IROS2019国际学术会议论文集 0557

Effect of arm swinging and trunk twisting on bipedal locomotion Ryo Onishi 1 Ryoma Kitamura1 Takashi Takuma1 and Wataru Kase1 Abstract It is expected that human locomotion in which the trunk twists and arms swing provides stability as well as compensation for the angular momentum because the trunk and arms are placed over legs and then their position and the acceleration infl uence the bipedal locomotion This paper presents a bipedal robot equipped with a trunk embedding a viscoelastic joint and two arms away from the midline of the trunk Physical experiments show that a passive oscillation of the viscoelastic trunk joint around the yaw axis vertical to the ground and a swing of heavy arms provided an oscillation of zero moment point ZMP in the lateral direction and a small oscillation in the anteroposterior direction This is despite the fact that the robot does not have a roll joint and the arm swings back and forth Numerical analysis supports the results of the physical experiments through a simple model and by expressing ZMP trajectory showing that the arm swinging facilitates anti phase locomotion in which right arm and left leg swings ahead and vice versa I INTRODUCTION A passive walker that utilizes its body dynamics such as a center of mass and joint viscoelasticity has been gathering attention because of its energy effi ciency and autonomous generation of the locomotion A design of a quasi passive walker is based on the passive walker The design equips a small number of actuators that compensate for energy loss due to landing impact Wisse et al adopted McKibben pneu matic actuator to drive joints of the quasi passive walker 1 We developed a 3D bipedal robot driven by the McKibben pneumatic actuators 2 One of the prominent designs of the walker is that the robot equips a human like trunk mechanism by embedding viscoelastic joints and a suffi ciently heavy arm It does not embed roll joints to move sideways for a minimum number of joint and due to mechanical limitations From the viewpoint of the passive walker that utilizes body dynamics behavior of the upper body including the trunk and arm mass position and acceleration is very important because the positions of the trunk and arms are higher than the legs This means that stability of the locomotion is infl uenced by the behavior of the upper body In a research fi eld of bipedal locomotion based on zero moment point ZMP in 80s and 90s the motion of the upper body is discussed 3 Some researchers have proposed a method to compensate for angular momentum while walking 4 and the fl ying phase of running using the upper body 5 Although some research on the trajectory based locomotion mentioned above have focused on the effect of the upper body in a research fi eld of passive and quasi passive walker that utilizes body dynamics including an upper body few 1 Ryo Onishi Ryoma Kitamura Takashi Takuma and Wataru Kase are with Faculty of Engineering Osaka Institute of Technology Japan takashi takuma oit ac jp studies have discussed the infl uence of the upper body 1 and few attempted to utilize such an effect of the upper body Authors reported an effect of the viscoelastic trunk joints though the robot is restricted on a sagittal plane 6 In human locomotion the motion of the trunk and swing ing arms are effectively utilized Collins et al compared the walking performances of a person whose arm swing was restricted to an individual with unrestricted arm swing and they concluded that the person who was able to swing the arms achieved higher performance 7 Mirelman et al reported the effect of the arm swinging 8 Rotation of the upper body is also an important factor for locomotion Some researchers have observed the rotation of the human pelvis 9 and shoulder rotation 10 In particular a combination of arm swinging and trunk rotation around yaw axis which is vertical to the ground is a key mechanism for bipedal locomotion Because the trunk and arms are placed above legs as mentioned above the motion of the upper body infl uences the stability of the locomotion as well as the compensation for the angular momentum We then focused on the twisting of the trunk and swinging arms The trunk is supported by the viscoelastic muscles and then the trunk oscillates not only actively but also passively The arms are set from the midline of the trunk and the motion of the arm infl uences the motion of the upper body not only in anteroposterior but also