IROS2019國(guó)際學(xué)術(shù)會(huì)議論文集 0992

1 Abstract This paper presents a three degrees of freedom DOF gravity compensation mechanism for the waists of cooperative robots whose centers of mass change according to the arm poses It comprises 2 DOF and 1 DOF gravity compensation mechanisms in series and is capable of natural and agile motions such as bobbing and weaving The 2 DOF mechanism for the upper part of the waist acts as a universal joint To compensate for the gravity of this 2 DOF motion a simple and robust link mechanism with one compressive spring is proposed Moreover for the complete gravity compensation regardless of the arm poses a three dimensional 3D parallel link structure that maintains the upper body parallel to the ground is introduced The 1 DOF gravity compensation mechanism which provides the motions of the hip and thigh also has a parallelogram structure to maintain the waist parallel to the ground The implemented 3 DOF waist mechanism can compensate for up to 23 kg and its own weight It has an adjusting mechanism that can easily calibrate the amount of compensation in case the weight of the upper body changes The large workspace enables the upper body to move in any direction in a 3D space without singularity Therefore the robot with this waist can touch the ground to pick up objects on the ground as well as reach an object at a height of 2145 mm I INTRODUCTION Cooperative robots have been researched to take over physically demanding tasks for human workers or to help people safely in the same workspace with humans To make cooperative robots have humanlike performance many improvements are needed One of the difficult problems of humanoid robots or cooperative robots with mobile bases is that it is difficult to make a waist having human like agility compliance and workspace For instance most robots with waist mechanisms cannot touch the ground with their hands or grippers and reach objects on a high bookshelf which is easy for humans In addition they tend to be bulky because they require substantial torque because of the heavy weight of the upper body To lower the required torque of the waists gravity compensation mechanisms can be applied By utilizing them the actuator size can be reduced and the efficiency and control performance can be improved Accordingly various types of gravity compensation mechanisms have been introduced The Research supported by NAVER Labs Co Yong Jae Kim is with Korea University of Technology and Education Koreatech Cheonan City Rep of Korea corresponding author to provide phone 82 41 560 1424 fax 82 41 564 3261 e mail yongjae koreatech ac kr Seong Ho Yun Jiwon Seo Junsuk Yoon Hansol Song and Yun Soo Kim are with Korea University of Technology and Education Koreatech Cheonan City Rep of Korea e mail dnstjdgh koreatech ac kr cbw00 koreatech ac kr nkb0401 koreatech ac kr tan44 koreatech ac kr yunsu335 koreatech ac kr one degree of freedom DOF gravity compensation mechanism using a linear spring with a trigonometric structure is a well known and widely used mechanism because it can completely compensate the gravity with a relatively simple mechanism 1 2 To compensate for the nonlinear property of gravitational torque cam shaped pulleys can be used 3 4 They achieve a large range of motion but fine adjustment according to the load change is difficult To locate a large spring in the robot frame a gravity compensation mechanism using a crank and a compressive spring was introduced 5 For heavy industrial robots pneumatic gravity compensators 2 6 are also used To extend the gravity compensation functionality to multiple DOFs various mechanisms have been developed 7 8 9 10 The PR2 robot 7 has two 7 DOF arms with 3 DOF gravity compensation mechanisms By using a unique linkage structure with constant force springs it achieved complete gravity compensation for the upper and lower limbs 2 DOF shoulder mechanisms with gravity compensation capability by using bevel gears cables and linear springs were researched 8 A yaw pitch gravity compensation mechanism using multiple springs was presented 9 A roll pitch joint mechanism with a single spring was also introduced 10 To apply these gravity compensation mechanisms to the robot waists the following requirements should be satisfied a high payload sufficient to endure the weight of the upper body high DOFs for agile and smooth motions a wide workspace to aid the dexterity of the arms and consistent gravity Seong Ho Yun Jiwon Seo Junsuk Yoon Hansol Song Yun Soo Kim and Yong Jae Kim 3 DOF Gravity Compensation Mechanism for Robot Waists with the Variations of Center of Mass a b Fig 1 Developed 3 DOF waist mechanism mounted to a robot LIMS2 AMBIDEX a standing pose b fully crouched pose touching the ground with hands 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 IEEE3565 compensation capability regardless of arm position Considering these requirements a waist mechanism as shown in Fig 1 a is proposed It is composed of 2 DOF roll pitch and 1 DOF pitch gravity compensation mechanisms in series It can move in arbitrary directions in three dimensional 3D space without singular poses and provides a large workspace for arms to manipulate dexterously The 2 DOF mechanism for the upper part of the waist acts as a universal joint To compensate for the gravity of this 2 DOF motion a simple and robust link mechanism with one compressive spring is proposed Moreover for the complete gravity compensation regardless of the arm poses a 3D parallel link structure that makes the upper body keep in parallel to the ground was introduced The 1 DOF gravity compensation mechanism which acts as the motions of the hip and thigh also has a parallelogram structure to keep the waist in parallel to the ground The implemented 3 DOF waist mechanism can compensate for as much as a 23 kg load and its own weight completely Its nonsingular structure has the advantage of not only widening the workspace but also absorbing shock