Online Free Walking Trajectory Generation for Biped Humanoid Robot KHR-3(HUBO)

Transcription

1 Proceedings of the 6 IEEE International Conference on Robotics and Atomation Orlando, Florida - May 6 Online Free Walking Trajectory Generation for Biped Hmanoid Robot KHR-3(HUBO) Ill-Woo Park, Jng-Yp Kim, Jngho ee and Jn-Ho Oh Hmanoid Robot Research Center (N9), Department of Mechanical Engineering Korea Institte of Science and Technology (KAIST) 373- Gseong-dong, Yseong-g, Daejeon 35-7, Repblic of Korea {mrqick\kirk\jngho77}@hbolab.kaist.ac.kr, jhoh@kaist.ac.kr Abstract - This paper describes an algorithm abot online gait trajectory generation method, controller for walking, brief introdction of hmanoid robot platform KHR-3 (KAIST Hmanoid Robot 3: HUBO) and experimental reslt. The gait trajectory has continity, smoothness in varying walking period and stride, and it has simple mathematical form which can be implemented easily. It is tested on the robot with some control algorithms. The gait trajectory algorithm is composed of two kinds of fnction trajectory. The first one is cycloid fnction, which is sed for ankle position in Cartesian coordinate space. Becase this profile is made by sperposition of linear and sinsoidal fnction, it has a property of slow start, fast moving, and slow stop. This characteristics can redce the over brden at instantaneos high speed motion of the actator. The second one is 3 rd order polynomial fnction. It is continos in the defined time interval, easy to se when the bondary condition is well defined, and has standard vales of coefficients when the time scale is normalized. Position and velocity vales are sed for its bondary condition. Controllers mainly se F/T(Force/Torqe) sensor at the ankle of the robot as a sensor data, and modify the inpt position profiles (in joint angle space and Cartesian coordinate space). They are to redce nexpected external forces sch as landing shock, and vibration indced by compliances of the sensors and redction gears, becase they can affect seriosly on the walking stability. This trajectory and control algorithm is now on the implementing stage for the free-walking realization of KHR-3. As a first stage of realization, we realized the marking time and forward walking algorithm with variable freqency and stride. Index Terms - HUBO, Hmanoid, Biped walking, Trajectory planning I. INTRODUCTION The research in hmanoid robot is now on its way of diverging into varios categories. The research on sch areas as artificial intelligence, hardware development, realization of biped locomotion, and interaction with the environment are gaining a rapid phase of development with the help of the rapid growth of technology. The research on hmanoid robots has gained a particlar interest in this new phase as hmanoids tend to change the concept of the robot. In the past, robots were confined to the indstry carrying ot sch jobs as welding, and parts-assembly (atomobile and electronic devices) in that the objectives, specification and optimal design parameters were clearly defined with concern to the economic aspects, prodctivity and efficiency. As the economical paradigm is changing from mass prodction to small qantity batch prodction, people s concept of the robot has been gradally diverging. By today, it has come to a sitation, where the robot shold be able to perform a wide variety of fnctions that helps people in their daily life. The important featres of biped hmanoid robots are the hman-like shape and movements. The robot always gets the expectation of people that this type of robot can walk and move like a hman. It is also expected that it can climb p stairs, walk on neven terrain, rn, and dance. Many researches now show the realization of them. Honda hmanoid []~[3], WABIAN series of Waseda University [4],[5], H6,7 of Tokyo University [6],[7], HRP of AIST [8],[9] and JOHNNIE [9] are the well known hman scale biped hmanoid robots. Mostly, the dynamic walking control strategy of biped robots is based on the walking pattern generation and modification, which considers the stable ZMP (Zero Moment Point) trajectory and online balance control. We made walking trajectory first, and its validity is proved by experiment with the real platform. This research process has been