三指灵巧手结构设计与控制实验
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摘要
具有多感知功能的机器人灵巧手作为提高机器人系统作业水平和智能水平的重要工具,成为机器人领域中一个重要的研究方向。灵巧手本体的结构和控制的研究是灵巧手研究的两个重要方面,它们对于灵巧手的操作性能具有致关重要的意义。本文源于国家863计划“新一代五指仿人灵巧手及其协调控制的研究”,并结合与南京理工大学合作的国防科工委“十一五”计划基础研究项目“微小型地面移动机器人轻型智能手臂的研究”,主要进行了新一代模块化的三自由度手指本体结构设计和控制的研究实验,并对三指灵巧手手掌和腕关节进行结构设计。
三指灵巧手是由三个新一代模块化设计的三自由度手指组成,手指具有多种感知、集成化和模块化、高度数字化等特点。新一代三自由度灵巧手指采用机电一体化设计思想,将机械本体设计与传感、驱动、传动以及电气系统等统一考虑、合理布局,实现系统的最合理设计。通过采用盘式电机作为驱动及谐波减速器、齿形带传动方案,减小了手指的体积、降低了单手指的重量。模块化的手指结构简化了灵巧手的设计过程,提高了系统的互换性,便于维护。另外,灵巧手的手指布置方式、手掌的结构特点决定了灵巧手的抓取性能。本文根据手指的结构特点、尺寸等设计了三指灵巧手的手掌结构,并进行了抓取运动仿真。
腕关节的功能是为了提高灵巧手的灵巧性能,简单的运动学和大角度运动范围是设计中追求的目标。本设计中采用驱动传动系统与关节分离的结构,使关节部分的尺寸结构更为合理。
单手指控制是灵巧手控制系统的底层,其控制性能直接影响灵巧手的操作性能。本文首先基于手指结构,分析了手指和手掌的运动学。本文基于抗积分饱和PID控制算法,进行了手指的关节位置跟踪控制,并进而完成了笛卡尔空间的指尖位置控制。当灵巧手在完成与环境接触的作业时,手指的柔顺性十分重要,阻抗控制是实现手指主动柔顺的主要方法之一,得到深入研究和广泛应用。本文以关节力/力矩传感器提供的力信息和位置控制为基础,实现了基于位置的关节空间的手指阻抗控制。
As an important tool to improve intelligent and manipulative levels of the robot, multi-sensory dexterous robot hand has become one of the most promising researches in robot field. Robot hand body and its control research are two main aspects of robot hand research, they decides to manipulative levels. Based on NanJing Institute of Technology’s program“Research on light mechanical arm of small vehicle”, a three freedom of degree modularized finger on international top is developed, a three-fingered dexterous hand and a two DOF wrist is design.
The three-fingered dexterous hand has three identical modularized fingers. The finger has features of multi-sensor, modularity, integration, digitalization and so on. Adopting the idea of mechatronic integration and taking into account disposition of all mechanical part, electrical part, driver and sensors, the three-fingered hand has realized system optimization design. As a small workable robot system, every modular finger is integrated with drivers, sensors and communication system. Modular of finger reduces the design complexity of the hand, and enhances replacement ability and maintain ability. In addition, the collocation configuration of fingers and the structure of palm will decide the grasping ability of the dexterous hand. This paper will design the mechanical structure of the palm based on the finger’s dimension and structure, and process grasping analysis.
The function of wrist is to improve the dexterity of three-fingered hand, simple kinematics and large angle workspace are the targets of the design. In the design ,the drive and transmission system and the joints are separate ,this make the dimension appropriate.
As the base level of the hand control system, finger control directly influences the manipulative ability of robot hand. According to the finger structure, finger kinematics and dynamics is firstly analyzed, which will be used in finger control. By using a trajectory interpolation algorithm proposed by Paul, a joint position antintergral-saturation control algorithm is proposed, and then position control of finger tip in Cartesian space is done. When dexterous hand works, the finger compliance is very important. As one of main ways realizing compliance, the impedance control is studied deeply and implemented widely. According to the information of joint force sensor and position control of joint, a joint impedance control is achieved in the dissertation.
