Kinematic Analysis and Leveling Control Method for a Novel Wheel- Legged Robot

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1 Send Order for Reprint to The Open Mechanical ngineering Journal, 5, 9, Open Acce Kinematic Analyi and Leveling Control Method for a Novel Wheel- Legged Robot Sun Zhibo, Liu Jinhao *, Yu Chunzhan and Kan Jiangming School of Technology, Beijing Foretry Univerity, Beijing, China Abtract: The paper introduce a novel auto-leveling ytem applied to the obtacle-urmounting robot with ix wheelleg. The leveling model of the robot with ix wheel leg and one articulated teering i analyzed. Beide, the kinematic model of the robot i preented. In order to optimize the leveling algorithm, a pecial PID control trategy with the leveling matrix i applied to the leveling ytem. The experiment how that the new leveling ytem can improve the efficiency and the tability of the leveling performance: the leveling time i reduced by.5 econd and the obviou tilt fluctuation are decreaed by 5 time. Keyword: fficiency, kinematic equation, leveling ytem, wheel-legged robot.. INTRODUCTION In recent year, there ha been a trong demand for the mobile robot operating on uneven urface []. Such equipment have found numerou application in a wide variety of arena uch a exploration of extraterretrial, rough unprepared and harp lope environment [, ]. Wheel-Legged locomotion ytem i a preferred olution for maneuvering on uch rough terrain, e.g. Chariot III [4-8], HyLoS erie (four-legged robot) [9], NOROS erie [] and ATHLT (ix-legged robot) [-]. Compared with the traditional wheeled machine, high mobility, obtacleurmounting capability and maneuverability are the major merit of the wheel-leg locomotion ytem. With the development of the control technology, automatic leveling ytem ha made great progre [4, 5]. The ytem ha been widely ued in engineering and military arena [6, 7]. Hydraulic method and electromechanical method are two type of driving method applied to the leveling ytem. The leveling algorithm can be mainly divided into two kind: location error method and angle error method [8]. Studie [9] how that leveling time can be controlled within minute, and leveling preciion can reach within by automatic leveling ytem. Three major factor will impact the performance of leveling ytem: tracking performance of the upport leg, robot tructure and leveling method. Due to the pecial character of the robot, the kinematic model i different from the traditional four-legged tructure. In thi paper, a novel obtacle-urmounting robot with ix wheel-leg i preented. According to the new kinematic model and the claic PID controller, an improved leveling ytem which ha good performance on the leveling efficiency i achieved.. STRUCTUR OF WHL-LGGD ROBOT Thi mobile robot i an equipment deigned to urmount obtacle actively on foret road. A hown in Fig. (), the preented robot i a combination of two frame, two rear wheel-leg and four front wheel-leg. The two frame are connected by an articulated haft []. Wheel-leg are attached to the frame and ditributed in both ide ymmetrically, each with a wheel in the end. The rear wheelleg with one degree of freedom (DOF) i independently actuated by motor (for wheel driving) and linear actuator (for leg lifting). The front wheel-leg are divided into two part. ach part i a modular with DOF and actuated by motor and linear actuator. In order to cro the obtacle and keep the robot level, the wheel-leg can change the height when the robot move on the rough urface.. LVLING ALGORITHM According to the location error method, leveling ytem actually level the key point on the urface of the robot []. A hown in Fig. (), four attached joint point between wheel-leg and frame are defined a point A, B, C, D. A level plane paing through point A i marked a A'B'C'D'. The Carteian coordinate A-XYZ i etablihed for the leveling kinematic model at point A. Z-axi i parallel to the direction of gravity. Y-axi i parallel to AD. And X-axi i determined by the right-hand crew rule. When point B, C, D rie or fall to fit the plane A'B'C'D', the platform i level. Plane ABCD i related to the plane A'B'C'D' by the tranformation matrix T, Rot(y,β) defined a rotation of angle β along the Y-axi, Rot(x,α ) defined a rotation of angle α along the X-axi. The correponding tranformation matrix i given in: *Addre correpondence to thi author at the School of technology, Beijing Foretry Univerity Qinghua at Road, Beijing, Potcard: 8, China; Tel: ; -mail: liujinhao@vip.6.com X/5 5 Bentham Open

