IROS2019国际学术会议论文集 2239

Abstract For safety enhancement reasons passive gravity compensation is widely applied in robotic systems used in minimally invasive surgery MIS MIS robotic systems have a remote center of motion RCM in which a surgical instrument conducts a fulcrum motion around a point of invasion RCM mechanisms include three degrees of freedom 3 DoF roll pitch and translation Existing studies to date have focused on multi degrees of freedom MDoF gravity compensation mechanisms by installing springs and wires in a robot However a gravity compensation mechanism with 3 DoF that simultaneously uses all three directional movements roll pitch and translation has not yet been researched Here we propose a novel gravity compensation mechanism applicable to a 3 DoF MIS robotic arm with an RCM mechanism When a translational motion is exerted the proposed gravity compensator can adjust the roll pitch directional compensating torque by utilizing a reduction gear box and wire cable To verify the 3 DoF gravity compensation a gravity compensated robotic arm for MIS and customized torque sensors were manufactured and calibrated Results showed the proposed static balancing mechanism can compensate for the gravitational torque with respect to roll pitch and translation The total torque error along the roll and pitch axis was less than 0 38 Nm In particular the torque variation due to the translational motion was less than 0 13 Nm Index Terms Surgical Robotics Laparoscopy Mechanism Design Robot Safety I INTRODUCTION obotic systems for minimally invasive surgery MIS have rapidly developed over the last several years 1 5 Minimally invasive robotic surgery utilizes a robotic manipulator instead of a human hand to control a laparoscope and other surgical instruments Many advantages exist in terms of surgical performance when robotic surgery is employed including precise manipulation dexterity and This work is supported by the Korea Health Technology R D Project through the Korea Health Industry Development Institute KHIDI funded by the Ministry of Health Welfare Republic of Korea grant HI17C2012 1 Chang Kyun Kim Deok Gyoon Chung Minho Hwang and Joonhwan Kim are with the Division of Mechanical Engineering School of Mechanical Aerospace and Systems Engineering KAIST Daejeon Korea e mail chang9097 kaist ac kr jdk0403 kaist ac kr gkgk1215 te108715 2 Byungsik Cheon and Hansoul Kim are with the Robotics Program KAIST Daejeon Republic of Korea e mail cbs15 kaist ac kr robotgksthf kaist ac kr 1 3 Dong Soo Kwon corresponding author is a professor of the Division of Mechanical Engineering School of Mechanical Aerospace and Systems Engineering KAIST Daejeon Korea e mail kwonds kaist ac kr and is also a CEO of EasyEndoSurgical Inc ergonomic control However safety concerns and malfunctions have been reported thus far 6 For example a robot may perforate an organ if it moves by gravity when the power goes out regardless of the surgeon s intention Efforts to prevent this include various methods such as employing electric brakes or passive gravity compensation mechanisms When an electric brake is used the surgical robot can remain in a motionless or stationary even when the power goes out This enhances safety However because of its non backdrivable property the surgical assistant cannot manually reposition the robot easily 7 Furthermore even when the power is turned on the surgical assistant must physically hold the robotic arm as the surgical assistant releases the electric brake and manually positions the robotic arm Passive gravity compensation when applied to robots can enhance safety because the system can remain in a stationary state even when the power goes out 8 Furthermore because the robotic arm is backdrivable the surgical assistant can manually position the arm even in an emergency Passive gravity compensation uses the counterweight and spring wire methods In the case of gravity compensation with counterweights 9 10 the arm s center of mass remains in a regular position and thus can maintain a stationary state However because additional masses are attached to the robotic arm the overall mass and volume increase The actuator load also increases because of an inertial force 8 11 In the case of gravity compensation by a spring the robotic arm not only can maintain a stationary state but also decreases the overall weight and volume of the robotic arm as well as the load of the actuator Considerable research has focused on one degree of freedom 1 DoF gravity compensation mechanisms which use wires and springs to compensate for gravitational torque 12 14 In previous studies static balancing mechanisms using springs and wires for multi degrees of freedom MDoF manipulators were examined including those with roll pitch 15 pitch translation 16 and multiple pitch motions 17 18 In particular many studies on gravity compensation mechanisms have been conducted for MIS robotic systems including roll pitch DoF gravity compensation that utilizes a Scotch Yoke mechanism 19 and 2 DoF static balancing mechanisms for orientating laparoscopes 20 Robotic systems for MIS uses a remote center of motion RCM in which a surgical instrument implements a fulcrum motion around a point of invasion RCM includes a 3 DoF of roll pitch and translation In particular the translational movement of a surgical instrument occurs frequently in MIS Chang Kyun Kim1 Deok Gyoon Chung1 Minho Hwang1 Byungsik Cheon2 Hansoul Kim2 Joonhwan Kim1 and Dong Soo Kwon1 3 Three Degrees of Freedom Passive Gravity Compensation Mechanism Applicable to Robotic Arm with Remote Center of Motion for Minimally Invasive Surgery R IEEE Robotics and Automation Letters RAL paper presented at the 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 Copyright 2019 IEEE Thus a precise gravity compensation mechanism that is adaptive to translational motion is required Little research has focused on the gravity compensation mechanism that simultaneously contains all