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1 BOLETIM TECNICO DA PETROBRAS VOL. 61, 017 Guest Editors: Hao WANG, Min DUAN Copyright 017, PB Publishing ISBN: ISSN: EISSN: Design of humanoid robot s complex martial 0art action and study of similarity / Projeto da ação complexa de arte marcial do robô humanóide e estudo de similaridade Guangjing Li Department of Physical Education, Tianjin University of Commerce, Tianjin , China Abstract: A motion trajectory generating method is proposed based on the base section. First, it divides the human body s motion into a basic motion segment, gives the kinematic constraints, and discusses the adjusting method of the stability of complex dynamic action. Then, it proposes the similarity function of the humanoid robot which imitates human action and considers the moving rhythm, and gives the trajectories solving method that meets the kinematic constraints and dynamics stability and has high similarity. Finally, by carrying on the experiment of Chinese kung fu sabreplay on humanoid robot BHR-, it verifies the effectiveness of this method. Keywords: humanoid robot, similarity, rhythm, dynamics stability, kinematic constraints Resumo: Um método de geração de trajetória de movimento é proposto com base na seção de base. Primeiro, divide o movimento do corpo humano em um segmento de movimento básico, dá as restrições cinemáticas e discute o método de ajuste da estabilidade da ação dinâmica complexa. Então, propõe a função de similaridade do robô humanóide que imita a ação humana e considera o ritmo em movimento e fornece o método de resolução das trajetórias que atende às restrições cinemáticas e à estabilidade da dinâmica e tem alta similaridade. Finalmente, ao realizar o experimento de sabreplay chinês do kung fu no robô humanóide BHR-, ele verifica a eficácia desse método. Palavras-chave: robô humanoide, semelhança, ritmo, estabilidade dinâmica, restrições cinemáticas BOLETIM TECNICO DA PETROBRAS 1

2 1. Introduction People hope that the humanoid robot can do complex and flexible actions like humans, only in this way, it can finish the mission to collaborate with human or replace human to do jobs. Takano and other people [1-3] proposed a method by capturing human action feature symbols to divide action mode, recognize action and generate action of humanoid robot, thereby establishing action patterns database. By capturing the human upper limb motion, Kim and others [4] proposed the mathematical representation method of characterizing the human upper limb motion. Using this method enables to make a humanoid robot do the similar motion with human upper limb. Nakazawa and other people [5, 6] proposed the method to mix humanoid robot action through matching body motions keyframes. Also, they studied the method of synthesizing humanoid robot realistic style action finally by action capture system to capture human motion and decompose according to action characteristics. By capturing body motion data, Yamane and others [7, 8] studied the gait dynamics simulation of humanoid robot and humanoid robot whole body action design method which is based on human motion data. By capturing the actor s dance action, Pollard and others [9] proposed the solution that meets the joint motion range and motion velocity of robot, to achieve the dance show of the humanoid robot upper body. The above discussion only describes the generating method of humanoid robot action at a relatively low speed. If the motion is fast, the dynamic stability of humanoid robot will become a key issue. In addition, the action of humanoid robot may be considered as the imitation to human action, and how to ensure that has a high degree of similarity with human action is an important subject which will be studied. This paper presents a humanoid robot action design method which considers the dynamic stability and rhythmic similarity. First, it divides the human body s motion into segments according to action characteristics. Then, it discusses how to solve the robot motion algorithm which has high similarity and meets the kinematic constraints. Finally, it proposes the humanoid robot motion trajectory generation algorithm which has high rhythmic similarity under the premise of meeting the kinematic constraints and kinetic stability.. System introduction.1 Model of Humanoid Robot The study object of this paper is humanoid robot BHR-, which has 3 degrees of freedom. The specific parameters is shown in Table 1. The appearance of BHR- humanoid robot is shown in Figure 1.. System Introduction Using the infrared passive digital optical motion capture system to obtain human body motion data. The system uses 1 optical cameras, the whole body of performer is posted 38 marker points, and the capture system record all the space coordinates of the marker points with the rate of 100 frames per second to obtain human motion data, and the accuracy can reach 0.mm. The process of extracting human body motion data by motion capture system is shown in Figure 1. The humanoid robot model is different from the human body model, the human body motion data can be transformed into the humanoid robot motion data with kinematic constraints through kinematic mapping. Dynamic matching is in dealing with the data after the kinematics mapping, to make it conform to the dynamic stability of the robot. It can be used to drive the humanoid robot to complete the stable motion process. The next section will discuss these two aspects in detail. 