第6卷第5期 智能系统学报 Vol.6 No.5 2011年10月 CAAI Transactions on Intelligent Systems 0ct.2011 doi:10.3969/j.issn.16734785.2011.05.012 A desired landing points walking method enabling a planner quadruped robot to walk on rough terrain MA Hongwen,WANG Liquan,ZHONG Zhi,YAO Shaoming College of Mechanical and Electrical,Harbin Engineering University,Harbin 150001,China) Abstract:It is necessary for legged robots to walk stably and smoothly on rough terrain.In this paper,a de- sired landing points(DLP)walking method based on preview control was proposed in which an off-line foot motion trace and an on-line modification of the trace were used to enable the robot to walk on rough terrain. The on-line modification was composed of speed modification,foot lifting-off height modification,step length modification,and identification and avoidance of unsuitable landing terrain.A planner quadruped robot simu- lator was used to apply the DLP walking method.The correctness of the method was proven by a series of sim- ulations using the Adams and Simulink. Keywords:legged robot;preview control;desired landing points;planner quadruped robot CLC Number:TP242.6 Document code:A Article ID:1673-4785(2011)05-0464-06 Legged robots were first developed more than half he used preview control in ZMP to generate a real-time a century ago.For all kinds of structures,satisfactory walking pattem Park used cycloid functions and drivers and sensors have been designed and manufac-3rd order polynomial functions to generate a real-time tured.However,legged robots are still not suitable for walking pattern.Heliot proposed a method to syn- walking on rough terrain in a natural environment as chronize the motion of a robot or another device with human beings or other animals can do easily,the rea- respect to the output signal of the sens Fukuoka son is that the walking pattern generation method for proposed a CPG control method based on biological this kind of robot is not consummate. concepts for a quadruped robot to walk at medium ZMP is widely used to control legged robots, walking speed on irregular terrain.Arbulu addressed and it performs excellently in static walking conditions.the problem of generating dynamic motion for a human- Symmetrical running is a good method for dynamic oid robot between two predefined postures using ZMP feedback contro;however,the robot using this preview contro Zonfrilli proposed a walking gener- method can hardly walking on rough terrain.Passive ator and controller based on the inverted pendulum ap- walking sve the problem of efficient walkingbut proach with the innovative feature of fully using the it is unsuitable for complex feedback control. double support phase for the walking generation and Recently,the real-time walking pattern generator contro Kurazume proposed a methodology for gen- has attracted the attention of many scholars.Kajita erating a straight legged walking pattern for a biped ro- proposed a three-dimensional linear inverted pendulum bot utilizing the up-and-down motion of an upper mode to generate a real-time walking patterns Later, body[12.Diedam proposed a method to generate a walking gaits online based on a linear model predictive Received Data:2010-03-31. control.Huang proposed a walking control method Foundation Item:This work was supported in part by the National Natu- ral Science Foundation of China under Grant consisting of a feedforward dynamic pattern and a feed- 60875067,the Natural Science Foundation of Hei- back senry reflex However,most of these meth- longjiang Province under Grant F200602,and the Technical Innovation Talent Foundation of Harbin un- ods are imperfect for enabling a multi-legged robot to der Grant 2010RFQXG010. Corresponding Author:MA Hongwen.E-mail:mahongwen@hrbeu. walk smoothly on rough terrain. edu.cn. In this paper,a walking method using desired
5 MA Hongwen,et al:A desired landing points walking method enabling a plamner quadruped robot to walk on ou terain ·465· landing points and adopting a preview controller is pro- trunk coordinate system,the motion trace of the foot posed for a point-shape-foot planner quadruped robot. can be shown as in Fig.3. It allows the robot to walk smoothly on rough terrain. In section I,the concept of the controller is briefly presented,and the details of controller,i.e.the real- time foot motion trace generator,are introduced in sec- tions II and III.In section IV,simulations are provid- ed to prove the correctness of this method. Flying period 1 Desired landing points Flying flying period As shown in Fig.1,while feet 2 and 4 make con- Lifting-off