1. Complete Coverage Path Planning Based on Ant Colony Algorithm International conference on Mechatronics and Machine Vision in Practice, p.p. 357-361, Dec. 2008.

2. Outline Abstract INTRODUCTION COMPLETE COVERAGE PATH PLANNING BASED ON ANT COLONY ALGORITHM EXAMPLES AND SIMULATION CONCLUSIONS

3. Abstract The complete coverage path planning algorithm after the order of all cells is gotten. This is similar to the integrating local sub- area coverage with global planning was traveling salesman problem (TSP). It is a population-based proposed. According to the characteristic of Boustrophedon heuristic simulation evolution algorithm in swarm intelligent cellular decomposition, the robot covers local sub-area through research area. Based on ant colony algorithm, the robot back and forth motion.

4. The distance between every sub-areas uses the distance matrix to get the optimization sequence of was redefined, which including connectivity, least distance and the sub-areas after decomposed the coverage environment number of obstacles between sub-areas. The new distance matrix of sub-areas in environment is built for global planning. Based on ant colony algorithm, the robot uses the distance matrix to get The basic mathematical model of Ant Colony Algorithm the optimization sequence of the sub-areas after decomposed the as follows: coverage environment. Experiments on a simulation of environment verify the validity of the proposed algorithm.

5. INTRODUCTION Based on boustrophedon cellular decomposition algorithm, a new CCPP algorithm, which included globe path planning and local path planning, was introduced. After the new distance matrix of each cell in environment is built for global planning, the robot can complete coverage the environment after the order of all cells is gotten. This is similar to the traveling salesman problem (TSP). It is a population-based heuristic simulation evolution algorithm in swarm intelligent research area. Based on ant colony algorithm, the robot uses the distance matrix to get the optimization sequence of the sub-areas after decomposed the coverage environment.

6. COMPLETE COVERAGE PATH PLANNING BASED ON ANT COLONY ALGORITHM Boustrophedon cellular decomposition algorithm scan from the left of the map to the right of the map by a virtual scan lines paralleled to the absolute coordinates of Y-axis, through the judgments of the change of connectivity to generate converge sub-area, As shown in Figure 1,the line scans from the left of Figure 1. The result is to generate sub-area I. When scan line go though obstacle 1, it will generate converge 2 and 3 because of the change of connectivity. After Boustrophedon cellular decomposition, the map is decomposed to a number of the reachable s and the obstacles.

7. The coverage of every sub-area can be achieved by robot moving back and forth. On the basis of coverage a single sub- area, determine the order of converge can achieve the objective of completely converge the environment.

9. Figure 2 is the structure map of figure 1 cellular decomposition, under the regular condition. It is unrealistic to implement the converge algorithm according to the connection of figure 2, especially Ant Colony Algorithm require put the visited sub-areas into the visited sites of inhibition table. This paper aims this situation, use the connectivity and distance of each sub-area and obstacle between each sub-area in the figure 1 to redefine the distance of each sub-area. Further add the existing connection of sub-areas; the result is to format a fully connected map. From the definition of Hamilton pathway, the figure 2 meets the sufficient condition of the Hamilton pathway.

10. We know there exists a path that cover all the areas once and only once in the complete coverage structure diagram.

12. From figure 2, we can get the matrix A as follows, if converge sub-area i and j are adjacent, the value of aij is 1, instead the value of aij is zero for the non-adjacent sub-areas.

16. For example, number of obstacles matrix N in the coverage sub-areas of the electronic map as follows:

17. Obstacles matrix N is gotten when 1 is added to the elements of non-diagonal in matrix N in order to reserve the elements in the diaggonal as zero

18. Distance matrix D show the real distance between coverage sub-areas, the variable dij is the distance value of the nearest vertices of two sub-areas i and j. The distance of adjacent sub- areas is a, the distance of non-adjacent sub-areas is determined by absolute coordinate. The matrix D below is the distance of figure 1.

20. A integrated distance matrix D' is concluded when multiplying the variable with the same position in obstacles matrix, distance matrix, connectivity matrix together and then multiply the variable that is non-simple connected by coefficient.

21. A integrated distance matrix D' of figure 1 is calculated as follows.

22. EXAMPLES AND SIMULATION Using ant colony algorithm to simulate the environment map of figure 3, there are some dimensionless factors, such as pheromone heuristic factor, expectation heuristic factor, pheromone volatilization factor, pheromone intensity factor Q, distance factor a, b and so on, which will affect route optimization.

24. An optimal solution is concluded by refining step length of every factor and exhausting combination of those factors. It is: Optimized coverage order is, Percentage of coverage area is more than 95%, coverage overlap rate is less than 10% after neglecting the influence of body size of robots.

27. CONCLUSIONS A distance matrix is defined according to the information between two sub-area connectivity. Ant colony algorithm is used to optimize the coverage order according to the distance matrix. Simulation result shows that this algorithm not only ensures to coverage all work space but also gets a shorter planning path,a smaller overlap rate of path and a higher efficiency of planning. The complete coverage process had been carried out by the robot we developed.

28. The algorithm we proposed is highly real time and has less information to be deal with. But sometimes, it is hard to avoid recovered area nearby the obstacle. However, it is a great improvement to the precious algorithms. Optimization of the modeling for complex environment is the next subject to be studied.