Planning of scooping position and approach path for loading operation by wheel loader

Transcription

1 22 nd International Sympoium on Automation and Robotic in Contruction ISARC 25 - September 11-14, 25, Ferrara (Italy) 1 Planning of cooping poition and approach path for loading operation by wheel loader Shigeru Sarata, Yoewee Weeramhaeng and Takahi Tubouchi Abtract Our group developed a method for planning of cooping point and approach path a a part of our ongoing reearch on autonomou loading operation of wheel loader at contruction ite. The planning of cooping poition and direction i obtained through proceing pile model. The pile model repreent hape and volume of the pile, change of hape and volume by cooping, and falling behavior accompanied cooping. Scooping direction hould be perpendicular to lope of the pile to avoid unbalance of reitance force around the center line of the bucket. The reitance force impoed on the bucket i etimated uing the pile model and bucket trajectory model. The cooping direction with leat unbalance of reitance force i elected. V hape path between the cooping poition and the loading poition to dump track i compoed of traight line and clothoid curve. For given cooping poition and loading poition, the path with the leat length i produced by the propoed planning method uing optimization by Lagrange multiplier. For election of the next cooping point, V hape path for candidate of cooping point are planned by propoed method. Index Term loading operation, path generation, cooping wheel loader I. INTRODUCTION The front end wheel loader ( loader hereinafter) i one of the major loading machine for earth moving operation in contruction, mining and other many field. The workite in contruction and mining include irregularly haped material that change hape a operation progre, uch a pile of and, oil, and fragmented rock. The unmanned ytem in thee field hould be intelligent ytem with the capacity to decide their action baed on the changing condition at workite. Our group developed a method for planning of cooping point and approach path a a part of our ongoing reearch on autonomou loading operation of wheel loader at contruction ite[1][2]. For an autonomou ytem, planning function i one of the eential element. Several reearche have been conducted on automatic operation ytem of wheel loader [3][4]. Thee developed ytem employed a guidance method S. Sarata i with the National Intitute of Advanced Indutrial Science and Technology (AIST), Tukuba, Ibaraki Japan. Y. Weeramhaeng i with The Univerity of Tukuba, Tukuba, Ibaraki Japan T. Tubouchi i with The Univerity of Tukuba, Tukuba, Ibaraki Japan or a teaching-playback method for traveling. Path generation function wa not included. The mot coon path between the cooping poition and the loading poition on the dump truck i V Shape path including witchback in the middle of the path a hown in Fig.1. The loading operation i carried out by repetition of thi cycle of cooping and loading. The cooping poition of each cycle i changed a operation progre. The determination of the cooping direction and the generation of the path between the cooping point and the loading point are eential function for an autonomou loading ytem. Thi paper decribe a planning method of V hape path including determination of the cooping direction baed on the hape of the pile. Loader Dump Truck Fig.1 V hape Path Pile II. MODEL OF THE PILE AND THE SCOOPING DIRECTION A. Reitance Force Applied On The Bucket The bucket i ubjected to large reitance force from the pile during cooping. The magnitude and direction of the reitance force are affected by the hape of the pile and trajectory of the bucket. The reitance force can be claified into everal element of force. The dominant element are the penetrating force and the force required to move the material in front of the bucket. From the reult of the baic experiment on the reitance force between the bucket and material in the pile, both of the force have cloe relation to depth of the material of the pile at the tip of the bucket. The depth of the material at the tip of the bucket change a the bucket advance during the cooping operation. The bucket trajectory of a tandard coop i compoed of the three ection hown in Fig. 2. In the firt ection, the bae of the bucket