3. The generating of humanoid robot motion trajectory The motion of the human body is deemed to be composed of a series of basic motions, which are the smallest units of the motion sequence, in this paper, we call it base section for short. A base section may be repeated throughout the performance, which reflects the basic characteristics of the motion. Through the analysis of martial arts, dance and other human motions, we found that some typical actions frequently occur, and the performer will pause rhythmed in a certain position at a certain time, we call the paused posture a key pose, the transition action between the two key poses is known as the base section. The base section can be segmented according to the action of the whole body, and also according to the action of a certain body, which is because the action of each limb is different, the pause time may also be different, in this case, we can segment these parts base section respectively. The Key pose parameters of legs is shown as Table. Table1 Parameters of Humanoid Robot Parameters Head Torso Arm Thigh Calf Foot Length (mm) Quality (kg) SEPTEMBER 017

3 Human body motion capture Structure figure of joint maker point Human body model Motion retargeting to man-robot simplified model Figure 1 Process of human motion data acquiring In this paper, the humanoid robot will mimic the Chinese Kung Fu sabreplay. Sabreplay is based on sabreplay head wrapped in brain, adding other knife techniques such as splitting, chopping, hanging, lifting, clicking, collapsing. The style is bravely quick, impetuous, tightly-linked and powerful. The appearance action of sabreplay show is the key pose, so according to the appearance action segment base section of sabreplay. Note that the segmentation of upper and lower limbs is independent. Upper limb motion in space, which can not interfere with the surrounding environment, so that we can directly segment it based on the appearance action. Figure- is partial result after upper limb proceeding base section segmentation. The curve in the figure is the angular velocity of human arm sixth joint. Zero-speed region is lower limbs actions compared to upper limbs in appearance stage I. When carrying on base section segmentation and touching the ground in different appearance, Ground contact condition need to be combined. There are 4 main key postures in lower extremity s sabreplay action. They are feet supporting (level step), striding forward (One foot in the front, the other foot in the back), side step, posing as a pheasant standing on one foot, as shown in Figure 3. Each key pose is determined by a number of key parameters. In table 1, Pɷ -Waist position, D 1 -step lengths, Dɷ -step width, H a -ankle height. The key parameters are adjusted when matching the kinematics and dynamics of the lower limbs. Any of the transition action in two key positions can be used as the base section of the lower limb. The Segmentation result of arms in sabreplay action is shown as Figure. The key pose of legs in sabreplay action is shown as Figure Kinematics mapping Carry on kinematics mapping after the completion of the segmentation of the base section. Dynamic mapping is the processing procedure of data after kinematics mapping, so that it is in line with the dynamic stability of the robot and drive humanoid robot completing the steady motion. On the other hand, humanoid robot s action after kinematic mapping and dynamic mapping may be quiet different from human body. If required to reach the body s action standards as a sample and maintain consistency with the human body action, the humanoid robot should meet the constraint BOLETIM TECNICO DA PETROBRAS 14