three directional movements of roll pitch and translation In our previous study we devised a 3 DoF gravity compensation mechanism that involves roll pitch translation motions to enhance safety 21 However this previous mechanism compensated for gravity when the axes of roll pitch and translation intersected at one point Therefore it was not completely applicable to an RCM mechanism Here we propose a novel 3 DoF gravity compensation mechanism suitable for a robotic arm with RCM used in MIS by employing a reduction gear box and wire cable The proposed mechanism enhances safety by accurately compensating the gravitational torque of the 3 DoF roll pitch translation robotic arm with RCM for MIS The remainder of this paper is organized as follows Section II includes an analysis of the gravitational and compensating torques of the robotic arm Details of the operating principles and how the gravity compensator balances the gravitational torque are also described Section III explains the robotic arm and customized torque sensors that were specifically devised to assess the compensation of the gravitational torque An experiment to verify the proposed gravity compensation mechanism is described in Section IV A discussion and conclusion are given in Section V and VI II METHOD In this section the gravitational torque of the robotic arm with RCM is analyzed Then the manner in which a 1 DoF static balancing mechanism compensates for the gravitational torque is explained The overall design and operating principle of a 3 DoF gravity compensator equipped robotic arm is also described Finally we analyze how the gravitational torque is compensated for by the proposed mechanism A Gravitational torque of robotic arm with RCM Fig 1 shows an example of a robotic arm with RCM for MIS The mass distribution of the robotic arm can be represented by Fig 2 The mass of each link of the robotic arm as shown in Fig 1 can be represented as for 1 4 in Fig 2 Similarly and in Fig 2 are the rotating angles of the roll and pitch motions shown in Fig 1 respectively where and indicate the angle of rotation along the counter clockwise direction of the 0 and 1 axes respectively In addition represents the acceleration of gravity which is the direction along the 0 axis If the distance between and the 0 axis when 0 is represented by the potential energy of the whole system due to gravity is computed by the following equation 1 1 2 2 3 3 4 4 1 From 1 the gravitational torque along the roll and pitch directions and can be represented by partial derivatives of potential energy with respect to and 1 1 2 2 3 3 4 4 2 B 1 DoF static balancing with spring and wire This section explains the principle of the gravity compensation mechanism with springs and wires for a 1 DoF manipulator 12 14 The mechanism of a 1 DoF gravity compensator can be further extended to the proposed 3 DoF gravity compensation mechanism Fig 3 represents a 1 DoF spring wire gravity compensated manipulator that moves on the 0 0 plane The acceleration of gravity acts parallel to the 0 axis and the spring constant is We assumed the use of a zero length spring that applies zero force when the length is zero and this was arranged by springs and wires 13 We did not consider friction One end of the spring is fixed at point A which is remote from the origin O by 1 on the reference frame and the other end is fixed at point B which is remote from the origin O by on the link The potential energy of the system due to gravity is computed by the following equation 3 Next 2 which is the square of the increased length of the spring is as follows Figure 2 Mass distribution of a parallelogram robotic arm Figure 3 1 DoF gravity compensator with spring wire mechanism Figure 1 Robotic arm with parallelogram RCM mechanism for MIS 2 12 2 2 1 4 The elastic potential energy derived from the spring can be determined by 1 2 2 1 2 1 2 2 2 1 5 The potential energy of the whole system is as follows 1 1 2 1 2 2 6 For the potential energy to be constant regardless of the angle the spring constant should satisfy the following equation 1 7 where is a constant Therefore the potential energy of the whole system is constant regardless of the angle as shown by the following equation Thus 1 DoF gravity compensation is achieved 1 2 1 2 2 8 C 3 DoF gravity compensation mechanism This section describes the overall design of the gravity compensated robotic arm with a parallelogram structure The manner in which the proposed 3 DoF gravity compensation mechanism compensates for the gravitational torque is also examined 1 Operating principle of gravity compensated robotic arm Fig 4 shows the overall structure of a proposed gravity compensated robotic arm As shown this arm has a parallelogram structure and consists of three motors that drive the roll pitch and translational movements The robotic arm for MIS is mainly equipped with surgical instruments in the translational movement section However in this study for the sake of simplification a dummy mass translational moving mass in Fig 4 was attached instead The dotted yellow and red lines in Fig 4 indicate the axis of the roll pitch translational movement and gravity compensation wire cable respectively Fig 5 shows the components of the robotic arm used to compensate for the roll pitch directional gravitational torque 15 The wire cables red line in Fig 5 are fixed at the ends of the moment arms 1 and 2 which are themselves fixed to bevel gears 1 and 2 respectively The fixed bevel gear in Fig 5 does not rotate and is fixed to the base structure of the robotic arm which is attached to the reference frame When a roll pitch motion occurs the gravitational torque can be compensated for by the movement of three bevel gears that have a 1 1 1 gear ratio However when a translational motion occurs the gravitational torque with respect to the roll pitch direction changes Thus the compensating torque must be adapted accordingly Considering this the proposed robotic arm