三指灵巧手是由三个新一代模块化设计的三自由度手指组成,手指具有多种感知、集成化和模块化、高度数字化等特点。新一代三自由度灵巧手指采用机电一体化设计思想,将机械本体设计与传感、驱动、传动以及电气系统等统一考虑、合理布局,实现系统的最合理设计。通过采用盘式电机作为驱动及谐波减速器、齿形带传动方案,减小了手指的体积、降低了单手指的重量。模块化的手指结构简化了灵巧手的设计过程,提高了系统的互换性,便于维护。另外,灵巧手的手指布置方式、手掌的结构特点决定了灵巧手的抓取性能。本文根据手指的结构特点、尺寸等设计了三指灵巧手的手掌结构,并进行了抓取运动仿真。
腕关节的功能是为了提高灵巧手的灵巧性能,简单的运动学和大角度运动范围是设计中追求的目标。本设计中采用驱动传动系统与关节分离的结构,使关节部分的尺寸结构更为合理。
单手指控制是灵巧手控制系统的底层,其控制性能直接影响灵巧手的操作性能。本文首先基于手指结构,分析了手指和手掌的运动学。本文基于抗积分饱和PID控制算法,进行了手指的关节位置跟踪控制,并进而完成了笛卡尔空间的指尖位置控制。当灵巧手在完成与环境接触的作业时,手指的柔顺性十分重要,阻抗控制是实现手指主动柔顺的主要方法之一,得到深入研究和广泛应用。本文以关节力/力矩传感器提供的力信息和位置控制为基础,实现了基于位置的关节空间的手指阻抗控制。
As an important tool to improve intelligent and manipulative levels of the robot, multi-sensory dexterous robot hand has become one of the most promising researches in robot field. Robot hand body and its control research are two main aspects of robot hand research, they decides to manipulative levels. Based on NanJing Institute of Technology’s program“Research on light mechanical arm of small vehicle”, a three freedom of degree modularized finger on international top is developed, a three-fingered dexterous hand and a two DOF wrist is design.
The three-fingered dexterous hand has three identical modularized fingers. The finger has features of multi-sensor, modularity, integration, digitalization and so on. Adopting the idea of mechatronic integration and taking into account disposition of all mechanical part, electrical part, driver and sensors, the three-fingered hand has realized system optimization design. As a small workable robot system, every modular finger is integrated with drivers, sensors and communication system. Modular of finger reduces the design complexity of the hand, and enhances replacement ability and maintain ability. In addition, the collocation configuration of fingers and the structure of palm will decide the grasping ability of the dexterous hand. This paper will design the mechanical structure of the palm based on the finger’s dimension and structure, and process grasping analysis.
The function of wrist is to improve the dexterity of three-fingered hand, simple kinematics and large angle workspace are the targets of the design. In the design ,the drive and transmission system and the joints are separate ,this make the dimension appropriate.
As the base level of the hand control system, finger control directly influences the manipulative ability of robot hand. According to the finger structure, finger kinematics and dynamics is firstly analyzed, which will be used in finger control. By using a trajectory interpolation algorithm proposed by Paul, a joint position antintergral-saturation control algorithm is proposed, and then position control of finger tip in Cartesian space is done. When dexterous hand works, the finger compliance is very important. As one of main ways realizing compliance, the impedance control is studied deeply and implemented widely. According to the information of joint force sensor and position control of joint, a joint impedance control is achieved in the dissertation.
引文
1姜力.具有力感知功能的机器人灵巧手手指及控制的研究.哈尔滨工业大学博士论文. 2001.
2刘伊威.DLR/HIT仿人灵巧手系统及手指柔顺控制的研究.哈尔滨工业大学博士论文.2007.
3蔡自兴.机器人学.清华大学出版社.2000:265~272
4 Mark E. Posheim. Robot Evolution—the Development of Anth-robotics. The MIT Press, 1987:197~231
5 Okada T. Computer control of multijointed finger system for precise object-handing. IEEE Transactions on Systems,Man and Cybernetics. 1982, 12(3): 289~299.
6 S.C.Jacobsen, J.E.Wood, D.F.Knutti, K.B.Biggers. The UTAH/MIT Dextrous Hand: Work in Progress. The International Journal of Robotics Research. 1984, 3(4): 21~50.