done in all KHR []~[] series. Several online controllers based on the sensory feedback are reqired becase the actal ZMP trajectory is different from the desired ZMP trajectory de to reasons sch as the nevenness of the srface, sensing errors, and imperfect dynamic model of the robot. Takanishi et al. have stdied abot online walking pattern generation and walking stabilized control by sing pper body motion based on the ZMP information [4],[5]. Kajita et al. introdced a method of the biped walking pattern generation by sing a preview control of ZMP that ses ftre reference [8],[9]. Kagami et al. sed a torso position compliance control method to track a given ZMP trajectory [6],[7]. We describe a novel gait trajectory method for online free walking pattern generation method, controllers for stabilization sing F/T sensor, a brief introdction of the robot platform KHR-3 (HUBO), and its simlation and experimental reslt (marking time mode with variable walking period) are presented in this paper. The gait trajectory algorithm ses simple and continos fnctions which can be easily implemented on the real robot. We can measre the grond reaction force, moment, and ZMP directly. The controller algorithm which modifies the trajectory stabilizes the robot by tilizing the data /6/$. 6 IEEE 3

2 II. ONINE GAIT GENERATION A. Coordinate frame for gait trajectory with y. We make pelvis - y trajectory on the y frame and translate it onto y frame. Z z X x x y y Y B. Trajectory generation on sagittal plane (X - direction) We se cycloid fnction for swing leg ankle position, and 3 rd order polynomial interpolation for pelvis center in x- direction. For simplicity, we describe the trajectories with respect to x -coordinate frame. Eqation () and () are the trajectory eqations of the swing leg ankle position and the pelvis center position. A Fig. Coordinate frame for gait trajectory x B t t t Fig. Sagittal plane view of coordinate frame y y y Y y t t t Fig. 3 Coronal plane view of coordinate frame Fig. shows the coordinate system. x-y-z is local coordinate frame which is located on the pelvis center and X- Y-Z is global coordinate frame, which has same origin initially. Walking pattern for lower body is generated on the basis of these coordinate frames. We made three position parameters, left/right ankle position and pelvis center position. Those position parameters are implemented to the robot after coordinate transformation onto x-y-z coordinate frame. Fig. shows coordinate frame for forward walking. x is located on the front spporting foot dring the other leg swings in x direction. t is the start time of swing from DSP (Doble Spport Phase) and t is the end time of swing to the other DSP. If t exists, t is that the swing ankle and pelvis center coincide with the spporting ankle in x direction. We make the pelvis center - x trajectory to have the position be in the center of two ankles at t and t. First, we generated the pelvis and the swing leg trajectory in this local coordinate frame - x, and implemented to the robot on the basis of x frame by translating the coordinate frame. Fig. 3 shows y and y coordinate frame. y is on the grond and has same direction x C _ ( ) t t sin t t Ank x t b f b () t t t t 3 tt tt tt 3 t t t t t t P _ x t a a a a () Where, b and f are the swing ankle positions with respect to the coordinate frame x when the time t is t and t. a i (i=,,, 3) are polynomial coefficients which can be fond by the bondary conditions as following. The bondary conditions of P _ xt () are fallowed as, P _ xt ( ) b/, P _ xt ( ) f/, P _ xt ( ) b, P _ xt ( ) f. If t exists, bondary conditions and time intervals are slightly modified. The time intervals are divided into t t t and t t t, the trajectory conditions at time t are P_ x ( t) and P _ xt ( ) f b. Where, and are constant coefficients. Those conditions mean that the pelvis center position, when t is t, t and t, is on the center of two ankles, and their velocities (at t= t, t, and t ) are in proportion to the displacement between ankles. This condition preserves the trajectory continity between the end of crrent step and the start of next step. We can find ot the vale of t from the condition that two ankles are coincided in x -direction at t. t t b cos t t b f The spporting front ankle and swing ankle position profiles can be calclated by simple coordinate translation. C. Trajectory generation on coronal plane (y - direction) We se 3 rd order polynomial interpolation method as a pelvis center trajectory in y frame. 3 tt tt tt 3 t t t t t t P _ yt ( ) a a a a (4) Where a (i=,,, 3) is polynomial coefficient. i Eqation () is a cycloid fnction. This type of fnction is a part of ellipsoidal eqation written in parametric form. (3) 3