but also lateral direction In this paper we assume that the trunk oscillates passively around the yaw axis with viscoelasticity and the oscillation is generated by an active arm swinging We observe a stability of the locomotion by changing the motion of the swinging arm ZMP is used as a criterion of the stability and a locus and a trajectory of ZMP is observed In the physical experiment a locus of ZMP is observed according to different weights of the arm and types of the trunk In the analysis a simple model based on the physical robot is constructed and a trajectory of ZMP that supports the result of the physical experiment is calculated The contents of the paper is that the construction of the physical robot is explained in Section 2 the physical experiments are shown in Section 3 trajectory of ZMP is derived by using a simple model in section 4 and they are concluded in Section 5 II PHYSICAL ROBOT MODEL A Frame model Figure 1 displays the 3D bipedal robot developed in this study 2 The robot is driven by McKibben pneumatic actuators and it has a trunk and arms Figure 2 shows the framework of the developed bipedal robot 2 As shown in the fi gure an absolute coordination whose origin is set 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE799 at the center of foot is set The x y and z axes in the fi gure are referred to as the pitch axis roll axis and yaw axis respectively The knee and hip joints of the robot rotate around the pitch axis Unlike 2 the ankle joint around the pitch axis is fi xed The robot does not have a roll joint on the ankle and hip The trunk has a viscoelastic joint at the bottom of the trunk Therefore the joint does not actively drive but passively oscillates under the infl uence of an external force The arm rotates around the pitch axis The size and mass of each link are shown in Table I The mass and length are based on the physical robot as will be explained later In the experiment arms 1 and 2 are switched to observe the difference in their behavior For the comparison the trunk is fi xed such that it functions as the rigid body Fig 1 Physical 3D bipedal robot 2 Trunk joint x z a Front view qa y z b Side view Fig 2 Robot frame B Muscle confi guration Figure 3 a shows the muscle confi guration of the physical robot arm A joint is driven by the antagonistic and agonistic muscles attached to it Muscles number 1 and 3 in Figure 3 a are set at the rear side and the muscles number 2 and 4 are set at the front side Furthermore muscles number TABLE I SIZE AND MASS OF THE LINKS Length mm Width mm Weight kg arm 1380250 3 arm 2700701 1 trunk600601 2 thigh460600 5 shank450500 5 foot3501000 4 1 and 2 are made of antagonistic and agonistic muscles to drive one joint The details of the joint mechanism have been explained in 11 The swinging of the arms is driven by four muscles while the hip and knee joints are not muscle driven rather their joints are fi xed by setting the inner pressure of the muscle higher to fi x the joints 12 34 a Muscle confi gu ration 1 2 3 4 Time Exhaust Supply right left b Valve operation Fig 3 Antiphase swinging using pneumatic actuators muscles number 1 and 3 are at the rear side of the actuator Figure 3 b illustrates the supply and exhaust time se quence of air valve that causes the arm to swing The on Off valve SMC VQZ1321 6L1 C6 was used because it is lighter than a conventional fl ow control valve Therefore a joint trajectory is not sinusoidal but a rectangular wave In the experiment the air supply was adjusted such that the arm swings forward at a 30 and backward at a 10 C Trunk confi guration Figure 4 a shows the schematic design of the trunk mech anism attached with an elastic joint The trunk is constructed using rigid chemical wood and viscoelastic rubbers as shown in Figure 4 b and 4 c Each part has two holes and a non extensible string passes through each hole One of the terminals of the string connects with the winch to maintain a certain viscoelasticity by tuning the angle of the winch as shown in the Figure 4 a Because the trunk has some joints and the rubber is deformed around not only the yaw axis but also the pitch and roll axes a unit that restricts the rotation around only the yaw axis is attached at the bottom trunk joint while the others are fi xed The parts for the restriction are attached to the upper and bottom rigid bodies that sandwich the bottom rubber and prevent rotation around the roll and pitch axes In order to rotate around the yaw