2 ISARC 25 2 remain flat againt the ground. A the loader advance on it wheel, the bucket penetrate the pile from point A to B (ection 1). From point B to C (ection 2), the bucket arm move the tip of the bucket upward along a line or curve and increae the tilt. Once filled with the piled material, the bucket move upward almot vertically from point C to D (ection 3). The horizontal length of cooping, AB and BC, depend on the capacity of the bucket and hape of the pile. In a tandard coop, the total length of cooping AC i about 1.5 time a long a the length of the bucket bae. D from perpendicular, a hown in (b), the reitance force around the center line of the bucket i ayetrical, impoing undeirable tre on the bucket link mechanim. The unbalance of the reitance force impoed on the bucket i etimated by etimating the reitance force at each point on tip of the bucket uing the column model and bucket trajectory model (Fig. 6). The cooping direction with the leat unbalance of reitance force hould be elected to obtain the proper cooping motion. Pile A B C Fig.2 Bucket Motion trajectory B. Pile Model The column model [1] i a ueful ytem for etimating the interaction between the bucket and piled material. Though imple in tructure, the model can repreent the hape of the pile, a well a change in both hape and volume. Fig.3 how the tructure of the column model. The working area i teellated into ection, each forming the bae of a column. The height of each column repreent the height of the pile at that poition. The ize of the ection and unit of height have no relation to the particle or fragment diameter of the material making up the pile. Fig.3 Column Model (a) Fig.4 Scooping Angle (b) Fig.5 Column model and cooping area The column model i formed baed on the reult of threedimenional hape meauring of the pile. Stereo-viion ytem with two CCD camera i ued for the hape meauring. A the pile of gravel or fragmented rock ha random texture on the urface, correlation method i employed for finding correponding point on the two image taken by CCD camera. 3D recontruction i obtained through trigonometry with diparity. C. Determination of Scooping Direction If poible, the cooping direction hould be perpendicular to lope of the pile (Fig. 4 (a)). If the cooping direction i far Dicreet point are plotted on the cooping area a hown in Fig. 6. Let w j be the ditance from the center of the bucket and h ij be the average depth of the material piled in the unit width at that point. The variable m ij i defined a: m = h w. (1) ij ij j Thu, m ij i a value related to the moment around the center of the bucket. M i defined a the um of all m ji value in cooping area. M = m (2) ij M i the um of all value related to the moment applied on the bucket during one cooping cycle. M change with change in the cooping direction from the ame initial cooping poition. The mallet M i expected when the cooping i executed in a direction normal to the lope, but the value i alo affected by the hape of the cooping area on the pile. The cooping direction with the mallet M i determined by comparing the etimated M value in different direction around the normal vector in the ection neighboring the initial coop poition.

3 ISARC 25 3 path a a curve element. Thi clothoid curve can be decribed by the following formulae: 2 () co( k ) x = d (4) w Fig. 7 Dicreet point for etimation of reitance force III. V SHAPE PATH PLANNING A. Steering Sytem of The Wheel Loader The wheel loader employ an articulate teering ytem of the type hown in Fig. 7. The body of the loader i eparated into a front part and rear part connected by a center pin. The angle around the center pin i controlled by hydraulic cylinder. The placement of the front and rear axle at equal ditance from the center pin enure that the front and rear wheel travel over the ame path, conferring high mobility on off-road urface uch a mud or oft oil. L j φ R Fig. 7 Steering ytem The relation between the articulate angle φ and curvature κ i decribed by (1). Where L i the ditance from the center pin to the front or rear axle. 1 φ = 2tan ( κ L ) (3) 2 When φ i mall, curvature κ i proportional to φ linearly. The operational range of the articulate angle i about 4 degree. The relation between κ and φ i almot linear in thi range. i () in( 2 ) y = k d, (5) where i the length of the path and k i a coefficient related to the harpne of the path. If the curvature change a hown in Fig. 8( ), the path become the ame clothoid joined in revere direction, or what we call a yetrical clothoid (Fig. (b)). Given that the curvature i zero at both end of the yetrical clothoid, the curve can be connected to traight line with continuouly (a) curvature (b) Path Fig. 8 Syetrical clothoid Here we conider a V hape path contituting two yetrical clothoid and traight line. For convenience, we aume that the loader move from the cooping poition to the loading poition and the loader i initially poitioned on the origin of the coordinate ytem and move in a negative direction on the x axi, a hown in Fig. 9. The grey zone in Fig. 9 i the area that can be reached via the combination of traight line l 1, yetrical clothoid c 1, traight line l 2, yetrical clothoid c 2, and traight line l 3. l 1, l 2 and l 3 are the direction of the loader at the initial poition, at the witchback, and at the final poition, repectively. The traight line egment can take a negative direction for the backward run of the loader. From requirement of the operation, the line egment l 1 hould be negative and l 3 hould be poitive. C. Path Planning When the end poition and direction of the yetrical clothoid are given, the correponding clothoid can be obtained by olving formulae (4) and (5). Thee formulae cannot be olved analytically, however, a both are Frenel integral. Numerical olution can be reached uing the Taylor extenion, but the complexity of the whole procedure call for implification. Here we implify the procedure by limiting the curvature κ to everal value. Thi provide a large practical advantage. B. Path Planning With Path Element A path from the given initial poition to a final poition can be eaily generated by combining path element uch a traight line and curve. In the propoed method for path planning, we ue a clothoid with a curvature proportional to the length of the

