_{1}

^{*}

Aiming at the disadvantages of the basic ant colony algorithm, this paper proposes an improved ant colony algorithm for robot global path planning. First, adjust the pheromone evaporation rate dynamically to enhance the global search ability and convergence speed, and then modify the heuristic function to improve the state transition probabilities in order to find the optimal solution as quickly as possible; and finally change the pheromone update strategy to avoid premature by strengthening pheromone on the optimal path and limiting pheromone level. Simulation results verify the effectiveness of the improved algorithm.

The path planning is an important ability in many applications, such as UAV (Unmanned Aerial Vehicle), robotics, unmanned car and so on. Its task is to find a path from the current point (or the start point) to the target point, which is a shortest or a minimum price path without barrier in the environment which has obstacles.

The path planning is further divided into two categories [

In recent years, many researchers have studied the global path planning on various intelligent methods, such as genetic algorithms [

M. Dorigo, Italian scholar, who was inspired from ant foraging behavior and first proposed the ant colony algorithm in 1991 [

The paper is organized as follows: Section 2 and 3 describes the method of grid modeling and the basic ant colony algorithm; Section 4 describes the improved ant colony algorithm for the robot; Section 5 presents the experimental results on robot global path planning based on ant colony algorithms. Section 6 presents brief concluding remarks.

Grid method was proposed by the W. E. Howden in 1968, and its mainly task is to build a path grid map depending on the environment. The basic principle is to divide robot working environment into numerous tiny grid units, and the specifications of each grid is determined by the robot steps, namely one step is one grid unit. The grid is divided into two kinds: free gird and obstacle grid. Free grid is represented by white grid, and obstacle grid is represented by black grid. The grid map can be represented by a binary matrix, which 1 represents obstacle and 0 is free grid. The obstacle can occupy a grid or multiple grids, if it less than one grid is also expressed by one grid. Robot can only move in the free grid and must avoid when it encounter obstacles grid.

Depending on the position of grid, the grid can be divided into intermediate grid and boundary grid. For intermediate grid, robot may have eight directions for the next motion. Such as up, down, left, right, right-up, right-down, left-up and left-down.

The paper uses two-dimensional grid represents robot environment, and encodes the grid from left to right, from top to bottom.

In

where,

Ant colony algorithm (ACO) is an intelligent heuristic search algorithm by simulating the ant behavior to find the optimal path between the food source and their nest. Ants release pheromone on the path which they passed. Through these pheromones, ants can communicate with each other and find the shortest path to food finally. When the ant reaches an intersection at first time, it will randomly choose a motion direction forward. The more ants follow a given path, the more pheromone will be left on the path, and also the more attractive this path becomes to be followed by other ants. The probability of other ants selecting the path is increased. Ants can also adapt to environmental changes, when there is an obstacle on the path, they will find a new path quickly. This process can be expressed as a loop of positive feedback.

The probability of the ant k moving from the grid i to j is defined as follows [

where,

grid i and j; _{k} denotes a set of grids the ant k selecting in next step.

The process of robot path planning based on ant colony algorithm can be divided into two stages: optimization stage and stagnation stage. In optimization stage, the algorithm should have stronger ability of global search and can rapidly converge; and during stagnation stage, the algorithm should can automatically jump out of local optimal solution and continue to search the global optimal solution. To avoid premature to fall into local optimal solution and blind searching, the algorithm requires randomness of search and accuracy of solution. But randomness and accuracy are usually both contradictory and interrelation. In order to overcome defects of ACO, this paper presents an improved ant colony algorithm (IACO).

For the basic ant colony algorithm, the searching time is too long. One of the reasons is that the direction of the initial moment when the ants begin to search is uncertain. To improve the problem, and speed up the search, we initialize pheromone decreasing with distance so that the ant has a clear motion direction during the initial search, the method is as follows:

where,

In ACO, pheromone evaporation rate

where, k represents the current number of cycle;

In ACO, the heuristic function is:

where,

In grids map, when the target position is known, a ant can calculate distances from its surrounding eight grids to the target point. The smaller the distance, the larger the value of

where,

Scholars have proposed several different pheromone update models, there are three mainly models: Ant-Cycle model, Ant-Quantity model and Ant-Density model. The paper chooses Ant-Cycle model, which can be expressed as follows:

where Q is a constant of pheromone,

All ants move one step called once iteration, after n iterations, all ants finish a cycle. In a cycle, there is a current optimal solution

When the pheromone quantity is too high, the algorithm is prone to premature, and it will reduce the optimization capability. The paper introduces Max-Min ant method to pheromone update strategy, which can be described as follows:

In Formula (12), the pheromone quantity is limited between

Step 1: Initialization parameter: setting the start and target point, the maximum number of cycles

Step 2: Put all ants on the start point, and each ant determines which path it will select according to the transition probability equation;

Step 3: Save the path and the path length of each ant in each cycle;

Step 4: When one cycle finish, update pheromone quantity according to pheromone strategies;

Step 5: Loop execution Step 2 to 4 until the optimal solution is got or reach the maximum number of cycles.

In order to verify the effectiveness of the improved ant colony algorithm, the paper simulates on Matlab 7.1 platform. The main parameters as follows: ρ = 0.7; α = 1; β = 5; Q = 1000.

To compare with the basic ant colony algorithm (ACO), we design the five different grid maps as Figures 3-7, which are the results of the simulation.

In the different five maps, each map simulates 20 times independently.

Type of map | The average number of cycles | The average length of the optimal path | ||
---|---|---|---|---|

ACO | IACO | ACO | IACO | |

31 | 21 | 15.7279 | 14.8995 | |

43 | 34 | 22.799 | 21.3848 | |

99 | 50 | 30.2668 | 29.1153 | |

153 | 95 | 37.0692 | 36.2885 | |

212 | 147 | 44.5269 | 43.1838 |

This paper proposes an improved ant colony algorithm and applies it to the robot path planning. In the improved algorithm, pheromone quantity is reinforced in some short paths of each cycle, and pheromone evaporation rate is adjusted dynamically and so the transition probability is improved. The simulation results show that these measures are effective and can enhance global optimization ability, searching speed, and can avoid premature.

JingangCao, (2016) Robot Global Path Planning Based on an Improved Ant Colony Algorithm. Journal of Computer and Communications,04,11-19. doi: 10.4236/jcc.2016.42002