3 The bondary conditions of (4) are similar to (3) case. We made the pelvis sway amplitde to have a peak vale at t=(t+t)/. Their bondary conditions at t, (t+t)/ and t are P_ y ( t), P _ ~ y (( t t) / ) Sy, P_ y ( t), P _ y ( t), P _ ~ y (( t t) / ), and P _ ~ y ( t). Where, Sy and are sway amplitde and velocity of pelvis at the time. We assme that the vale of is constant becase of the trajectory continity. The sign of Sy and is to be changed by lifting p the other leg. We se the -cos() velocity profile fnction as y-direction ankle position. This means whatever the body center trajectory to be, we can add it as shown in Fig. 4 and its position trajectory has a shape of cycloid fnction. Position Trajectory (Px, Py, Pz) Velocity Profile (Vx, Vy, Vz) Inverse Kinematics Fig. 4 Trajectory implementation block diagram Robot Joint Command This gait generation method preserves its continity and differentiability with the change of walking cycle and stride. Fig 5. shows the simlation reslt. Where, t j denotes t i i time at j-th step and the other vales are b =, f =4, b =4, f =. This figre is described in the global X-Y-Z coordinate frame. stride. It is becase the gait is generated by combination and sperposition of smooth fnctions with proper conditions. We have the experimental reslt with variable walking period in marking time mode in section V. ) Simplicity: It is easy to implement into the biped robot, becase we se 3 rd order interpolation trajectory and cycloid fnction and we can simply pdate the bondary conditions and step period in every step. 3) Decopled property: The trajectory on each axis X-Y- Z is decopled from each other. displacement (mm) Pelvis center - X ankle Pelvis center - Y time (msec) Fig. 6 Profile simlation sample (t does not exist) t t Pelvis center - X ankle ankle Pelvis center - Y t t t t Walking Parameters Setting III. CONTROER displacement (mm) 3 Walking Type Selection Walking Pattern Generation Real-Time Balance Control anding Timing Controller time (msec) Inverse Kinematics Fig. 5 Profile simlation sample (t exists) When b f is negative, t does not exist. This means the swing foot (shown in Fig. 6: ankle) does not cross over the spporting foot. This gait generation method has following merits. ) Continity: This gait generation method can make smooth trajectories in any walking period and X-Y direction Joint angle Ref. Joint Angle PD controller ROBOT Forces at feet anding Detection Damping Moments at foot anding Orientation Controller We can adjst the DSP ratio by setting the vale t j and t j+ differently. b and f are all positive in forward walk and all negative in backward walk. Fig. 7 Controller block diagram for trajectory implementation 33

4 Fig. 7 shows overall control architectre for experiment. All joints of the robot are controlled by PD servo controller. After we generate the walking patterns and joint angles described in previos section, we modify them with controllers by sensory feedback. We control the ankle joint angles by sing F/T sensors which can detect the grond reaction forces and moments. Those controllers can redce the oscillations and shocks indced by abnormal contact of the foot by modifying the original angle trajectory. Those are enabled and disabled by switching (as shown in Fig. 7 and ) on the base of gait pattern and F/T sensor data. A. Controllers for walking We se following controllers for walking experiment. ) Damping: The vibration of whole body in SSP (Single Spport Phase) is mainly cased by the compliance of F/T sensor and harmonic drive redction gear at ankle. We modeled the robot in SSP as the inverted pendlm with compliant joint as shown in Fig. 8. g K l T m where, C : damping coefficient, K : the stiffness, : the reference ankle joint angle, and : the compensated reference ankle joint angle. m 