AGV PATH PLANNING BASED ON SMOOTHING A* ALGORITHM

Transcription

1 International Journal of Software Engineering & Applications (IJSEA), Vol.6, No.5, Septeber 205 AGV PATH PLANNING BASED ON SMOOTHING A* ALGORITHM Xie Yang and Cheng Wushan College of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai 20620, China ABSTRACT The path consuption of the digital ap in the grid as the environent expression way is discrete, for Autoated Guided Vehicle(AGV) to achieve low consuption and sooth path planning target, the A* algorith is applied to the path planning based on grid, and the optial path is realized. A path soothing ethod is proposed and applied to the path of A*. The soothing ethod satisfies the AGV turning radius, akes the path sooth transition at the break point, and realizes the sooth path deviation. The siulation results are verified by using the grid ethod, and the path of the proposed ethod is soother, the path consues less and the path error is less than that of the A*. KEYWORDS Autoated Guided Vehicle (AGV), A* Algorith, Sooth Path. INTRODUCTION Path planning technology is one of the key technologies of AGV. Its task is to find a path fro the initial state (including position and attitude) to the target state (position and attitude) in the environent with obstacles. The A* algorith is based on the grid ap, and the grid ap is a way of environental expression which can be obtained by the discretization of the actual environent. In the cell interior, the path is the sae, and the path between the adjacent grid and the grid is not continuous [-2]. Because the path of each unit cell is discrete, each grid is used as a whole to participate in the path planning algorith, such as A* algorith, the final design of the path is coposed of a representative unit grid (or center) endpoint connection, the path direction changes the increent only is pi / 4, so the design path are usually not the actual environent optial, sooth path [3-4]. A* algorith can achieve the continuous path, but the path of the change is usually not continuous, which is due to the approxiate expression of the path. The design of the final path ust eet the dynaic characteristics of AGV itself, such as: the initial speed direction, turning radius and so on, the algorith needs to calculate the path of sooth [5]. According to the inforation around the obstacles, this paper presents a tangential soothing ethod based on A* algorith, to realize continuous change of the direction of the path. The proposed soothing ethod is applied to the path planning algorith, the path of the final path is optiized and the sooth transition of the path is satisfied. DOI : 0.52/ijsea

2 International Journal of Software Engineering & Applications (IJSEA), Vol.6, No.5, Septeber PRINCIPLE OF A* ALGORITHM The search space is described as a set of nodes and the edges are connected to each side, each side length is given to the path value, so that the path of the search can be represented by the nodes in the space. A* searches for the shortest path by selecting the node sequence of the path between the start node and the destination node. The AGV path search area is required to be grid, and the AGV runtie environent ap is partitioned into a set of size unifor squares, each of which represents a certain position in the environent (as shown in Figure ). The core part of the A* algorith is the evaluation function: * * * f n = g n + h n ( ) ( ) ( ) (-) In the forula: n represents the current node to search; f * ( n ) is the evaluation function, which eans that the cost of the optial path fro the initial position to the target position after the node n is reached; g * ( n ) represents the actual value of the iniu path fro the initial position to the node n, if n is the starting point, then the g * ( n ) = 0 ; the optial path to "estiate" fro the node n to the target location. h * ( n ) is the cost value of n Figure. A* algorith developent node orientation ap An evaluation function of h * ( n) is the type (-2), the current node n coordinates ( x, y ), and the target node coordinates are ( x2, y 2) : Then the evaluation function is: * h ( n) = [( x x2) + ( y y2) ] (-2) f ( n) = g ( n) + [( x x ) + ( y y ) ] * * The A* algorith is extended fro the 8 directions of the starting node, and the direction is shown in Figure. We select the node as the h * ( n ) value of the second nodes in the 8 nodes, and then expand the sequence of second nodes. This way, the path can be siply iterated until the destination node is searched. The A* algorith is set up to two lists: one is open list (OPEN), the other is closed down list (CLOSED). When the node is expanded, the existing obstacles and the existing node direction will not be extended, and stored in the closed list. 2