is designed to compensate for the change of gravitational torque with respect to the roll pitch direction because of the translational motion The proposed mechanism compensates for the Figure 5 Components for compensating for roll and pitch directional torque Figure 4 Overall structure and DoF of the gravity compensated robotic arm Figure 6 Components of the adapting moment arms of the gravity compensator according to translational motion Figure 7 Parameters and variables of the gravity compensator in a translationally moving situation gravitational torque in an adaptive manner by varying the moment arm length of the gravity compensator The components to implement this function are shown in Fig 6 As Fig 7 shows when the translational movement section moves by length the wire cable green line in Fig 4 6 and 7 is either pulled or released by length This wire cable is connected to reel 1 and rotates together with it as the translational motion occurs Reel 2 rotates by the rotated angle of reel 1 multiplied by the reduction ratio of the reduction gear box Because the wire cable wound on reel 2 the purple line in Fig 4 5 and 6 is connected to the spring substructure Reel 2 also moves the spring substructure by that distance multiplied by the reduction ratio c in Fig 7 Because of this mechanism the spring substructure moves as much as the reduction ratio multiplied by the displacement of the translational moving mass As the spring substructure moves the moment arm of the gravity compensator changes which can be represented by the change of the from to in Fig 7 Therefore the changed gravitational torque can be more precisely compensated 2 Torque analysis of the robotic arm We next analyze the roll pitch gravitational torque of the proposed gravity compensated robotic arm with a parallelogram structure and the compensating torque resulting from the proposed static balancing mechanism We also want to find the spring constant and reduction ratio of the gravity compensator that enable the sum of the gravitational and compensating torques to be zero Fig 8 represents the mass distribution of the robotic arm that includes the proposed 3 DoF gravity compensation mechanism where 1 2 and 3 represent the mass of the parallelogram links 4 indicates the mass of the translationally moving part and 5 represents that of the spring substructure which contains springs and linear bushing for gravity compensation Here 5 is the new mass produced by applying gravity compensation The gravitational torque due to 1 5 can be expressed by adding the term for 5 to 2 1 1 2 2 3 3 4 4 5 5 9 denotes the distance between and the 0 axis when 0 as in 1 In Fig 7 is the displacement of the translationally moving mass from the initial position 4 4 can be expressed by the constant 4 and variable as 4 4 10 Next is the reduction ratio of the reduction gear box and this determines the distance travelled by 5 5 5 11 The gravitational torque of the robotic arm equipped with the proposed gravity compensator can be expressed by substituting 10 and 11 into 9 1 1 2 2 3 3 4 4 5 5 12 Fig 9 represents a 2 DoF static balancing mechanism to compensate for the roll and pitch directional torque 15 The compensating torque by the springs can be expressed using the parameters shown in Fig 7 and 9 1 1 2 2 1 1 1 2 2 and 1 2 Because of the relative motion of the three bevel gears 1 and 2 in Fig 9 can be represented by and as 1 2 11 11 13 From 13 the compensating torque by the springs can be derived as 1 11 11 1 2 2 1 14 As shown in Fig 7 the end point of the moment arm moves together with the spring substructure from to Therefore the distance changes from the initial position according to the motion of the spring substructure 15 By substituting 15 into 14 2 1 16 Because the total sum of torque should be zero to make the system statically balanced the following equation holds 2 1 1 1 2 2 3 3 4 4 5 5 17 Figure 9 2 DoF static balancing mechanism using bevel gears and two 1 DoF spring wire gravity compensators Figure 8 Mass distribution and parameters of the proposed gravity compensated robotic arm The condition to establish 17 regardless of and can be expressed as 2 1 1 1 2 2 3 3 4 4 5 5 0 18 Because of the spring should be a constant 4 5 2 1 2 1 19 where 1 1 2 2 3 3 4 4 5 5 The condition to establish 19 for any values of can be derived as 4 5 20 The parameters in 20 are all constants determined from the design of the robotic arm Thus the reduction ratio is also a constant The spring constant can be obtained by substituting 20 into 19 as follows 2 1 21 3 Torque effect on the translational motor Because of the reaction force of the gravity compensator there is a torque effect on the translational motor as shown in Fig 10 If the torque effect on the translational motor is too high it may disturb the translational motion of the robotic arm In this section the amount of torque delivered to the translational motor as a result of the proposed gravity compensation mechanism is analyzed As shown in Fig 7 when the angle between the axis i e connecting the rotation center O of the moment arm and point A and the 2 axis i e passing through the pitch link is the angle between the wire from the moment arm and the pitch link can be represented as 1 1 12 2 2 1 22 The tension of the wire the red lines in Fig 10 connected to the moment arm can be expressed as follows 12 2 2 1 23 As shown in Fig 9 when the angles between the pitch link and moment arm 1 and moment arm 2 are 1 and 2 the total force applied to the spring substructure can be derived as cos 1 1 cos 2 2 24 As in previous studies of robotic systems for MIS 5 in this study we utilized a slide screw to demonstrate the translational motion Let the lead of the slide screw be and the tension of a wire connected to the translational moving part green lines in Fig 10 be Tt The torque transferred to the translational motor can be expressed as 2 2 25 By substituting 13 15 23 and 24 into 25 can be expressed as 2 cos