and trembling coming from the ground when it is mounted on the mobile base The remainder of this paper is organized as follows Section II introduces the fundamental principle of the 2 DOF gravity compensation mechanism and the 3D parallel link mechanism that decouples the change of the center of mass COM position In Section III the detailed mechanical design is presented In Section IV the experimental result is reported and Section V concludes the work II FUNDAMENTAL CONCEPT A 2 DOF Gravity Compensation Mechanism Fig 2 a illustrates the basic concept of a widely used 1 DOF gravity compensation mechanism 1 The torque caused by the gravitational force on the COM is as follows sin 1 where m l and denote the mass of the load length of the link and joint angle respectively Using this mechanism the gravitational torque can be completely compensated at arbitrary angles of if a spring with a proper stiffness is applied Assuming that the system is in static equilibrium the gravitational force on the COM can be considered the force on point A using the following equation 1 2 where 1 denotes the distance between the joint pivot and point A As the link is in static equilibrium the net force of and the spring tension is parallel to link Therefore if the length of the spring is defined as the following relationship can be obtained considering the similarity between the triangle by the points A B and O and the triangle formed by the two force vectors and as 2 3 Substituting into Eq 3 with Eq 2 can be expressed as follows 1 2 4 where 1 and 2 of Eq 4 are all constants Therefore the spring force changes linearly in accordance with the change of It implies that the gravitational torque can be completely compensated regardless of using a linear spring with the stiffness as k 1 2 5 Note that means the elongated distance of the spring as well as the distance between points A and B It implies that the rest length of the spring should be zero when there is no tension on the spring Because this zero length spring is not feasible the actual spring should be properly modified to act as a virtually zero length spring which is explained at the end of this subsection Fig 2 b shows several variations of the 1 DOF compensation mechanism which are exactly the same principle as Fig 2 a To extend this 1 DOF gravity compensation mechanism to 2 DOFs a mechanism using two 2 DOF universal joints one spherical joint and one linear spring is proposed which has the similar concept as 10 Fig 2 c shows the basic concept of the proposed mechanism The universal joint 1 corresponds to a 2 DOF joint of the waist and the two actuators are connected to this joint The zero length spring is located between the universal joint 2 and the spherical joint If one considers this mechanism by projecting it to the plane containing the link and the spring the force and moment relationship is the same as in the 1 DOF case as shown in the upper figure of Fig 2 b Therefore the 2 DOF gravity compensation can be feasible using one zero length spring By applying this mechanism to the waist mechanism the robot can lean forward and backward as well as move to the left and right side similar to human motion a b c d Fig 2 a Basic concept of 1 DOF gravity compensation b Variations of the gravity compensation concept c and d Simplified models of the 2 DOF gravity compensation mechanism 2 Universal joint 1 Universal joint 2 Spherical joint 1 2 3566 The Gruebler equation of the mechanism of Fig 2 c is as follows 6 1 6 4 0 2 6 where 1 2 3 and 4 denote the number of the links including the base link the DOFs of the universal joint 1 the universal joint 2 and the spherical joint respectively i e 1 2 3 and 4 are 4 3 2 2 and 1 respectively Thus it has 2 DOFs as expected Fig 2 d illustrates other possible structures with the same principle When it comes to the implementation there are several difficulties First the zero length spring should be implemented by using actual springs Second the spherical joint should be replaced by other joints because the actual spherical joint has a substantially small range of motion Also all joints should be properly positioned to have a large workspace at the same time to prevent the singular pose Fig 3 shows the test mechanism satisfying these requirements which realizes the concept of Fig 2 d It is composed of the seven revolute joints considering the range of motion and the strength The universal joints 1 and 2 of Fig 2 c were replaced with the set of revolute joints o d and b e The spherical joint was also replaced with two revolute joints c and f The joints d and o are named the roll joint and pitch joint respectively and the angles of these joints are indicated by and respectively These two joints are actuated by joint actuators for the waist motion and the others are passively rotating joints As a result the range of motion of the roll joint d is from 70 to 70 and pitch joint o is from 0 to 80 To realize the zero length spring by using an actual spring a compression spring is used as shown in Fig 4 a As the bottom figure shows joints b and c coincide when the compression spring has no force At the right end of the spring there is a tapered roller bearing to allow the rotation around the joint g and to withstand the large compressive force of the spring In practice adjustment of 1 or 2 is needed because it is difficult to estimate precisely and the load can be changed according to the applications Therefore the test mechanism has a slider for the fine adjustment of 1 as illustrated in Fig 4 c B Parallel Link Mechanism Accepting COM Change The COM position of the upper body with arms changes according to the arm poses as shown in Fig 5 a If the gravity compensation mechanism of Fig 3 is used complete compensation is not possible For instance the mechanism adjusted to compensate the upper body as shown at the center and right figures of Fig 5 a cannot exactly compensate for the upper body with different arm poses as