3 International Journal of Software Engineering & Applications (IJSEA), Vol.6, No.5, Septeber AGV MOTION MODEL Single steering wheel is a coon AGV wheel structure types, including a ain navigation wheel, two driven wheel, and a plurality of universal auxiliary supporting wheel, its structure is shown in figure 2. This structure of the AGV turning radius is sall, and the oveent is flexible. Aong the, the ain navigation wheel is both the driving wheel and the steering wheel, which is driven by different servo otors. A driven wheel is fixed on the lower part of the support body after landing fork, do not rotate about the direction can be realized. According to the kineatic odel of AGV and the return data of the encoder, it can be used to solve the position and attitude of AGV, and then realize the real-tie positioning of AGV. ϕ θ Figure 2. The kineatics odel of single wheel AGV Considering the iniu turning radius as AGV kineatic constraints in the running process, figure 2 is a siplified odel of the single wheel AGV [6]. Assue that AGV's posture is ( x, y, θ ), the x, y is the position coordinates of the AGV, θ is the direction angle of the AGV, ϕ is the central axle and the front wheel of the AGV driving direction angle, known as a steering angle. AGV wheel steering echanis has the echanical characteristics of the constraint: ϕ ϕ ax (-3) There is an upper bound of the path curvature ρ of the path of AGV: ρ = R L cotϕ in ax (-4) In the forula, L is the front and rear wheel axis distance, as shown in Figure 2, the iniu turning radius is: 3

4 International Journal of Software Engineering & Applications (IJSEA), Vol.6, No.5, Septeber 205 R = L cotϕ in ax (-5) Therefore, when the AGV turn, we take the iniu turning radius as its kineatic constraint. We will use it as a path to sooth processing. 4. SMOOTH PATH PLANNING METHOD 4.. Inscribed circle soothing ethod The inscribed circle soothing ethod is independent ofθ, the inscribed circle to achieve the sooth transition of the path, with the radius of the arc is R in we replace the original line in the corner, the arc tangent to two lines, as shown in Figure 3, and then the broken line S Q QS2 will be replaced by S. Q θ Max _ error S R o i Figure 3. Inscribed circle soothing ethod The path is soothed: iss2 = i R + SO S2 (-6) The axiu error deviation fro the original route is calculated as follows: R Max _ error = - R = R( -) θ θ sin( ) sin( ) 2 2 (-7) In the selection of the path soothing ethod, we first deterine whether it can eet the requireents of security, here to deterine the axiu deviation of the path of the path of the unit path. When the path of the bias point is far greater than the discount of the unit path, that is, the deviation can be regarded as an obstacle, and then the soothing ethod cannot be applied to the sooth [7-9]. For the inscribed circle sooth ethod, when the angle θ between the connected paths is saller, and turning radius R is larger, soothed path of axiu deviation Max _ error is bigger, so we take the iniu turning radius of AGV is R in, the sooth two section path angle isθ. 4

5 International Journal of Software Engineering & Applications (IJSEA), Vol.6, No.5, Septeber Special Case If the corner is sufficient for two sooth arc tangent to the path, as shown in Figure 4 (a), we draw Inscribed circle with i and i+ and respectively, tangent point is S and S 2 S3 and S 4 respectively, and the new path is i + SS2 + + S3S4 + i + 2. If the corner is not enough for the two sooth arc tangent to the path, as shown in Figure 4 (b), we draw Inscribed circle with i and, tangent point is S and, and the new path is i + S S2 +. i S o o2 R in Rin S 2 S3 (a) S 4 i R in o S S2 (b) Figure 4. Special case 4.3. Special Case 2 If the corner is sufficient for two sooth arc tangent to the path, as shown figure in Figure 5 (a), we draw Inscribed circle with i and i+ and respectively, tangent point is S and S 3 ands 4 respectively, and the new path is i + SS2 + + S3S4 + i + 2. If the corner is not enough for the two sooth arc tangent to the path, as shown in Figure 5 (b), we draw Inscribed circle with i and i+ and respectively, tangent point is S and S 2 S3 and S 4 respectively, and we draw Inscribed circle with i and S S and, the final processing ethod is shown in Figure 5 (a). 5