4 ISARC Pl l3 l2 l3 Ph l2 Fig. 9 Zone reachable via the combination of clothoid and traight line The path planning proceed in the following tep. Let P be the cooping poition, θ be direction at that poition, P e be the loading poition, θ e be direction at that poition and θ h be direction at P h :the witch back point or the end of c 1. θ h take value between θ and θ e. Path conit of l 1 - c 1 - l 2 - c 2 - l 3 In the planning procedure, the path i eparated into c 1 - c 2 and l 1 - l 2 - l 3. At the firt tep, et κ at a certain value and calculate c 1 : the yetrical clothoid which turn the loader by angle θ h -θ. Next, calculate c 2 for angle θ e -θ h in the ame manner and connect c 1 and c 2 at the witch back. In the econd tep, generate the path l 1 - l 2 - l 3 between the end point of c 1 - c 2 :P t and the cooping point P e with optimization on length of l 1 - l 2 - l 3. Function Z for the optimization of the length l 1 - l 2 - l 3 i defined in (6), Z l l l = + + (6) Contraint condition are: C = ( x x ) ( l + l coθ + l coθ ) (7) 1 e t 1 2 t 3 e C = ( y y ) ( l inθ + l inθ ). (8) 2 e t 2 t 3 e Function F on the aforeaid i defined a: F = Z + µ C + µ C, (9) where µ 1 and µ 2 are Lagrange multiplier. From thee equation, the combination of l 1 - l 2 - l 3 with the hortet length i obtained. Fig.1 how an example of proce of the path planning. The cooping point P i located at ( ) and the angle θ =-1. The loading point P e i located at (-1 1) and the angle θ e =8. The bold line repreent the hortet path at θ h =48. The thin line repreent the path at θ h =1.and θ h =7. l1 l1 C1 Pt C2 P Fig.1 Proce of path planning The total length of the path at every 2 degree of θ h i calculated out a hown in Fig.11. In the example cae, the length of the path change from 3973 at θ h =-1 to 337 at θ h =48. The length of l 1 and l 3 are hown in Fig.12. Black triangle and gray quare repreent length of l 1 and l 3 repectively. l 1 take negative value in the whole range of θ h, but l 3 take negative value at θ h =-1~. Thee reult do not fill the requirement for V hape path. The reult at θ h =~8 fill the requirement and the total length become the hortet at θ h = θh degree Fig.11 Total length of the path θh degree Fig.12 Length of l 1 and l 3