2 468 The Open Mechanical ngineering Journal, 5, Volume 9 Zhibo et al Front frame. Linear actuator. Front wheel-leg 4. Rear wheel-leg 5. Motor 6. Rear frame 7. Articulated haft Fig. (). Structure of the wheel-legged robot. A M Y Z X Bğ Z Dğ D Z Cğ Z C N B Fig. (). Leveling model of the wheel-legged robot. T = Rot(y,β) Rot(x,α ) = = coβ in β inβ coβ coβ inα inβ coα inβ coα inα inβ coβ inα coα coβ coα inα inα coα The coordinate of point A B C D are defined a A (,,), B (,x b,y b,z b ), C(x c,y c,z c ), D(x d,y d,z d ), and the initial coordinate matrix i a follow: M = A B C D = x b x c x d y b y c y d z b z c z d In the leveling model, the coordinate of point A, B, C, D can be obtained a matrix M : () M =! a + acoγ + binγ b bcoγ ainγ a + acoγ binγ b + bcoγ ainγ b where γ i the articulated teering angle, a i half length of the traight line AD, and b i half length of the polyline MN. Baed on coordinate tranformation equation [], the matrix M can alo be decribed a following: M ' = T M () The difference of vertical ditance Δz can be calculated a follow: Δz = z b z c z d = (a + acoγ + binγ )coα inβ (b bcoγ ainγ )inα (a + acoγ binγ )coα inβ (b + bcoγ ainγ )inα binα

3 Kinematic Analyi and Leveling Control Method for a Novel Wheel-Legged Robot The Open Mechanical ngineering Journal, 5, Volume P X O O P6 Y P5 Fig. (). Kinematic model of one ide wheel-leg. Fig. () how the kinematic model of wheel-leg on one ide of the frame. In the model, coordinate ytem X O Y i etablihed. In order to make the relationhip clear, relevant parameter are defined, a can be een in Table. Baed on the law of coine, a group of contraint equation are a follow: co(θ + λ ) = + coθ = co(θ + λ ) = The vertical coordinate of the wheel center play an important role in the frame leveling ytem, which i determined by θ θ θ. A group of contraint equation i a follow: y w = l coθ + l co(θ +φ θ ) y w = l coθ + l co(θ θ ) y w = l coθ The kinematic equation between vertical velocity of the wheel center and the velocity of the angle i a follow: () (4) y = J( θ ) θ (5) T where, y w = y w y w y w, θ T = θ θ θ. From q. (4) and (5), the Jacobian matrix J( θ ) can be extracted a: ( ) = J θ l in(φ θ +θ ) l inθ l in(φ θ +θ ) l in(θ θ ) l inθ l in(θ θ ) l inθ The velocity of the angle which i determined by the velocity of the actuator, can be written a follow: θ = J( ) (6) T where θ = θ θ θ, T =. From eq. () and (6), the Jacobian matrix J( ) can be extracted a: J( )=I The velocity relationhip between wheel center and the actuator i deduced from q. (5) and (6). The reulting equation i a follow: T Table. Parameter definition of one ide wheel-leg. Fixed Angle Swinging Angle Marked in Fig. () PO X P6O -X w Ow X OP POP4 -XOP5 Parameter λ λ φ θ θ θ Fixed Length Length of Actuator Marked in Fig. () PO Parameter PO PO P4O P5O P6O OO wo w O PP PP4 P5P l l l

