1. Department of Electrical Engineering, Southern Taiwan University Robotic Interaction Learning Lab 1 The optimization of the application of fuzzy ant colony algorithm in soccer robot Juing-Shian Chiou, Kuo-Yang Wang, and Ming-Yuan Shieh Department of Electrical Engineering, Southern Taiwan University, Tainan County, Taiwan, R.O.C.

2. Department of Electrical Engineering, Southern Taiwan University 2 Robotic Interaction Learning Lab Outline Abstract Introduction Using generalized predictive control to predict the goal position The application of fuzzy ant colony algorithm on optimized speed of robot Ant colony algorithm used in obstacle avoidance Experiments Conclusion

3. Department of Electrical Engineering, Southern Taiwan University 3 Robotic Interaction Learning Lab Abstract This article provides a theory which is based on the Fuzzy Ant Colony Optimization, and then uses this theory to design an optimal speed for the football robots, and then we also apply Ant Colony Optimization to design its routes to avoid obstacles. Afterward, we add Generalized Predictive Control to predict the position which its target might appear at the next sampling time.

4. Department of Electrical Engineering, Southern Taiwan University 4 Robotic Interaction Learning Lab I ntroduction Here we design a GPC to help the robot quickly predict the position of the target at the next sampling time, after which it extrapolates the time required to reach the target and the next sampling time target to decide the route. We use the fuzzy control machine to design the speed of both right and left wheels, and then we add Ant Colony algorithm to adjust its fuzzy rule, to reach optimized result. When make up its obstacle-avoiding routes under Ant Colony algorithm to finish the attribution of the efficiency and effectiveness of the strategy.

5. Department of Electrical Engineering, Southern Taiwan University 5 Robotic Interaction Learning Lab Simulation platform Fig.1 Five-versus-five simulation platform

6. Department of Electrical Engineering, Southern Taiwan University 6 Robotic Interaction Learning Lab System architecture Fig. 2 System architecture.

7. Department of Electrical Engineering, Southern Taiwan University 7 Robotic Interaction Learning Lab Using generalized predictive control to predict the goal position(1/5) We utilized the current position and sampling time of the target to predict the target position at the next sampling time. The following steps illustrate the procedure followed. (I) Although this system is nonlinear, extremely short sampling times were used to make the system linear. (II) At first, we gathered useful conditions from the system:

8. Department of Electrical Engineering, Southern Taiwan University 8 Robotic Interaction Learning Lab Useful conditions 1) The position of the robot 2) The former position of the target 3) The current position of the target (The former and current positions were determined on the basis of the sampling time, as shown in Fig.3.) Fig.3. sampling time.

9. Department of Electrical Engineering, Southern Taiwan University 9 Robotic Interaction Learning Lab Using generalized predictive control to predict the goal position(2/5) (III) We calculated the distances between the former and current positions of the target, and we determined the speed of the target by using the sampling time. The equation below shows the calculations involved.

10. Department of Electrical Engineering, Southern Taiwan University 10 Robotic Interaction Learning Lab Using generalized predictive control to predict the goal position(3/5) (IV) After calculating the velocity of the target, we designed a GPC by using, the direction of the target and the sampling time, which was then used to find the subsequent position of the target, as calculated by means of the equation below and illustrated in Figure 4.

11. Department of Electrical Engineering, Southern Taiwan University 11 Robotic Interaction Learning Lab Subsequent position of the target Fig.4. Subsequent position of the target.

12. Department of Electrical Engineering, Southern Taiwan University 12 Robotic Interaction Learning Lab Using generalized predictive control to predict the goal position(4/5) (V) We then calculated the time needed for the robot to reach the target at its central speed, based on the distance ( ) that it had to cover to reach its current position. The equation below shows the calculations involved ( is the speed of the left wheel of the Robot, is the speed of the right wheel).

13. Department of Electrical Engineering, Southern Taiwan University 13 Robotic Interaction Learning Lab Using generalized predictive control to predict the goal position(5/5) (VI) If is larger than, then the robot followed to the next position of the target; if is smaller than, the robot proceeded to the current position of the target. By repeating steps I to VI, the target could be reached in less time.

14. Department of Electrical Engineering, Southern Taiwan University 14 Robotic Interaction Learning Lab The application of fuzzy ant colony algorithm on optimized speed of robot The design of a fuzzy logic controller The state equation The ant colony algorithm

15. Department of Electrical Engineering, Southern Taiwan University 15 Robotic Interaction Learning Lab The design of a fuzzy logic controller We designed an FLC to generate the velocity of both wheels of the robot. Two input parameters of an FLC are the distance and the angle. Fig.5. Relationship between d and ψ.

16. Department of Electrical Engineering, Southern Taiwan University 16 Robotic Interaction Learning Lab Membership function Each input parameters can be divided into seven classes, as shown in Fig. 6 and Fig. 7. Fig. 6. The distance between the robot and the goal. Fig.7. The orientation of the robot with respect to the straight line path to the goal.

17. Department of Electrical Engineering, Southern Taiwan University 17 Robotic Interaction Learning Lab Fuzzy rule table

18. Department of Electrical Engineering, Southern Taiwan University 18 Robotic Interaction Learning Lab The state equation With the velocities generated by the FLC, we determined the maximum velocity of the robot. We defined the mathematical model of the equation of the robot’s movements as follows:

19. Department of Electrical Engineering, Southern Taiwan University 19 Robotic Interaction Learning Lab The state equation Having defined the state variables, We were able to determine the state equation: Consequently, we identified the optimal vector of the velocity of the left wheel as, and that of the right wheel as

20. Department of Electrical Engineering, Southern Taiwan University 20 Robotic Interaction Learning Lab The ant colony algorithm First, we will find four rules triggered by fuzzy control machine like Fig. 8 shows. Let’s suppose the triggered rules are A,B,C,D. Fig. 8 Let’s suppose the triggered rules are A,B,C,D.