4 Table Key Pose Parameters Of Legs key pose key parameter feet supporting striding forward side step posing as a pheasant standing on one foot Base section, D T, D w, D w, D t,, H a Apperance stage This paper uses the trajectory of the joint angle to evaluate the action similarity between human and robot. Apply motion capturing system and through the inverse kinematics calculation can directly get a simplified model of the human body s joint angle trajectory. T Use vector quantity θ h = [ q h1, qh,..., qhm ] as the joint angle of anthropometric dummy, vector quantity T θ r = [ q r1, qr,..., qrn ] is the robot s joint angle, and the similarity function can be written as: 1 S( qhi, qri ) = n qr q i hi (1) 1+ ( ) q q i= 1 ri max ri min q ri max and q ri min is the maximum and minimum values of joint angles in the motion range of humanoid in the joint I. n is the number of degrees of freedom. The similarity function value is 0 < S 1. When S = 1. The humanoid robot motion similarity reached the maximum value, which indicate humanoid robot/s joint motion trajectory is the same as human body. 4. Kinematics Constraints and Mapping Figure Segmentation result of arms in sabreplay action When the joint angle of humanoid robot is exactly same as that of human body, similarity function value is maximized. But with the difference between models in geometry and joint range, all above may have conflict with kinematics constraints of humanoid robot. (a) Mechanical constraints Mechanical constraints include joint angle range, motion space, and other physical contact. First, joint angle range must be within a certain range, the formula is: q ri min q q () ri ri max Figure 3 Key pose of legs in sabreplay action condition of action similarity. In the following part, we mainly discuss the kinematic constraint conditions and humanoid robot s motion similarity 4.1 Similarity Function The similarity evaluation of human and robot action can be classified as evaluation geometry similarity between objects. Wherein, i = 1,... n. n is the number of degrees of freedom. Taking into account the physical contact, the following constraints must be met: d jk 0 1 d jk = min ( ( x j xk ) + ( y j yk ) + ( z j zk ) ) (3) Wherein, (x j, y j, z j,) and (x k, y k, z k,) are humanoid robot. In space coordinate of any two point (P j, P k ) of body, d jk is the shortest distance. (b) Ground contact constraints Ground contact constraints between foot and ground is the key issue. Since the length of humanoid robot s leg and that of human skeleton disproportionate, ground constraints tend 15 SEPTEMBER 017

5 not to be met, leading to such issues such as sliding, missing step, falling into. In the process of one leg to two legs supporting on ground, the swinging foot should fall on ground in planned position and direction. In the condition of stepping off, foot is vacated, shown in Figure 4(a). Conversely, the foot is into the ground below the surface, seeing Figure 4 (b). When two legs stand, feet should be fixed on ground without sliding. However, when the joint angle data of human s body is directly applied to humanoid robot, the position of one foot or two feet may change, that is to say sliding, shown in Figure 4(c). In order to keep the position and orientation of feet and ground, you must meet the following kinematic constraint equations, the formula is: Pr z + F w rf = z = P l lf = 0 + F lw = P Where in, z lf, z rf is the space coordinate value of the feet of humanoid robot in Z direction.p l P r is the position vector of feet. F lw, F rw is the motion position relationship between feet and waist. is the position vector of waist. According to the spatial coordinate of feet, the equation calculates the result of kinematics which must be equal to the space coordinate value of waist in contact with the ground under feet. (c) Motion solver Based on the above analysis, when meeting the kinematic constraints, the highly similar humanoid robot motion can be attributed to the following questions: w (4) maxs(q ri, q hi ) (q ri, q hi ) equation () ~ (4) (5) Humanoid robot has two stages in motion: supporting with single leg and supporting with two legs. The phenomenon of missing foot and falling into occurs in the process that change from supporting with single leg to supporting with two legs. Sliding phenomenon occurs in the stage of supporting with two legs. Therefore, we discuss the two cases in the humanoid robot motion which are shown by equation (5): the motions from supporting with single leg to two legs, and supporting with two legs to two legs. Figure 5 is the motion matching algorithm of supporting with single leg to two legs. First, according to constraints (4) to calculate the landing range of the dangling leg, and then, by traversing algorithm to find all the landing motion trajectory sets which satisfy the kinematic constraints () and (3), according to equation (1) to calculate the similarity function value of each landing motion trajectory and compare with each other, and finally, determine the humanoid robot landing motion trajectory that has the largest action similarity from the sets of landing motion trajectory. The trajectory obtained through kinematic mapping is the key frame of robot motion similarly, it needs to used cubic (b)falling into (a)stepping off Figure 4 Ground contact problems Calculate the position of the waist by the supporting leg Calculate the landing range of the dangling leg by equation (4) xf ( xf min, xf max ) y ( y, y ) f f min f f f min f max x = x + x y = y min + y f f f Inverse kinematic solutions Similarity function solutions xf x y y f f (max)? f (max) Satisfy the constraints (), (3) Determine the final trajectory with the maximum similarity (c)sliding Increase x, y Figure 5 Motion mapping algorithm from supporting with single leg to two legs spline interpolation method again to solve the actual trajectory of humanoid robots. f f BOLETIM TECNICO DA PETROBRAS 16