4 47 The Open Mechanical ngineering Journal, 5, Volume 9 Zhibo et al. =J ( ) - J( θ ) - y w (7) On the other ide of the robot, the econd kinematic equation between wheel center and the actuator can be obtained a: = J ( ) - J ( θ ) - y w (8) Different poition are correponding to different velocitie in the leveling ytem. In order to accelerate the leveling peed and improve the leveling accuracy, the peed of the actuator hould be changed with the vertical ditance. According to the different center poition of the wheel, the vertical ditance matrix i defined a T Δ z = z b z b z c z d. By combining q. (7) and q. (8), the leveling matrix i derived a: J( L)= J( )- J θ J ( ) - ( ) - J ( θ ) -. The momentary peed variation of the actuator are calculated by the pot-multiplication of the leveling matrix and the vertical ditance matrix. 4. CONTROL STRATGY AND SIMULATION The level of the frame i determined by motion of the wheel-leg all the time, o level control ytem hould be deigned with trong robutne. Cloed loop feedback PID control ytem i adopted a the leveling control trategy, a hown in Fig. (4). Articulated teering angle and tilt-angle of X-axi and Y-axi are the parameter input into the ytem. The ytem control linear actuator extended or hortened by the ignal ent from PID-controller. So the leveling of the frame i achieved. According to the control trategy, model of the control ytem i imulated by the combination of Simulink and Adam. The tructure of the imulation i hown in Fig. (5). Initial poition of the robot i et a: α=5, β=, γ=, =66mm, =9mm, =447mm, 4 =7mm, θ =5, θ =7. The parameter are input into the imulation ytem. Fig. (6) how the imulation proce in Adam. A the reult, velocitie of the linear actuator and change of tilt-angle are obtained, which i hown in Fig. (7). 5. LVLING TST OF TH ROBOT PROTOTYP 5.. The xperimental Sytem and Method The entire tet ytem conit of part: control ytem, performing ytem and detecting ytem. A can be een in Fig. (8), control ytem include power upply, tilt enor and PC controller; performing ytem contain the linear actuator and the actuator power upply; detecting ytem i compried of ADIS IMU (inertial meaurement unit) and PC. The control ytem i programmed by Codey. The proce of the tet i a follow:. Connect control ytem, performing ytem and detecting ytem, and enure the ytem running well.. Reet all of the actuator, and enure the frame are level.. Adjut the intallation poition of the two tilt-angle enor and ADIS IMU, and then make ure the output degree of X-axi and Y-axi tilt-angle are both, and the output acceleration ignal of the ADIS IMU only ha value in Z-axi. 4. Tilt the body 5 with x-axi and with y-axi, and turn the rear frame to make articulated teering angle. 5. Load traditional leveling program (without leveling matrix) and the improved leveling program (with the leveling matrix) repectively, experiment time with each method and read the data of ADIS IMU from PC. 5.. Analyi of xperimental Reult A can be een in Fig. (9), the leveling performance i ignificantly enhanced by the improved leveling ytem. Compared with the traditional one, the improved method tilt enor for x-axi tilt enor for y-axi Ideal tilt for x-axi + - Ideal tilt for y-axi Steering angle + - vertical ditance matrix Leveling Matrix PID controller Actuator Robot poition Parameter Fig. (4). Control trategy of the leveling ytem. Leveling aglorithm

5 Kinematic Analyi and Leveling Control Method for a Novel Wheel-Legged Robot The Open Mechanical ngineering Journal, 5, Volume 9 47 Fig. (5). Structure of the leveling ytem imulation. 4 Fig. (6). Leveling proce of the robot in Adam. reduce the fluctuation of the tilt-angle at the early time. After 5 econd, the leveling peed of the improved ytem i obviouly quicker than that of the traditional method. Fig. (, ) how the the leveling rate through the leveling proce. The data are obtained by differentiation proceing of the tilt. It i clear that the leveling rate ha changed gently after improvement. A hown in Table, tatitic ugget that the improved method can reduce leveling time by.5 econd and obviou tilt fluctuation (Amplitude exceeded degree/) by 5 time( time for x-axi and time for y-axi). Through the reult of the experiment, ome concluion can be obtained a follow:. The new method with leveling matrix can really improve the leveling performance, which may be attributed to the following reaon: () At the beginning of the leveling, actuator run quickly. The improved method reduce the contact exchange time between wheel and ground by enhancing the cooperation of the actuator. So the improved method can reduce the fluctuation of the tilt-angle at the early time () From 5 to econd, actuator low down with different rate, a hown in Fig. (7). The improved method which involve leveling matrix can adjut the velocitie of the actuator more accurately and the leveling efficiency i improved at the ame time.