Touching-down tact with the ground,feet 1 and 3 lift off simultaneous- period period ly at the current time.At the desired time the lift-off Supporting Supporting period period feet,1 and 3,then touch down to the ground.The po- Fig.2 Motion trace of one foot in Cartesian world co- sitions of desired landing points (DLP),1'and 3'are ordinate system calculated before the current time according to the de- Flying period sired moving distance of the trunk,D,,and the desired Freeying perid6d、 moving distances of feet 1 and 3. The key of this method is the calculation of DLP 冷Lifting-off Touching-down period for flying feet at the current time. --------p0d」 Supporting period Fig.3 Motion trace of one foot in Cartesian trunk co- ordinate system b 2 Off-line foot motion trace on plain terrain To simplify the analysis,only transitional joints are used by all robot legs,as shown in Fig.4. (e) Fig.1 Planner quadruped robot walks using the de- sired landing points method Fig.1(a)illustrates the state of current time.Fig.1 (b)illustrates the state of desired time.Fig.1(c)illus- trates the composition of Fig.1(a)and Fig.1(b). Fig.4 Planner quadruped robot with transitional joints Fig.2 illustrates the motion trace of one foot in the Cartesian world coordinate system.The motion trace can be separated into two parts:flying period and sup- porting period.The flying period can be further separa- ted into three parts:lifting-off period,freely-flying pe- riod,and touching-down period.The characteristic of Fig.5 Motion trace of a foot the traces in the lifting-off and touching-down periods Suppose the trunk of the robot moves at uniform is that they are perpendicular to the ground,which de- speed in the positive direction along axis x.To main- creases the interaction between foot and ground in the tain this movement,a kind of foot motion trace is lifting-off and touching-down periods.In the Cartesian shown in Fig.5.to-'is the flying period and
·466 智能系统学报 第6卷 ts'is the supporting period.Amongto,to' measured in this paper. is the lifting-off period,t'is the freely flying pe- 3.1 Speed modification riod,and'ts'is the touching-down period. Speed modification of the trunk is accomplished u- Supposing the initial speed of the trunk is v,then sing supporting feet.Suppose the initial speed of the the initial foot speed along axis is-v,and the initial trunk is v,and the speed is changed to at the end of foot speed along axis y is 0 in the trunk coordinate sys- a walking step.The change of the speed is in uniform tem.All the accelerations of one foot in each period acceleration.The acceleration along axis x of the sup- are given in Table 1. porting foot is Table 1 Accelerations in every periods %.=- (1) Accelerations along Accelerations along T Periods axes x d axes y a The moving distance of the trunk is to-t 0 D.=T(o+v) (2) 2 1- △t 0 3.2 Lifting-off height modification 2D.+6u·△t 2-3 2T·△t-10·△7 -A To adapt the lifting-off feet to the morphology of the ground,the lifting-off height should be modified. t3-t4 0 0 2D,+6e·△t The top of Fig.6 shows the motion trace of a lifting-off 4-5 2T·△t-10·△7 -A foot in a world coordinate system and the bottom of Fig.6 shows the trace in a trunk coordinate system. ts-t6 0 t6- 0 A 1-ts 0 0 Accelerations are described in trunk coordinate D system.A is a constant determined by the maximum lifting-off height.T is the period of walking step.At is the lifting-off period or touching-down period.Where 61-0=2-1=3-63=65-t4=t6-t5=-t6= h △t,andt4-t3=T-6△t. A walking step means a period from the lifting-off Fig.6 Planner quadruped robot with transitional joints time to the touching-down time for a flying foot or a pe- Take both A and B in consideration,data in Table riod from the touching-down time to the lifting-off time 1 are changed as shown in Table 2.Aa is determinate for a landing foot.The flying foot moves from its initial by h in Fig.6. time,to,and the supporting foot moves from its initial Table 2 Accelerations in every Period. time,,simultaneously. Accelerations along Accelerations along When each foot of the robot moves according to Periods axes x d. axes y a, the above motion trace,the robot can walk at uniform to -t 0 A+△a speed on a plain terrain. U t1-t2 △t 0 3 On-line modification of the foot 2-6 2D,+3m·△t+3知'·△t -(A+△a) 2T.△t-10·△2 motion trace 3-4 0 0 2D.+3m·△t+3'·△t To walk on rough terrain,the morphology of the 4-s -(A-△a) 2T·△t-10·△t2 terrain ahead should be detected in advance.Many methods can be used to accomplish such a task:struc- ts-t6 -At 0 ture light vision,laser scanning,etc.The morphology 6-5 0 A-△a of the ground in a world coordinate system has been 名~名 0 0