6 International Journal of Software Engineering & Applications (IJSEA), Vol.6, No.5, Septeber 205 o 2 R in S 4 S 3 S R in o i (a) o 2 R in S 4 S 3 S R in o i (b) Figure 5. Special case 2 5. SIMULATIONS We take L = ( 2 + ), ϕax = 45 o, and then R in = L cot ϕ ax = ( 2 + ). Using the iniu turning radius circle to replace the key points of the broken line, cobined with the analysis of the path of the above, the path is shown in Figure 6.In the graph, the black path is the path before the sooth, and the red path is the path of the process. It can be seen that the path of the process is uch soother than the previous path. 6

7 International Journal of Software Engineering & Applications (IJSEA), Vol.6, No.5, Septeber 205 Figure 6. Siulation results For the evaluation of the path can be used in the path of the consuption of the path as an evaluation index, the path is less consuption of the path is ore excellent. Table. Coparison of siulation results Path consuption () A* Algorith 29.6 Soothing A* algorith 27.8 Maxiu deviation () 0.2 7

8 International Journal of Software Engineering & Applications (IJSEA), Vol.6, No.5, Septeber CONCLUSIONS When the A* algorith searches path, each step is to the adjacent eight grid search, and then into the next grid. If the siple lattice to the grid is acceptable, but if it is a real experient in particular the obile robot which needs to sooth, which is unacceptable. Taking into account the new path in the presence of soe abrupt turning point and local area have jitter, cobined with the AGV otion constraints, w extract the key points in the path, and follow the path to the sooth processing. The path soothing ethod proposed in this paper can be very good to eet the dynaic characteristics of AGV, especially to eet the AGV turning radius. In addition, the local path deviation is iniized by the judgent of the inforation of the obstacle, and the total deviation of the path is achieved. REFERENCES [] Liu Wei,Zheng Zheng,Cai Kaiyuan,(202)Sooth path planning for unanned aerial vehicles in unknown coplex environents[j],control Theory & Applications,Vol.29,No.,pp [2] Zhang Jinxue,Li Yuanyuan,Zhang Ming, (202)Path panning ethod for car -like obile robot[j],coputer Siulation,No.0,pp [3] Stentz A,(995)The focussed D* algorith for real-tie replanning[c], Proceedings International Joint Conference on Artificial Intelligence, Montreal, Canada: IJCAI, pp [4] Wang Dianjun,(202)Indoor obile-robot path panning based on an iproved A* algorith[j],journal of Tsinghua University(Science and Technology),Vol.52,No.8,pp [5] Wu Chaoshuai,(202)The iproved A * algorith and its application in ASR obile robot for path planning[d],college of Inforation Engineering. [6] Shan Wei,Meng Zhengda,(200)Sooth path design for obile service robots based on iproved A* algorith[j],journal of Southeast University(Natural Science Edition),Vol.40,No.40,pp55-6. [7] Gao Bo, Xu Dein, Yan Weisheng, Zhang Fubin,(2009)Method of Designing Optial Sooth Way for Vehicle[J],Journal of Syste Siulation,Vol.2,No.23,pp [8] Li Hongchao,Huang Yalou,Que Jialan,Xu Jun,Sun Fengchi,(200)An approach to path soothing for wheeled obile robots based on quadtree environent odel[j],robot,vol.23,no.5,pp [9] Shu Lei,(203)Mission-level path planning and soothing of lunar rover based on grid ap[d],harbin Institute of Technology. AUTHORS Corresponding author: Xie Yang (990-), ale, aster of engineering, research direction for robotics and intelligent control.e-ail:xie yang@26.co 8