile Robot in Dynamic Environment

^{1}School of Computer Science and Engineering, Big Data Computing Key Laboratory of Hebei Province, Hebei University of Technology, No. 5340 Xiping Road, Shuangkou, Beichen District, Tianjin 300401, China^{2}School of Computer Science and Engineering, Hebei University of Technology, No. 5340 Xiping Road, Shuangkou, Beichen District, Tianjin 300401, China^{3}School of Information Engineering, Tianjin University of Commerce, Tianjin, China

Received 30 November 2015; Accepted 10 May 2016

Academic Editor: Sook Yoon

Copyright © 2016 Yong-feng Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In the smart home environment, aiming at the disordered and multiple destinations path planning, the sequencing rule is proposed to determine the order of destinations. Within each branching process, the initial feasible path set is generated according to the law of attractive destination. A sinusoidal adaptive genetic algorithm is adopted. It can calculate the crossover probability and mutation probability adaptively changing with environment at any time. According to the cultural-genetic algorithm, it introduces the concept of reducing turns by parallelogram and reducing length by triangle in the belief space, which can improve the quality of population. And the fallback strategy can help to jump out of the “U” trap effectively. The algorithm analyses the virtual collision in dynamic environment with obstacles. According to the different collision types, different strategies are executed to avoid obstacles. The experimental results show that cultural-genetic algorithm can overcome the problems of premature and convergence of original algorithm effectively. It can avoid getting into the local optimum. And it is more effective for mobile robot path planning. Even in complex environment with static and dynamic obstacles, it can avoid collision safely and plan an optimal path rapidly at the same time.

#### 1. Introduction

The development of science and technology makes smart home concept realizable, where mobile robots play a very important role. There is a heavy need in daily life for a robot to work continuously in an environment which contains disordered and multiple destinations. Path planning for a mobile robot working in such an environment is a challenging task and has attracted more and more attention of scholars worldwide. This paper presents disordered and multiple destinations path planning methods for mobile robot in an environment with dynamic obstacles. Path planning problem can be understood as an optimization problem with constraints. It refers to how a robot searches one optimal or approximates optimal route with specific performance (such as the shortest distance, less time, or the minimum energy consumption) from starting point to target point in the environment with obstacles.

There are many studies in the literature about path planning. Depending on the methods and principles used in the path planning, the robot path planning methods are divided into two types: traditional path planning methods and intelligent path planning methods. Traditional path planning methods include visibility graph method, grid decoupling method, graph searching method, and artificial potential method [1]. Intelligent path planning methods include fuzzy logic [2], ant colony algorithm [3], neural networks [4], and genetic algorithm [5]. In order to solve the shortcomings of these algorithms, scholars have conducted a lot of researches. In some particular work environments, the ants will fall into traps. Yu and Shiyong [6] proposed the ant rollback strategy to solve this problem, which could reduce the operating efficiency of the algorithm. By analysing the shortcomings of the artificial potential field method, Tang et al. [7] proposed an obstacle avoidance method based on gravity chain. For solving the “dead cycle” problem in U-shaped obstacles, a systemic neural-fuzzy control algorithm was proposed by Bao et al. [8]. An Obstacle Avoidance Algorithm (OAA) and Distinguish Algorithm (DA) were proposed to generate the initial population by Yun et al. [9] in order to improve the efficiency by selecting only the feasible paths during the evolution of genetic algorithm. But it inhibits the diversity of the population. To overcome the premature convergence in the traditional genetic algorithm, Hu and Feng [10] proposed a new way to generate the genetic operator, by means of modifying insert a space before (SAGA). In order to avoid infeasible path and improve the convergence speed, Tuncer and Yildirim [11] proposed a new mutation operation, which selected the mutated node with the best fitness value after being replaced with the original node (BMFGA). In dynamic uncertain environments, Wei et al. [12] proposed the incremental replanning which reused the information of previous. At the same time, it could also reduce the possibility of finding the optimal path. Zhu [13] used the virtual ants to predict the potential collision with the moving obstacles. The local motions planning for avoiding collisions were scheduled under the ACO, which can plan optimal path rapidly in cluttered environment. These algorithms solve only the problem with certain aspects, but they are not very comprehensive consideration. Some algorithms do not consider the operating efficiency, or the probability of finding the optimal path is too low, or the ability of real-time processing is poor. This paper presents a simple and effective dynamic obstacle avoidance strategy.

#### 2. The Mobile Robot Path Planning Based on the Evolutionary Genetic Algorithm

##### 2.1. Encoding Scheme

In this paper, we set the sequence number for each grid. The basic sequence is from left to right, top to bottom. The upper border is -axis, and the left border is -axis. We use grid method to model the working environment as the paper [14]. Minkowski and the principle of expanding obstacles [15] are adopted to divide the work space into a number of grids. In the grid domain, a black grid denotes an obstacle and a white grid denotes free space. Robot path is indicated by the index numbers, which can save memory and express more succinctly compared with the method of coordinate. What is more important is that the genetic operations (such as the selection operator, crossover operator, and mutation operator) are simpler.

##### 2.2. Sequencing

There are disordered destinations in the task of robot in practical work. For example, the robot goes to the kitchen to get a cup and pour water, goes to the living room to take drug, and finally goes to the bedroom. In the workflow, the sequence of robot taking drug and taking the cup is arbitrary. But the sequence of taking cup and pouring is determined. Therefore, the robot must determine the order of each destination according to the work environment firstly. We propose the sequencing rule to determine the order of each destination. The sequencing rule can be denoted by

is the fitness value of the disordered destination . is the number of barrier grids in the rectangle which diagonal is the line segment from the former destination (or starting point) to the destination . is the length from the destination to the former destination (or starting point). is the length from the destination to the next destination (or goal point). , , and are the weight coefficients, and . In considering the population diversity and the efficiency of finding the optimal path, through repeated testing, the best combination of weight coefficients is obtained (, , and ). If the value of is smaller, has the higher priority. Robot determines the destination sequence based on this standard. Within each branching process, execute genetic operation, find the optimal path, and then get the optimal path in the static environment.

##### 2.3. Initialization of Population

A good initial population in the feasible region is very effective to enhance the speed of evolution. We present the law of attractive destination. According to the relative position of the starting point and destination in each branching process, we adopt different strategy to generate the set of feasible paths. We categorize the relative positions of the starting point and its associated destination into four types as shown in Figure 1. Figure 1(a) represents that the destination is in the first quadrant of the starting point. Figure 1(b) represents that the destination is in the second quadrant of the starting point. Figure 1(c) represents that the destination is in the third quadrant of the starting point. Figure 1(d) represents that the destination is in the fourth quadrant of the starting point. represents the robot and represents the direction of destination. When the robot chooses the next grid to move, we give priority to the grid marked with “1,” which is closer to the destination in the region whose diagonal is a line segment from the starting point to the destination. If the grids marked with “1” are not in the feasible region of robot, we consider the grids marked with “2.” If the grids marked with “2” are also not in the feasible region of robot, we consider the grids marked with “3.” At the same time, the fallback phenomenon appears. We will set the current grid as the barrier grid to enhance the speed of population initialization and avoid the circuitous path effectively. When the starting point and destination are in the same horizontal or vertical line, we use the method in Figure 1(a). Looking for the next grid, the same horizontal (or vertical) coordinate is expanded 3 units from the left and right, respectively, and forms the search rectangle.