5 ISARC 25 5 IV. V SHAPE PATH PLANNING WITH EXPERIMENTAL MODEL The propoed method i evaluated uing the experimental model called YAMAZUMI-2 (YZ-2, Fig. 13) and a pile of fragmented granite. The YZ-2 ha the ame tructure and function of a wheel loader. A ditance of 27 eparate the front and rear axle and the bucket meaure 25 in width. The experimental pile conited of 5 fragment piled over a urface area of about 1 to a height of about 3. Two CCD camera were attached to the YZ-2 to meaure the hape of the pile by a tereo-viion ytem. In following planning, the teering angular velocity i et at 5 degree/l. θ =-15.8 and M at P- become at θ =25.8. Thee cooping angle eem to be perpendicular to the edge of the pile. Fig.17 how the V hape path for candidate of the next cooping poition P+ and P-. Bold line and thin line repreent the V hape path for P+ and P- repectively. The total length of the path i 295 for P+ and 575 for P-. In thi cae, P+ ha great advantage in the travel length of the loader. It i the additive effect of the ditance and the direction between the cooping poition and the loading poition. P+ hould be elected a the next cooping point in thi cae. Fig.18 how V hape path in ame ituation in Fig.@ except loading poition and angle. In thi cae, P e i et at (-5 5) and θ e =7. Becaue the poition P+ i too cloe to the loading poition, the path from P+ to the loading poition cannot fill the requirement on l 3 to be poitive. Becaue P+ doe not fill the requirement, P- ha to be elected a the next cooping point in thi cae Fig. 13 Experimental model YZ-2 Fig. 1 how the image of the pile by the CCD camera. The hape of the pile wa obtained by applying the correlation method on the image. A column model of the experimental pile i formed a previouly mentioned. The model conited of 3 x 3 column, each meauring 5x5. The column model repreented a 15 x 15 area in the experimental field Fig. 15 The Firt Scooping and V hape Path 6.x1 4 M.x1 Fig.14 Experimental pile Fig.15 how the firt cooping and V hape path to the loading poition. Gray bold line repreent the edge of the pile and the loading poition i (-5 1) and angle θ e =7. A the candidate of the next cooping poition, two poition are conidered. One i P+ :2 left of the firt cooping poition and the other i P- :2 right. Becaue the width of the bucket of YZ-2 i 25, thee next poition are overlapped to the firt cooping area. Fig.16 how the etimate moment M on the bucket. Dark triangle and grey quare repreent M for P+ and P- repectively. M at P+ become at -6.x Scooping Angle (degree) Fig. 16 Moment on the bucket

6 ISARC 25 6 V. CONCLUSION An itemized outline of the propoed method follow. (1) The cooping direction i determined baed on the reitance force applied on the bucket during cooping motion. The irregular hape of the pile i expreed numerically by a column model. The unbalance of the reitance force applied on the bucket i etimated uing the column model and bucket trajectory. The reult of thi etimation i ued to determine the appropriate cooping direction. (2) The planned path conit of two yetrical clothoid curve and three line egment. To implify the generation of the clothoid, the curvature i limited to everal value. The length of line egment are determined through optimization. (3) The total length of the V hape i affected by the angle at the witch back point. The angle providing the minimum length of the path i obtained by comparion among thee at different angle of the witch back point. (4) V hape path by the propoed method i affected from the ditance and direction between the cooping point and the loading point. Appropriatene of the planned path depend on the length of the path a well a the practicability on of reachable. REFERENCES [1] Sarata, S.: Model-baed Tak Planning for Loading Operation in Mining. Proc. of IROS, pp , 21 [2] Sarata, S.: Reearch and Development on Unmanned Loading Operation by Wheel Loader, Proc. Rapid Mine Development, pp , 21 [3] Gocho,T. et al: Autonomou Wheel-Loader in Aphalt Plant, Proc. 9th ISRAC, 1992 [4] Ohima, H. et al :Automation of Loading and Hauling Work in Mining and Quarry, Komatu technical report, Vol.43, No.1, pp.27-39, 1997 (in Japanee) P e (-5 1), θ e =7 Fig.17 V hape path for P+ and P P e (-5 5), θ e =8 Fig.18 V hape path for P+ and P-