7 Tetsuya Mouri,Haruhisa Kawasaki,Keisuke Yoshikawa,Jun Takai,Satoshi Ito. Anthropomorphic Robot Hand:Gifu HandⅡ:Virtual System Laboratory.2002:1288~1290.
8 Butterfass, G. Hirzinger, S. Knoch, H. Liu. DLR’s Multisensory Articulated Hand, Part I: Hard- and Software Architecture. Proceedings of IEEE International Conference on Robotics and Automation. 1999:2081~2086
9刘宏,G. Hirzinger.智能机器人灵巧手的研究—DLR Dextrous Robot Hand I and II.西安交通大学学报. 2003, 37(4):331~337
10 S. Haidacher, J. Butterfass, M. Fischer, et al. DLR Hand II: Hard- and Software Architecture for Information Processing, Proceedings of the 2003 International Conference on Robotics and Automation. 2003:684~689
11 Claudio Melchiorri,Gabriele Vassura. Implementation of Whole-Hand Manipulation Capability in the UB Hand System Design. Advanced Robotics. 1995,9(5):547-560
12 C.S.Lovchik, M.A.Difler. The Robonaut Hand: A Dextrous Robotic Hand for Space. Proceedings of the IEEE International Conference on Robotics andAutomation. Detroit, Michigan. 1999: 907~912.
13 Aaron Edsinger-Gonzales.Design of a Compliant and Force Sensing Hand for a Humanoid Robot.Computer Science and Artificial Intelligence Laboratory,Massachusetts Institute of Techology.2004.
14 Karsten Weib, Dirk Goger, Heinz Worn.Reactive grasping in industrial automation.Institute for Process Control and Robotics(IPR),University of Karlsruhe,Germany.2006.
15李剑峰,张玉茹,张启先.多指手手指机构的速度操作灵巧性分析.机器人.1999, 12(2):46~51
16王国庆,李大寨,钱锡康等.新型三指灵巧机械手的研究.机械工程学报. 1997,33(3):71-75
17 Y. Zhang, Z. Han, H. Zhang, et al. Design and Control of the BUAA Four-Fingered Hand, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, 2001:2517~2522
18刘伊威,刘宏,姜力,金明河,巍然.基于机电一体化的机器人灵巧手手指的研制.哈尔滨工业大学学报. 2005, 37(8): 1022-1024
19陆震.机器人多指灵巧手的最佳灵活度设计.中国第五届机器人学术会议论文集.哈尔滨工业大学出版社. 1997: 97~100 20 http://www.OttoBock.de
21 Russell D.Howard.Design of a Robotic Wrist and Tool-Exchange Mechanism for Satellite Servicing. University of Maryland.2002.
22 S.P.Bai, J.Angeles. The Design of A Gearless Pitch-Roll Wrist. Proceedings of the 2005 IEEE International Conference on Robotics and Automation Barcelona, Spain, April 2005:3224~3229
23 A.Caffaz, G.Cannata. The Design and Development of the DIST-Hand Dextrous Gripper. Proceedings of the IEEE International Conference on Robotics and Automation. Leuven, Belgium. 1998:2075-2080
24 A.Caffaz, G.Cannata. The Design and Development of the DIST-Hand Dextrous Gripper. Proceedings of the IEEE International Conference on Robotics and Automation. Leuven, Belgium. 1998:2075-2080
25 Nakano Y.,Fujie M.,Hosada Y.. Hitachi’s Robot Hand. Robotics Age. Vol.6,No.7,Jul.1984:18-20
26 G. Hirzinger, M. Ficsher, B. Brunner. Advances in Robotics: The DLR Experience. The International Journal of Robotics Research. 1999, 18(1):1064~1087
27 J. Butterfass, M. Grebenstein, H. Liu, G. Hirzingerr. DLR-Hand II: Next Generation of a Dextrous Robot Hand. Proceedings of the 2001 IEEE International Conference on Robotics and Automation. 2001:109~114
28陈铁鸣,王连明.机械设计.哈尔滨工业大学出版社.2004.
29 D. Lawrence. Impedance Control Stability Properties in Common Implementations. Proceedings of the IEEE International Conference on Robotics and Automation. 1988: 1185~1192.