21. Department of Electrical Engineering, Southern Taiwan University 21 Robotic Interaction Learning Lab The ant colony algorithm In short, domain is defined as the limit of the membership function, and then we can transfer this question as a route on a plain one. Fig. 9 the form of fuzzy rules transfered into the route one.

22. Department of Electrical Engineering, Southern Taiwan University 22 Robotic Interaction Learning Lab The ant colony algorithm We can let be the number of ants at time in city. However, in computation side, we will show as domain, and shows is the total number of ants. This gives the possibilities of choosing target and it means the possibilities for the ant to reach the next city under the affection of visibility and pheromone, and its possibilities to choose by follow equation.

23. Department of Electrical Engineering, Southern Taiwan University 23 Robotic Interaction Learning Lab The ant colony algorithm For ant, stands for the value of pheromone at time through route i to j. As shown in follow equations.

24. Department of Electrical Engineering, Southern Taiwan University 24 Robotic Interaction Learning Lab Ant colony algorithm used in obstacle avoidance We propose Ant Colony Algorithm that aims at planning obstacle avoidance path of moving object as Robot Soccer. As Fig. 10 shows: Fig. 10 obstacle avoidance path

25. Department of Electrical Engineering, Southern Taiwan University 25 Robotic Interaction Learning Lab Ant colony algorithm used in obstacle avoidance In order to improve searching speed of Ant Colony Algorithm and prevent Convergence Rate from becoming slow and optimizing partially, we take concentration which could be got by i into account to confirm path number e that ant could choose by follow equation:

26. Department of Electrical Engineering, Southern Taiwan University 26 Robotic Interaction Learning Lab Ant colony algorithm used in obstacle avoidance Robot Soccer will have to choose the best path. This part adopts Objective Function to describe the performance of path choice by follow equation. When Objective Function is confirmed, weight value of every path that soccer may pass is confirmed by follow equation.

27. Department of Electrical Engineering, Southern Taiwan University 27 Robotic Interaction Learning Lab Ant colony algorithm used in obstacle avoidance we simulate ant’s Pheromone in this way. When all the Robot Soccer find Feasible Solution of one planning path, but it may not the best solution because the Pheromone has been changed at this time, therefore it is necessary to make a overall amending, amending principle is follow equation.

28. Department of Electrical Engineering, Southern Taiwan University 28 Robotic Interaction Learning Lab Ant colony algorithm used in obstacle avoidance is the Pheromone variable quantity of path (i, j): Its formula just like Ant-Cycle type; as formula shows follow equation.

29. Department of Electrical Engineering, Southern Taiwan University 29 Robotic Interaction Learning Lab Ant colony algorithm used in obstacle avoidance Now we are going to explain the procedure of using Ant Colony algorithm. Step 1: Parameter Initialization. Step 2: Iterative process. And then calculate probability of path choice according to

30. Department of Electrical Engineering, Southern Taiwan University 30 Robotic Interaction Learning Lab Ant colony algorithm used in obstacle avoidance Step 3: Update Pheromone concentration of path according to follow equation. Step 4: Repeat Step2, Step3 until ant reach its target point. Step 5: Stop iterative search when one in m ants has already completed searching the path length and has exceeded the best path length of previous iteration. Step 6: Make N=N+1, place ant at starting point and target point again if N<NC, repeat STEP2; else output the best path and stop the Algorithm.

31. Department of Electrical Engineering, Southern Taiwan University 31 Robotic Interaction Learning Lab Experiments This part we have several points of simulation. The first part is the experiment for the robot to reach the top speed and predict the route of control. The second part is the simulation of the optimal route of the robot. The third part is the obstacle-avoiding route of the robot.

32. Department of Electrical Engineering, Southern Taiwan University 32 Robotic Interaction Learning Lab Simulations of the velocity and the GPC Fig. 11 Using Fuzzy Ant Colony algorithm to adjust the velocity of the soccer robot. Fig. 12 using GPC to predict the movement of the target and design the moving route for the robot.

33. Department of Electrical Engineering, Southern Taiwan University 33 Robotic Interaction Learning Lab Simulation of the robot’s path Fig. 13 using fuzzy ant colony algorithm control machine to chase the route of the target, and also apply MATLAB to simulate. Fig. 14 using control robot driven by fuzzy ant colony algorithm to look for the route of the target, and also using FIRA simulation.

34. Department of Electrical Engineering, Southern Taiwan University 34 Robotic Interaction Learning Lab Simulate obstacle avoidance path Fig. 15 simulate obstacle avoidance path of Robot Soccer by MATLAB Fig. 16 simulate obstacle avoidance path of Robot Soccer by using FIRA simulation.

35. Department of Electrical Engineering, Southern Taiwan University 35 Robotic Interaction Learning Lab Conclusion The result of the experiment above shows that the method we provided can apply on the wheel robot effectively, and the generalized predictive control machine we designed can clarify the position of the target appearing at the next sampling time. In the future, we will shorten the time for the fuzzy ant colony to weaken and also make the system to reach the optimal condition in a short time. By adding other different algorithms, we can find out the best combination of them.

36. Department of Electrical Engineering, Southern Taiwan University 36 Robotic Interaction Learning Lab Thanks for your attention!