axis a low friction board is inserted between the parts The other joints are fi xed using light aluminum boards as shown in Figure 800 a Fixing by using a string b Rigid ma terial c Viscoelastic material Aluminum board low friction board d Single viscoelastic yaw joint Aluminum board e Rigid trunk Fig 4 Trunk confi guration 4 d Furthermore as shown in Figure 4 e all trunk joints are fi xed using aluminum boards to achieve the rigid trunk in the experiment the behaviors of the rigid trunk is compared with that of the viscoelastic trunk The trajectory of the ZMP was used to evaluate the behavior When the ZMP oscillates and is placed on the foot the robot is considered to fulfi ll the necessary conditions for stable locomotion Furthermore to measure the ZMP the corresponding center of pressure CoP is recorded Figure 5 shows the equipment used for measuring the CoP As shown in Figure 5 a the reaction forces at the corner of foot fi i 1 2 8 are measured and the CoP is calculated For measuring the force strain gages are pasted on a board such that the corner of the foot contacts with the board and stoppers are attached at the side of the board to prevent rotation around the yaw axis Besides we assume that the stopper does not affect the vertical force Figure 5 b shows the physical measurement board The position of the CoP Px Py is calculated as follows Px P xifi P fi Py P yifi P fi where xi yi is the position of the pressure sensor based on the coordinate of x y z y x z front rear f1 f2 f3 f4 f5 f6 f7 f8 a Schematic design b Physical equipment Fig 5 Center of pressure measurement sensor III PHYSICAL EXPERIMENT A Experimental setup In the experiment the locus of ZMP of the robot was observed in cases where the trunk was equipped with the viscoelastic yaw joint with either light or heavy arms We also observed the locus of the ZMP with the rigid trunk and the heavy arms Figure 6 a shows the robot with the light arms attached to it arm 1 in Table I Similarly Figure 6 b shows the one with the heavy arms attached to it arm 2 in the table Both arms are made of aluminum The swinging cycle was 1 s and the locus of the ZMP was recorded by using the measurement equipment as explained in Section II for 10 cycles Considering that the distance between the inner edges of the left and right feet and the width of each foot are 60 and 150 mm respectively the ZMP should be placed between 30 and 180 mm 30 and 180 mm in the lateral direction In terms of the location of the ZMP in the anteroposterior direction we have the assumption that it is operated by the foot stepping on the sagittal plane In the experiment the knee and hip joints were not driven and the locus of the ZMP was recorded when the robot was in an upright position a Light arm b Heavy arm Fig 6 Swinging arms with different weights Figure 7 a and 7 b show the loci of the ZMP when light and heavy arms were attached respectively In both cases the trunk had the viscoelastic yaw joint Figure 7 c shows the locus of the ZMP of the trunk with a rigid body attached with heavy arms As shown in Figure 7 a the ZMP does not oscillate between the left and right feet which means that the ZMP does not lie between 30 to 180 mm and 801 30 to 180 mm in the lateral direction On the other hand for the trunk with the viscoelastic yaw joint attached with the heavy arm the ZMP was placed within both feet and we confi rmed that the robot rotated toward right side when the right arm swings ahead see the attached movie From this result it is expected that the robot achieves bipedal locomotion although it does not have a roll joint that allows the sideways movement of the robot As shown in Figure 7 c the ZMP does not lie on both feet Therefore the robot attached with the light arm or rigid trunk does not exhibit ZMP oscillation between two feet whereas the robot with the trunk made of the viscoelastic yaw joint and swinging heavy arms achieves a possibility of the stable locomotion as the ZMP is placed within the supporting foot 100 50 0 50 100 150 200 150 100 50 0 50 100 150 leftright position mm position mm front rear a Light arm with viscoelastic yaw trunk joint 100 50 0 50 100 150 200 150 100 50 0 50 100 150 left right position mm position mm front rear b Heavy arm with viscoelastic yaw trunk joint 100 50 0 50 100 150 200 150 100 50 0 50 100 150 leftright position mm position mm front rear c Rigid trunk with alminum arm Fig 7 Locus of ZMP IV DYNAMICS OF ARM SWINGING USING SIMPLE MODEL The