30刘伊威,姜力.机器人灵巧手手指耦合传动机构的研制.机械传动. 2004, 28(6):1-2
31谢宗武. HIT-1机器人灵巧手及其柔顺控制的研究.哈尔滨工业大学博士论文. 2003
32和平.基于物体阻抗的机器人灵巧手控制.哈尔滨工业大学博士论文. 2004
33杨磊.基于指尖传感器的DLR/HIT机器人灵巧手阻抗控制的研究.哈尔滨工业大学博士论文. 2005
34 R.M.Marry. Control Primitive for Robot Systems. IEEE Trans. On Sys.Man.Cyb.. 1992,22(1):183-193
35殷跃红,尉忠信,朱剑英.机器人柔顺控制研究. 1998,20(3): 232~240.
36李杰,韦庆,常文森,张彭.基于阻抗的自适应力跟踪方法.机器人. 1999, 21(1): 23~29.
37 T. Yoshikawa. Force Control of Robot Manipulators, Proceedings of the 2000 IEEE International Conference on Robotics & Automation, San Francisco, CA, April, 2000:1026~1031
38 Maples J.A, Becker J.J. Experiments in Force Control of Robotic Manipulators. Proc. IEEE Conf. on Robotics &Automat ion, 1986.
39 H. Liu, J. Butterfass, M. Grebenstein, G. Hirzinger. DLR Multisensory Articulated Hand I and II. Proceedings of the 2001 International Workshop on Bio-Robotics & Teleoperation, Beijing, China. 2001, 76~83.
40 H.Kazerooni. Robust Non-linear Impedance Control for robot manipulators. Proceedings of the IEEE International Conference on Robotics andAutomation. 1987: 741~750
41 H. Kazerooni. On the Robot Compliant Motion Control. Transactions of the ASME Journal of Dynamic Systems Measurement and Control. 1989, 111: 416~423
42 Claudio Melchiorri,Gabriele Vassura. Implementation of Whole-Hand Manipulation Capability in the UB Hand System Design. Advanced Robotics. 1995,9(5):547-560
43 Homayoun Seraji, Richard Collaugh. Adaptive force-based impedance control. Proceedings of the 1993 IEEE/RSJ International Conference Intelligent Robots and Systems, Yokonama, Japan. 1993: 1537 ~ 1544
44 S.Haidacher, G. Hirzinger. Estimating Finger Contact Location and Object Pose from Contact Measurements in 3-D Grasping. Proceedings of the 2003 IEEE International Conference on Robotics & Automation. Taipei, Taiwan. 2003: 1805~1810
45 Ziren Lu, Andrew A. Goldenberg. Robust Impedance Control and Force Regulation: Theory and Experiments. The International Journal of Robotics Research. 1995, 14(3): 226~254
46郑勇.六自由度关节型机器人自适应力控制的研究.哈尔滨工业大学工学博士学位论文.1995
47 H.Liu, G. Hizinger. Joint Torque Based Cartesian Impedance Control for the DLR Hand. International Comference on Advanced Intelligent Mechatronics. Atlanta, USA,Septemper19-23, 1999:695~700
48 Astr?m K.J., H?gglund T.. Automatic Tuning of PID Controllers. Instrument Society of America, Research Triangle Park, NC, 1994
49杨汝清等.智能控制工程.上海交通大学出版社,2001:181~201
50 M.H. Raibert and J.J. Craig. Hybrid Position/Force Control of Manipulator. Trans. ASME, J. DSMC, 1981,103(2):126~133
51 C.H. An and J.M. Hollerbach. The Role of Dynamic Models in Cartesian Force Control of Manipulators. International Journal of Robotics Research, 1989, 8(4):51~72
52 J.K. Salisbury. Active Stiffness Control of a Manipulator in Cartesian Coordinates. Proc. 19th IEEE Conf. on Decision and Control. 1980: 984~992
53 N. Hogan. Impedance Control of Robotic Manipulator: An Approach to Manipulation: Part I-Theory; Part II-Implementation; Part III-Applications. ASME J. Dynamic Systems, Measurement, and Control, 1985, 7(1):1~24
54 Markenscoff X., Ni L., and Papadimitriou C. H., The geometry of grasping. the International Journal of Robotics Research, 1990, 9(1): 61–74
2刘伊威.DLR/HIT仿人灵巧手系统及手指柔顺控制的研究.哈尔滨工业大学博士论文.2007.