6 47 The Open Mechanical ngineering Journal, 5, Volume 9 Zhibo et al.. At the end of the experiment, both method how almot the ame leveling accuracy and the leveling error can reach within. It prove that the final leveling preciion i irrelevant to the leveling method, but mainly depend on the device in the ytem.. The validity of imulation for the leveling ytem i verified by the experiment. The data in Fig. (9) fit well with that in Fig. (7), and the fitting degree i above 85%. Vibration of the tire may be the main reaon of the error. CONCLUSION Fig. (7). Simulation reult. (a) Velocitie of the linear actuator (b) Change of tilt-angle in imulation In thi paper, a novel ix-wheel-legged robot i preented. In order to keep the body remain level when it tand on the uneven road, the kinematic model of the robot leveling ytem i achieved baed on the kinematic equation. With the new leveling algorithm, a pecial PID control trategy i applied to the leveling ytem. According to the reult of the imulation by Simulink and Adam, the control trategy i proved to be viable in the leveling ytem. The improved method eem to be an effective way of the leveling ytem. The tet reult how that leveling time can be reduced by.5 econd(%) and obviou tilt fluctuation can be decreaed by 5 time(5%) with the leveling matrix applied to the leveling ytem. There are alo ome inadequacie of the leveling ytem which can be improved in the future.. The vibration between the tire and the road can influence the accuracy of the control ytem, o the fluctuation of the tilt become obviou during the proce.. Only two enor are ued in the ytem, and ome more parameter are worked out by calculating the integration of the enor data, which reduce the accuracy of the control ytem. Next tep, more factor hould be conidered in the kinematic model, and more device are needed to enhance the leveling efficiency. Tilt enor for y-axi ADIS IMU Controller Power upply PC Controller Actuator power upply Linear Actuator PC Tilt enor for x-axi Fig. (8). Control ytem of the leveling tet.

7 Kinematic Analyi and Leveling Control Method for a Novel Wheel-Legged Robot The Open Mechanical ngineering Journal, 5, Volume 9 47 Table. Comparion of the performance. Performance Traditional Algorithm Improved Algorithm Accuracy for x-axi.6 degree.6 degree Accuracy for y-axi.4 degree.4 degree Leveling time for x-axi 6.7. Leveling time for y-axi 4.. Time of obviou tilt fluctuation for x-axi Time of obviou tilt fluctuation for y-axi Fig. (9). Tilt-angle change curve of the tet. CONFLICT OF INTRST The author confirm that thi article content ha no conflict of interet. ACKNOWLDGMNTS Thi work i upported by the Fundamental Reearch Fund for the Central Univeritie TD-4. The author would like to thank Profeor Dr. Zheng Yili and Dr. Huang Qingqing for their important contribution to thi work. RFRNCS Fig. (). X-axi tilt rate curve of the tet. Fig. (). Y-axi tilt rate curve of the tet. [] S. Nakajima, Concept of a novel four-wheel-type mobile robot for rough terrain, RT-mover, In: 9 I/RSJ International Conference on Intelligent Robot and Sytem, IROS, St. Loui, MO, United tate, 9, pp [] R. Siegwart, P. Lamon, T. tier, M. Lauria, and R. Piguet, Innovative deign for wheeled locomotion in rough terrain, In: Intelligent Autonomou Sytem - IAS-6, July 5, - July 7,, Venice, Italy,, pp.5-6. [] S. K. Jun, G. D. White, and V. N. Krovi, Kinetotatic deign conideration for an articulated leg-wheel locomotion ubytem, Journal of Dynamic Sytem, Meaurement, and Control, vol. 8, pp. -, 6. [4] S. Nakajima, and. Nakano, Adaptive gait for large rough terrain of a leg-wheel robot (t report, gait trategy), Nihon Kikai Gakkai Ronbunhu, C Hen/Tranaction of the Japan Society of Mechanical ngineer, Part C, vol. 7, pp. 96-9, 6. [5] S. Nakajima, and. Nakano, Adaptive gait for large rough terrain of a leg-wheel robot ( nd report, gait for an upward tep), Nihon Kikai Gakkai Ronbunhu, C Hen/Tranaction of the Japan Society of Mechanical ngineer, Part C, vol. 7, pp. 9-99, 6. [6] S. Nakajima, and. Nakano, Adaptive gait for large rough terrain of a leg-wheel robot ( rd report, gait for a downward tep), Nihon Kikai Gakkai Ronbunhu, C Hen/Tranaction of the Japan Society of Mechanical ngineer, Part C, vol. 7, pp , 6. [7] S. Nakajima, and. Nakano, Adaptive gait for large rough terrain of a leg-wheel robot (4 th report, gait for getting over an obtacle), Nihon Kikai Gakkai Ronbunhu, C Hen/Tranaction of the Japan Society of Mechanical ngineer, Part C, vol. 7, pp , 6. [8] S. Nakajima, and. Nakano, Adaptive gait for large rough terrain of a leg-wheel robot (5 th report, integrated gait), Nihon Kikai Gakkai Ronbunhu, C Hen/Tranaction of the Japan Society of Mechanical ngineer, Part C, vol. 7, pp , 6.

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