3) anding timing: The landing timing controller prevents the robot from being nstable dring landing by the modification of walking pattern schedle. That is, if the foot does not land on the grond at the end of stretch at the prescribed schedle, the time schedler of the main compter will halt the motion flow ntil the foot contacts the grond. Therefore, the real walking motion can follow the prescribed walking pattern despite anomalies emerging dring walking. T anding orientation Fig. The landing orientation control Fig. shows controller activation timing diagram. The damping controller which controls roll and pitch angle of the ankles shown in Fig. by sing F/T sensor is activated in spporting phase and recovered in swing phase. Cartesian coordinate controller denotes that the control command acts on the position of ankles (landing timing controller) and pelvis (ZMP) in this paper. ZMP controller is activated in DSP at stop stage. m Fig. 8 Inverted pendlm model with compliant joint in SSP T mgl ml K( ) (5) m k d ˆ (6) The eqation of motion and the control law are (5) and (6). m K ( ˆ ˆ ) s ˆ s y T Fig. Schematic of KHR-3 kd where, T: measred torqe, ˆ : K ml g l, ˆ : K ml, k d : damping control gain, and m : ankle joint angle controller inpt. Fig. 9 Damping controller block diagram ) anding orientation: This controller integrates the measred torqe over time to achieve soft landing and stable contact by adapting the ankle joints to the grond srfaces (Fig. ) inclination. It makes the ankle joint to be compliant dring short period at landing. The control law of the landing orientation control is (7). m T ( s) (7) C s K Observer Damping R Damping Orientation R Orientation Timing R Timing ZMP SSP SSP+DSP SSP SSP Grond Air SSP DSP DSP F/T >= Spporting condition (DSP start) F/T >= Grond toch condition, -Z direction stretch stop F/T < Grond toch condition, -Z direction stretch controller recover Controller activation Control variable recover Ankle joint angle controller XYZ Cartesian coordinate controller DSP Fig. Controller timing diagram (Right foot starting case) 34

5 Fig 3 Motion control process in KHR-3 IV. HARDWARE DESCRIPTION We developed biped hmanoid robot KHR-3 since 4 shown in Fig. 4. Its height and weight is 5cm and 55Kg. It has 4-DOF (-DOF in leg, 8-DOF in arm, 6-DOF in head, 4-DOF in hand and -DOF in trnk). It has F/T sensors in the ankles and wrists, CCD-cameras in the head, tilt sensors to measre the inclination of grond in the feet, and inertia sensor in the trnk. It has distribted control hardware system based on CAN commnication. The robot has been pgraded from KHR-. Its mechanical stiffness of links and redction gear capacity of joints have been modified and improved. Increased stiffness makes it have low ncertainty of joint position and link vibration, which affect its stability. The joint controller, motor drive, battery, sensors and main controller (PC) are designed to be installed in the robot itself. All servo controller nits for each actator and all sensors are connected with CAN commnication as shown in Fig. 5. The overall specification of KHR - 3 is given in Table I. Fig. 5 System configration of KHR-3(HUBO) TABE I SPECIFICATION OF KHR-3 Research term 4. ~ Weight 55Kg Height.5m Walking Speed ~.5Km/h Walking Cycle, Stride.75~.95s, ~64cm Grasping Force.5Kg/finger Actator Servo motor + Harmonic Speed Redcer + Drive Unit Control Unit Walking Control Unit, Servo Control Unit, Sensor Commnication Unit, Commnication Unit Sensors Foot 3-Axis Force Torqe Sensor, Inclinometer Torso Rate Gyro & Inclination Sensor Power Battery 4V/3.3Ah EA, V/6.6Ah - Section External Power V, 4V (Battery and External Power Spply Changeable) Operation Section aptop compter with wireless AN Operating System (OS) Windows XP and RTX Degree of Freedom 4 DOF Fig. 4 Hmanoid robot KHR-3(HUBO) V. EXPERIMENT We had an experiment of marking time with variable walking period on the floor. The prpose of this experiment is to realize the gait generation method stated in chapter I. The trajectory has the continity and the smoothness for those periods as shown in Fig. 6. The periods that we sed are 75, 85 and 95ms. Sy for each period is 47, 6, and 67mm respectively. As the walking speed goes slow, we need to have large Sy to keep