1. Algorithm Research of Path Planning for Robot Based on Improved Artificial Potential Field(IAPF)
Fenggang Liu

2. 1. Traditional APF
2. IAPF Method
3. Modify Repulsion Direction
4. IAPF Simulation
5. Conclusion & Future Work
6. References

3. 1. Traditional APF

4. APF is proposed by Khatib [1] in 1986, we simply introduce it in this paper.
Suppose the goal imposes an attractive force on the robot, and th-e obstacle impose a repulsion force Combine two forces and form a virtual force which navigates the robot to the goal.

5. These two forces definitions are
(1) if
(2)
In the definition, k , are constants predefine, X is the position of the robot, is the position of goal, is the distance between the r-obot and the obstacle, and is the safe distance, affected by the vel-ocity and decelerate ability of the robot.

6. 2. IAPF Method

7. In paper [2] the author improved the potential field function , new potential field function consider the distant of between robot and ta-rget, to ensure the target is the global minima point in whole potent-ial field.

8. Improved repulsion field function:if
(3)
In the formula(3), is constants predefine, X is the position of the robot, is the position of goal, is the distance between the rob-ot and the obstacle, and is the safe distance, n is an arbitrary re-al number greater than zero.

9. Compare with the traditional APF , put in the relative distance of between robot and target , to ensure the target is the global mi-nima point in whole potential field.
Negative gradient of improved repulsion field function:
(4) if

10. There:
(5)
(6)
(8)
(7)

11. Figure 1: The robot moves in the a field with new forces
and are two component forces of , The direction of from the obstacles away from robot nearest point to the robot , and the direction of from the robot to the target point.

12. When n choose different value , the mathematical properties of the potential field function as follows:
1. If 0< n <1 :
(5)
(6)
With the robot toward the target , tends to zero, tends to infinity ,the robot in the joint action of and can reach the target point.

13. 2. If n =1 :
(7)
(8)
With the robot toward the target , tends to zero, tends to constant ,the robot in the joint action of
and forward to the target point.

14. 3. If n >1 :
(7)
(8)
With the robot toward the target , and tends to zero , the robot in forward to the target point.

15. 3. Modify Repulsion Direction

16. In paper [2] , the repulsive function is composed of two parts , in s-ome cases the angle between and greater than 90 degrees, which may produce local minima points . So , this method for solvi-ng the problem of local minima 2 and 3 basically no effect.
I still let repulsive function is composed of two parts , but one’s dir-ection is tangency with the control area of the obstacle and the ang-le between gravitation and repulsion is not more than 90 degrees while the other’s direction is consistent with the gravitation.

17. But there are two exceptions:
When the robot, obstacle, the target point along the same line , and robot is located between the obstacle and the target point, define and in the same direction that all point to the target point . As shown in Figure 5 .
When the robot, obstacle, the target point along the same line , and target point is located between the robot and obstacle, defi-ne and in the same direction that all point to the targ-et point . As shown in Figure

18. Figure 2: The forces when the obstacle center in the first quadrant

19. Figure 3: The forces when the obstacle center above the Y-axis

20. Figure 4: The forces when the obstacle center in the second quadrant

21. Figure 5: The forces when the obstacle center on the negative X-axis
robot between the obstacle and the target point

22. Figure 6: The forces when the obstacle center in the third quadrant

23. Figure 7: The forces when the obstacle center on the negative Y-axis

24. Figure 8: The forces when the obstacle center in the fourth quadrant

25. Figure 9: The forces when the obstacle center on the X-axis

26. Figure 10: The forces when the obstacle center on the X-axis
target point is located between the robot and obstacle

27. By redefining the repulsive direction, the angle between gravitation and repulsion is not more than 90 degrees .In this way, the resultant force of the robot couldn’t be zero before it reaches the goal . This method can overcome the local minimum problem for the resultant force of the robot being zero before it reaches the goal . So this met-hod can solve all minimum problems.

28. 5. IAPF Simulation

29. Figure 11: problem 1 of local minima simulation result

30. Figure 12: problem 2 of local minima simulation result

31. Figure 13: problem 3 of local minima simulation result

32. Figure 14: Many obstacles in two-dimensional environment 1 simulation result

33. Figure 15: Many obstacles in two-dimensional environment 2 simulation result

34. Figure 16: Many obstacles in two-dimensional environment 3 simulation result

35. 6. Conclusion & Future Work

36. In this way, the resultant force of the robot couldn’t be zero before it reaches the goal. This method can overcome the local minimum problem for the resultant force of the robot being zero before it rea-ches the goal. The IAPF method is convenient and high efficiency in path planning.
My future work is that use the IAPF in collision-avoidance planning for multiple mobile robots.

37. THANKS ALL