6 5. Experiment To carry out experimental verification by use humanoid robot BHR- performing Chinese Kung Fu sabreplay. In order to prevent the robot falls, real-time sensing reflex control is applied. The poses showed in Figure 6 (a) is the key poses of the sabreplay action performing by the martial arts athletes. Figure 6 (b) is the key poses of the corresponding people-robot simplified model after the action redirect. Comparing Figure 6 (a) with Figure 6 (b), it can be known that getting the action of people-robot simplified model may exhibit the main action features of sabreplay action, which are able to achieve the action quite close to human action. Figure 6 (c) is the sabreplay action performed by humanoid robot entity, it can be seen that the action of humanoid robot is similar to the action of human. Regarding the right arm shoulder joint of humanoid robot as the example, the solid line is the right arm shoulder joint angle trajectory in X direction obtained by this method, it can be seen that the track is smooth and continuous, the data is available. However, due to the kinematic constraints of humanoid robot is different from human body model, this joint angle trajectory can not be directly applied to humanoid robots. After kinematics mapping and stability adjustment, the joint angle trajectory becomes more smooth, and after processing the points beyond the scope of joint is within the joint angle range (such as point a); in the stage of the angle changes rapidly, by changing the rhythm of motion, the speed is slowed down. At the end of the sabreplay action, the speed of the motion is slow and the range of motion is small, at this time, the joint angle trajectory is consistent, which is very close to human action. (a) The sabreplay action performed by human actor (b) The sabreplay action performed by people-robort simplified model 6. Conclusions In this paper, we discuss the captured robot kinematics mapping and similarity evaluation based on human motion: (1) propose the motion trajectory generating method based on the base section. () discuss the kinematic constraints, such as ground contact conditions. It proposes the robot motion algorithm which has high similarity and satisfy the kinematic constraints. (3) by carrying on the experiment of humanoid robot s sabreplay, it verifies the effectiveness of this method. 7. Reference [1] Kanehiro F, Inaba M, Inoue H. Action acquisition frame work for humanoid robots based on kinematics and dynamics adaption. In: Proceeding of IEEE International Conference on Robotics and Automation. IEEE, ~1043 [] Cui, H.Y., et al. Semantic-based retrieval using various visual features for real-world images. Journal of (c) The sabreplay action performed by humanoid robot Fig. 6 The sabreplay action performed by human actor and humanoid robot Mechanical Engineering Research and Developments, (): p [3] Gao, Z.B. and H.Y. Gao, Theoretical analysis and confirmatory measurement for profile grinding of guide roller for tapered roller superfinishing. Journal of Mechanical Engineering Research and Developments, (1): p [4] Pollard S, Hondgins J, Riley M J, Atkeson C. Adapting human motion for the control of a humanoid robot. In: Proceedings of IEEE International Conference on Robotics and Automation. IEEE, ~1397 [5] Yamane K, Nakamura Y. Dynamics filter-concept and implementation of online motion generator for human 17 SEPTEMBER 017

7 figures. In: Proceeding of IEEE International Conference on robotics and Automation. IEEE, ~695 [6] Nakaoka S, Nakazawa A, Yokoi K, Hirukawa H, Ikeuchi K. Generating whole body motion for a biped humanoid robot from captured human dances. In: Proceedings of IEEE International Conference on Robotics and Automation. IEEE, ~3910 [7] Nakazawa A, Nakaoka S, Ikeuehi K. Matching and blending human motions using temporal scalable dynamic Programming. In: Proceedings of 004 IEEE/ RSJ International Conference on Intelligent Robots and Systems. IEEE, ~94 [8] Ruchanurucks M, Nakalka S, Kudoh S, Ikeuchi K. Generation of humanoid robot motions with Physical constraints using hierarchical B-spline. In: Proceedings of 005 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, ~679 [9] Noritata K, Kato S, yamakita T, Itoh H. A motion generation system for humanoid robots-taiji motion. In: Proceeding of International Symposium Micromechatronics and Human Science ~69 BOLETIM TECNICO DA PETROBRAS 18