stability. We changed the period from 75 to 95ms with ms step at 4.875(A),.85(B) and 6.55s(C). We added 4% of Sy in starting step time (~75ms) becase of the starting momentm effect. Fig. 7 shows the forward walking experiment reslt. We changed the step length of forward walking with 8ms step time. The step lengths are mm (start to 7.s), 7mm (7.s ~ 4.4s), 5mm (4.4s~). It is shown that the continity of the walking pattern with step length change is preserved. It is shown that there is an abnormal landing at time A. This sitation happens when there is no landing signal is detected in despite of its flly stretched leg. The landing timing controller is activated at that time. All motion flows are halted and the controller waits the land OK signal. 35

6 Pelvis Y-Position(mm) Ankle Joint Angle(Deg) Ankle Z-Position(mm) Ankle X-Position(mm) Pelvis Y-Position(mm) Ankle Joint Angle(Deg) Ankle Z-Position(mm) A 4.875sec B.85sec C 6.55sec Fig. 6 Experimental reslt (Marking time) Fig. 7 Experimental reslt (Forward walk) eft eft Right Right eft ankle Right ankle time(sec) 5-5 eft X Right X eft 4 eft Right Right eft Right time(sec) VI. CONCUSION We proposed a novel online gait trajectory generation method which has the continity in variable period and stride to realize the varios bipedal walking gaits. It also has simple mathematic form and coordinates decopled property. The method is proved by simlation and experiment, which we applied the control algorithm to the hmanoid robot platform KHR-3. VII. FUTURE WORK In this paper, we implemented the gait generation algorithm of marking time mode on the robot. We will realize varios walking modes sch as non-crossing gait (t does not exist case.) with variable freqency and stride. This is important for the free walking gait. ACKNOWEDGEMENT This research was mainly spported by MOCIE (Ministry of Commerce, Indstry and Energy) and partly spported by HWRS (Hman Welfare Robotic System) and BK- (Brain Korea - ) project. REFERENCES [] K. Hirai, Crrent and Ftre Perspective of Honda Hmanoid Robot, in Proc. IEEE/RSJ Int. Conference on Intelligent Robots and Systems, pp. 5-58, 997 [] K. Hirai, M. Hirose, Y. Haikawa, and T. Takenaka, The Development of Honda Hmanoid Robot, in Proc. IEEE Int. Conf. on Robotics and Atomations, pp.3-36, 998 [3] Y. Sakagami, R. Watanabe, C. Aoyama, S. Matsnaga, N. Higaki, and K. Fjimra, The intelligent ASIMO: System overview and integration, in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp , [4] J. Yamagchi, A. Takanishi, and I. Kato, Development of a Biped Walking Robot Compensating for Three-Axis Moment by Trnk Motion, in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp , 993 [5] H. im, Y. Kaneshima, and A.Takanishi, Online Walking Pattern Generation for Biped Hmanoid Robot with Trnk, in Proc. IEEE Int. Conf. on Robotics & Atomation, pp. 3-36, [6] K. Nishiwaki, T. Sgihara, S. Kagami, F. Kanehiro, M. Inaba, and H. Inoe, Design and Development of Research Platform for Perception- Action Integration in Hmanoid Robot: H6, in Proc. IEEE/RJS Int. Conf. on Intelligent Robots and Systems, pp , [7] S. Kagami, K. Nishiwaki, J. J. Kffner Jr., Y. Kniyoshi, M. Inaba, and H. Inoe, Online 3D Vision, Motion Planning and Biped ocomotion Control Copling System of Hmanoid Robot : H7, in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp , [8] K. Kaneko, F. Kanehiro, S. Kajita, K. Yokoyama, K. Akachi, T. Kawasaki, S. Ota, and T. Isozmi, Design of Prototype Hmanoid Robotics Platform for HRP, in Proc. IEEE Int. Conf. on Inteligent Robots and Systems, pp , 998 [9] S. Kajita, F. Kanehiro, K Kaneko, K Fjiwara, K Harada, K Yokoi, and H. Hirkawa, Biped Walking Pattern Generation by sing Preview Control of Zero-Moment Point, in Proc. IEEE Int Conf. on Robotics & Atomation, pp. 6-66, 3 [] Jng-Hoon Kim and Jn-Ho Oh, Realization of dynamic walking for the hmanoid robot platform KHR-, Advanced Robotics, Vol. 8, no. 7, pp , 4 [] Jng-Yp Kim, Ill-Woo Park, and Jn-Ho Oh, Design and Walking Control of the Hmanoid Robot, KHR-, International Conference on Control, Atomation and Systems, pp , 4 [] Jng-Yp Kim, Ill-Woo Park, Jngho ee, Min-S Kim, Baek-Ky Cho and Jn-Ho Oh, System Design And Dynamic Walking Of Hmanoid Robot KHR-, IEEE International Conference on Robotics & Atomation, 5. 36