5 MA Hongwen,et al:A desired landing points walking method enabling a planmer quadruped robot to walk on rough terrain ·467· 3.3 Step length modification and avoidance of To simplify the computation of ZMP,only the unsuitable landing terrain trunk is calculated in Eq.(3)because the mass and Some terrains are unsuitable for landing,such as a inertia of the trunk are much larger than those of other slope with steep gradient,as shown in Fig.7.The initial parts of the robot.A stability margin is adopted to pre- desired landing point,A,is unsuitable for landing. vent the overturning of the robot,as shown in Fig.8. 4 Simulation Key parameters are given in Table 3,as shown in Fig.9. Trunk …642 135… Calf Fig.7 Planner quadruped robot with transitional joints By setting the initial landing point as a center Fig.9 Structure of a planner quadruped robot point,then using an interval,Ad,to search the points in the range,R,as shown in Fig.7,we obtain a Table 3 Key parameters of planner quadruped robot suitable desired landing point,B. Parameters meaning value Step length of the robot should be modified for Munnk Mass of trunk(kg） 12.8 landing on the suitable desired landing point.The D. Maigh Mass of thigh (kg) 1.7 in Table 2 is used to modify the step length of the fly- M. Mass of calf (kg) 0.8 ing feet. I wuk Inertia of trunk (kg.mm2) 667350 I igh Inertia of thigh (kg.mm2) 2798 3.4 ZMP computation Iar Inertia of calf (kg.mm2) 1101 The modification of the foot motion trace obeys the y Initial position along axes y(mm) 300 ZMP rules.The ZMP can be computed by using the Initial position along axes x(mm) 300 following equations: Initial position along axes x(mm) 270 XIMP Initial position along axes x(mm) 190 无4 Initial position along axes x (mm)220 之m,(元+g)-三 m4-召1，n. All leg joints are controlled using a simple posi- (3) m(+g) tion PID controller,as shown in Fig.10. Where,m;is the mass of link i,I is the inertial com- Position PID Force Position Joint ponents,g is the gravitational acceleration.(0) is the coordinate of ZMP,and (y)is the coordi- nate of the mass center of link i in a Cartesian world Fig.10 Position PID controller of a joint coordinate system. All simulations are accomplished using the Adams and Simulink methods.The control code is written in Stability ZMP SFunction. margin boundary 4.1 Walking at uniform speed and variable speed on plain terrain The top view of Fig.11 illustrates when the robot Actural ZMP boundary walks at uniform speed,and the bottom view of Fig.11 Fig.8 ZMP boundary considering stability margin illustrates when the robot walks at variable speed.Fig. 12 shows the walking speed of the trunk measured by
·468· 智能系统学报 第6卷 the Adams method. trolled without and with avoidance control of unsuitable landing terrain respectively.At shown in Fig.15(a). the next desired landing points are calculated,which will be adjusted by the avoidance control method if they are unsuitable for landing.At shown in Fig.15(b), the feet land on an unsuitable point for the upper robot Fig.11 Robot walking on plain ground at uniform and the feet land on a proper point for the lower robot. speed and variable speed respectively Fig.15(c)and Fig.15(d)illustrate the sliding of the feet. 140 -o-Variable speed I20 -3-Uniform speed 100 60 40 20 812162024 (a) (b) t/s Fig.12 Trunk speed measured in Adams 4.2 Walking on rough terrain The top view of Fig.13 illustrates when the robot walks with the modification of foot lifting-off height, (c) (d) and the bottom view of Fig.13 illustrates when the ro- bot walks without the modification of foot lifting-off Fig.15 Avoidance of unsuitable landing terrain height.Fig.14 shows the component,z,of the trunk Conclusion posture measured by the Adams method. A desired landing points (DLP)walking method was proposed in this paper.The characteristics of this method are summarized as follows. 1)Point-shape foot was used in the analysis. 2)Speed,lift-off height,and step length modifi- Fig.13 Robot walking on rough terrain with and cation of foot motion trace was used to make a robot without lifting-off height modification walk smoothly on rough terrain. 3)The morphology of the terrain ahead should be 4-0Without hight control detected in advance to modify the foot motion trace. 2 -With hight control The dynamics of the robot is not considered in this 000- paper and will be covered in future analysis. References: 12 162024 [1]VUKOBRATOVI C M,BOROVAC B.Zero-moment point- 1/s thirty five years of its life[J].International Joural of Hu- Fig.14 Trunk pitch angle measured in Adams manoid Robotics8,2004,1(1):157-173. [2]RAIBERT M H.Legged robot that balance [M].Cam- 4.3 Avoidance of unsuitable landing terrain bridge,USA:Massachusetts Institute of Technology,1986. Fig.15 illustrates a sequence of foot sliding when [3]MCGEER T.Passive dynamic walking J].International the robot lands on an unsuitable landing terrain.The Journal of Robotics Research,1990,9(2):62-82. upper robot and lower robot in each segment are con- [4]COLLINS S H,RUINA A L,TEDRAKE R,et al.Efficient bipedal robots based on passive-dynamic walkers[J].Sci-