results of the physical experiments showed that the robot with the heavy arms attached to the trunk made of the viscoelastic yaw joint exhibited a wide ZMP oscillation range These results raise the following issues First despite the swinging of the arms it is not clear why the ZMP moved in the lateral direction i e the x axis in 5 a and not in the anteroposterior direction i e the y axis Second will ZMP be located within the supporting foot when the robot exhibits human like locomotion in which the right arm swings forward as the right leg supports and vice versa To investigate the dynamics of the robot that swings the arms a modifi ed model of the physical robot was constructed Figure 8 a shows the simple model in which two masses represent the arms which move back and forth along lines y1and y2 perpendicular to the shoulder link Although the arm in the physical experiment was driven by the antagonistic pneumatic actuators and the model of the actuator such as a that by Chou et al 12 should be adopted we modeled as point point mass oscillating on the line To further simplify the model the mass and inertia of the shoulder trunk and legs have been neglected Figure 8 b shows the top view of the robot The model rotates along the line perpendicular to the ground that is yaw axis The masses move along the y1 and y2axes Considering the swinging of the physical arm two masses move in opposite phase with respect to each other In order to analyze the dynamics of the arm swinging the positions of the masses along the y1and y2axes represented as Y1and Y2 respectively are expressed as sinusoidal waves with offsets Y1 A0 Asin t 1 Y2 A0 Asin t 2 where A0is the offset as a center of the oscillation which determines whether or not the oscillations are symmetrical For example if A0 0 each mass oscillates back and forth symmetrically based on the shoulder link If not it moves asymmetrically by the offset of A0 First the trajectory of the ZMP is calculated A position of ZMP Px Py is calculated as follows Px mg x1 x2 Zcm x1 x2 2mg 3 Py mg y1 y2 Zcm y1 y2 2mg 4 where x1 x2 y1 and y2are the positions of the oscillating mass x1 y1 and x2 y2 according to the absolute coordi nate as shown in Figure 8 a Zcis the position of the masses along the z axis according to the absolute coordinate The position of the oscillating masses are expressed by using the trajectory Y1and Y2 according to the coordinates x1 y1 z1and x2 y2 z2 as follows x1 y1 R l Y1 R l A0 Asin t R 0 A0 R l Asin t 5 802 rear y1 x1 z1 y2 x2 z2 front q x z y a Overhead view x1 x2 y1 y2 q m l A Asin t 0 w A Asin t 0 w b Top view Fig 8 Simple model based on the developed robot and x2 y2 R l Y2 R l A0 Asin t R 0 A0 R l Asin t 6 where R is a rotational matrix which is expressed as follows R cos sin sin cos Considering that the signs of the second terms in Equation 5 and 6 are opposite x1 x2and y1 y2are calculated as follows x1 x2 y1 y2 2R 0 A0 2 A0sin A0cos 7 By differentiating twice the values of x1 x2and y1 y2 are calculated Subsequently by substituting these terms into Equation 3 and 4 the trajectory of ZMP is calculated when the trajectory of the yaw joint t is derived Equation 7 indicates that the ZMP trajectory does not explicitly contain the amplitude of the oscillation of the arm mass A whereas the amplitude A infl uences a dynamics of the model i e A is implicitly contained in the trajectory of the yaw joint t Next the trajectory of the yaw joint t is numerically derived from the dynamics of the model The equation of the dynamics is constructed by the Lagrange method assuming that the mass and inertia of the trunk is zero as follows 2m l2 A2 0 A2sin 2 t 4mA2 sin tcos t 2mlA 2sin t 8 where is an external torque is the angle of the yaw joint m is an arm mass and l is the length from the joint to the origin of x1 y1 z1and x2 y2 z2coordinates i e half length of the shoulder As explained in Equation 8 the oscillation is forced by the swinging of the arm mass By substituting Kp Kd where Kp and Kd are the spring and damper coeffi cients respectively the trajectory of the joint angle t is calculated Figure 9 shows the trajectories of the joint t when Kp 1 0 10 0 and 100 0 Nm rad The joint is integrated by the Runge Kutta method using the dynamics equation using the following values m 0 75 kg l 0 31 m A0 0 05 m and A 0 15 m and Kd is set as 1 0 Nm rad s As shown in the fi gure the trajectory is similar with sinusoidal function and the amplitude of oscillation is very s