in the left figure of Fig 5 a By making the upper body parallel to the ground as illustrated in Fig 5 b the compensation regardless of the COM position is available Fig 6 is an illustration of the parallel link structure of the proposed mechanism In Fig 6 a a joint o is connected to the gravity compensation mechanism and the other three joints are freely rotating revolute joints Let it be assumed that the system in static equilibrium owing to the proper gravity compensation torque The gravity force the force exerted from the link A and the force exerted from the link B are applied to link C and the net force is zero By naming the force components of and in the directions of the x and y axis and the forces to the y axis can be obtained from the force equilibrium of and as a b c Fig 4 a Mechanical design for the zero length spring b straight pose 0 c fully rotated pose 80 deg bc g Compressive spring Tapered roller bearing g b c g e g e Slider for 1adjustment Fig 3 Test mechanism for the 2 DOF gravity compensation X Y Z d f b g c o e X Y Z c o g d e f b Pitch axis Roll axis a b Fig 5 a Gravity compensation mechanism under the variation of COM b gravity compensation mechanism with parallel link structure 3567 7 Because the torques of the joints at both ends of the link B are zero is always parallel to link B Therefore the relationship between and is tan 8 Because link C is in a static state the amount of horizontal force applied by link C to link A is equivalent to that of 9 Link A is also in a static state because the actuation torque and the moment caused by are balanced Thus by considering the moment equilibrium around the joint pivot o the following equation can be obtained sin cos 10 By rearranging 10 using 7 8 and 9 as follows sin cos sin tan cos 11 sin sin The required gravity compensation torque in Eq 11 is equal to Eq 1 It is not the function of and which means that the required torque is not related to COM position Consequently the proposed parallel structure can be compensated by using the previously introduced mechanism regardless of the COM position This fact is intuitively deducible from the fact that the sum of the potential energy of the COM and the elastic energy stored in the spring is constant for an exactly compensated mechanism The relationship between the COM height and the spring length of the mechanism in Fig 2 d is the same as the relationship of the mechanism in Fig 5 b which means that these two mechanisms can be compensated with the same principle To extend the proposed structure to a 2 DOF gravity compensation mechanism in 3 D space the structure illustrated in Fig 7 is proposed The mechanism is made of three parallel link structures and six universal joints This structure maintains the upper body parallel to the ground while allowing 2 DOF roll and pitch motions This mechanism has exactly the same COM height and spring length relationship as the mechanism in Fig 3 Thus as explained previously it can be completely compensated by the same principle of Fig 3 even though the COM position is changed III DETAIL DESIGN AND ANALYSIS Fig 8 a represents the kinematic design of the proposed waist mechanism which enables the robot to stand up and sit with the hands touching the floor Fig 9 b shows the implemented waist mechanism set to compensate for 20 kg of load Because it is similar in size and shape to a human it is human friendly and can be applied to an environment where humans work The main specification is shown in Table I To make it similar to a human the lengths of the upper link and the lower link were determined considering the length between the pelvis and the center of the chest and the length of the thigh which were 350 and 300 mm respectively In a standing position and sitting position the maximum and minimum heights of the mechanism were 1600 and 1172 mm respectively Considering the length of the arms the robot can pick up an object on the ground Furthermore it can reach up to 2145 mm The ranges of angle of pitch 1 pitch 2 and roll were 70 0 0 70 and 30 30 respectively and the upper body could move horizontally from 175 to 175 mm It could compensate for as much as 22 kg of load and the weight of the two arms To withstand the high force applied by gravity a sturdy structure with durable components was used The deep groove bearings which has a low coefficient of TABLE I MECHANICAL DESIGN PARAMETERS ItemSpecifications Size mm Width x Depth x Height 111 x 12 x 1122 Length of Upper link 350 Length of lower link 300 Load for Compensation kg Min 8 Max 22 robot weight 17 Siffness of Spring kgf mm 2 66 Spring Length mm Free load 150 Max compression 75 Max Spring Force kgf 200 at length 75mm Range of Motion deg Pitch 1 70 0 Roll 30 30 Pitch 2 0 70 Workspace mm x axis 458 317 y axis 280 280 z axis 608 1035 Reachable height with arm mm Min 41 Max 2145 Max Joint Speed deg sec 568 Joint Torque Nm Max 137 Cont 43 Fig 7 2 DOF gravity compensated parallel structure X Y Z a b Fig 6 a Parallel link structure with a load mg b force and torque diagrams of the parallel link structure Link O Link O 3568 friction were used for the universal joints and tapered roller bearings and bush bearings were used for the part where the large force was applied Practically the actual weight of the upper body is difficult to measure accurately Also it can be changed when replacing grippers or attaching additional devices Therefore the load adjustment mechanism was implemented as shown in Fig 9 By moving the slider to the z axis 1 in 4 can be adjusted finely to respond to the change of mass m It also has the sliders to x and y axis which are used for adjusting the COM displacement of the three parallel links The parallel link structure of the 2 DOF gravity compensation mechanism consists of two links at the front and one link at the back The two front links have a thin shape because these endure only compressive forces as illustrated in Fig 6 b The backside links should endure the