5 MA Hongwen,et al:A desired landing points walking method enabling a planner quadruped robot to walk on rough terrain ·469· ence,2005,307(5712):1082-1085. About the authors: 5]KAJITA S,KANEHIRO F,KANEKO K,et al.A realtime MA Hongwen received a B.S.degree pattem generator for biped walking[C]//Proceedings of the in automobile engineering in 1995 form Ji- 2002 IEEE International Conference on Robotics and Auto lin University of Technology,Changchun, mation.Washington,DC,USA,2002:31-37. China.He then eamned an M.S.degree in [6]KAJITA S,KANEHIRO F,KANEKO K,et al.Biped mechanical engineering and Ph.D.degree walking pattern generation by using preview control of zero- in instrument and instrumentation engi- moment point[C]//Proceedings of the 2003 IEEE Interna- neering,both from Harbin Institute of Technology,Harbin,Chi- tional Conference on Robotics and Automation.Taipei, na,in 1999 and 2005 respectively.In 2006,he joined the Col- China,2003:1620-1626. lege of Mechanical and Electrical Engineering,Harbin Engineer- [7]PARK I W,KIM J Y,OH J H.Online biped walking pat- ing Universigy,Harbin,China.Dr.Ma was awarded the First ter generation for humanoid robot KHR-3(KAIST humanoid Prize of Science and Technology of the Helongjiang Province Ma- robot-3:HUBO)[C]//The 6 IEEE-RAS International chinery Industry Association and the Second Prize of Science and Conference on Humanoid Robots.Genova,Italy,2006: Technology of Helongjiang Province in 2009 and 2010 respec- 398-403. tively.He has authored or co-authored more than 20 technical [8]HELIOT R,ESPIAU B.Online generation of cyclic leg traj- articles in jourals and conference proceedings in the area of ectories synchronized with sensor measurement[J].Robot- mechatronics and instrumentation. ics and Autonomous Systems,2008,56(5):410-421. WANG Liquan was bom in Hebei, [9]FUKUOKA Y,KIMURA H,COHEN A H.Adaptive dy- China in 1957.He received a PhD in con- namic walking of a quadruped robot on irregular terrain trol theory and control engineering from based on biological concepts[J].The International Journal Harbin Engineering University (HEU). of Robotics Research,2003,22(3/4):187-202. He is currently employed by HEU as a [10]ARBULU M,YOKOI K,KHEDDAR A,et al.Dynamic professor.His current interests include bi- acyclic motion from a planar contact-stance to another onics,underwater robots,underwater construction equipment, [C]//IEEE/RSJ International Conference on Intelligent sub-sea oil industry equipment,and intelligent control engineer Robots and System.Nice,France,2008:3440-3445. ing.He has guided more than 50 graduate students in mecha- [11]ZONFRILLI F,WOLLHERR D,NAKAMURA Y.Walk- tronics engineering sub-seaoil industry equipment,and intelli- ing control of the humanoid UT-theta[C]//Proceedings of gent wntrol engineering.He has authored or co-authored more the 12th International Conference on Advanced Robotics. than 50 technical articles in journals and conference proceed- Seattle,USA,2005:698-704. ings.He is the chief editor of 5 textbooks in related research [12]KURAZUME R,TANAKA S,YAMASHITA M,et al. fields. Straight legged walking of a biped robot[C]//2005 IEEE/ ZHONG Zhi received B.S.and M. RSJ International Conference on Intelligent Robots and S.degrees in communications engineering Systems.Edmonton,Canada,2005:3095-3101. and a Ph.D.degree in instruments and [13]DIEDAM H,DIMITROV D,WIEBER P,et al.Online instrumentation engineering,all from Har walking gait generation with adaptive foot positioning bin Institute of Technology,Harbin,Chi- through linear model predictive control [C]//IEEE/RSJ na,in 1999,2001,and 2005 respective- International Conference on Intelligent Robots and Sys- ly.In 2006,he joined the College of Information and Communi- tems.Nice,France,2008:1121-1126. cation,Harbin Engineering University,Harbin,China.His cur- [14 ]HUANG Q,NAKAMURA Y.Sensory reflex control for hu- rent research interests include optical wireless and optical-elec- manoid walking J].IEEE Transactions on Robotics, tronics measurement. 2005,21(5):977-984