3蔡自兴.机器人学.清华大学出版社.2000:265~272
4 Mark E. Posheim. Robot Evolution—the Development of Anth-robotics. The MIT Press, 1987:197~231
5 Okada T. Computer control of multijointed finger system for precise object-handing. IEEE Transactions on Systems,Man and Cybernetics. 1982, 12(3): 289~299.
6 S.C.Jacobsen, J.E.Wood, D.F.Knutti, K.B.Biggers. The UTAH/MIT Dextrous Hand: Work in Progress. The International Journal of Robotics Research. 1984, 3(4): 21~50.
7 Tetsuya Mouri,Haruhisa Kawasaki,Keisuke Yoshikawa,Jun Takai,Satoshi Ito. Anthropomorphic Robot Hand:Gifu HandⅡ:Virtual System Laboratory.2002:1288~1290.
8 Butterfass, G. Hirzinger, S. Knoch, H. Liu. DLR’s Multisensory Articulated Hand, Part I: Hard- and Software Architecture. Proceedings of IEEE International Conference on Robotics and Automation. 1999:2081~2086
9刘宏,G. Hirzinger.智能机器人灵巧手的研究—DLR Dextrous Robot Hand I and II.西安交通大学学报. 2003, 37(4):331~337
10 S. Haidacher, J. Butterfass, M. Fischer, et al. DLR Hand II: Hard- and Software Architecture for Information Processing, Proceedings of the 2003 International Conference on Robotics and Automation. 2003:684~689
11 Claudio Melchiorri,Gabriele Vassura. Implementation of Whole-Hand Manipulation Capability in the UB Hand System Design. Advanced Robotics. 1995,9(5):547-560
12 C.S.Lovchik, M.A.Difler. The Robonaut Hand: A Dextrous Robotic Hand for Space. Proceedings of the IEEE International Conference on Robotics andAutomation. Detroit, Michigan. 1999: 907~912.
13 Aaron Edsinger-Gonzales.Design of a Compliant and Force Sensing Hand for a Humanoid Robot.Computer Science and Artificial Intelligence Laboratory,Massachusetts Institute of Techology.2004.
14 Karsten Weib, Dirk Goger, Heinz Worn.Reactive grasping in industrial automation.Institute for Process Control and Robotics(IPR),University of Karlsruhe,Germany.2006.
15李剑峰,张玉茹,张启先.多指手手指机构的速度操作灵巧性分析.机器人.1999, 12(2):46~51
16王国庆,李大寨,钱锡康等.新型三指灵巧机械手的研究.机械工程学报. 1997,33(3):71-75
17 Y. Zhang, Z. Han, H. Zhang, et al. Design and Control of the BUAA Four-Fingered Hand, Proceedings of the 2001 IEEE International Conference on Robotics and Automation, 2001:2517~2522
18刘伊威,刘宏,姜力,金明河,巍然.基于机电一体化的机器人灵巧手手指的研制.哈尔滨工业大学学报. 2005, 37(8): 1022-1024
19陆震.机器人多指灵巧手的最佳灵活度设计.中国第五届机器人学术会议论文集.哈尔滨工业大学出版社. 1997: 97~100 20 http://www.OttoBock.de
21 Russell D.Howard.Design of a Robotic Wrist and Tool-Exchange Mechanism for Satellite Servicing. University of Maryland.2002.
22 S.P.Bai, J.Angeles. The Design of A Gearless Pitch-Roll Wrist. Proceedings of the 2005 IEEE International Conference on Robotics and Automation Barcelona, Spain, April 2005:3224~3229
23 A.Caffaz, G.Cannata. The Design and Development of the DIST-Hand Dextrous Gripper. Proceedings of the IEEE International Conference on Robotics and Automation. Leuven, Belgium. 1998:2075-2080
24 A.Caffaz, G.Cannata. The Design and Development of the DIST-Hand Dextrous Gripper. Proceedings of the IEEE International Conference on Robotics and Automation. Leuven, Belgium. 1998:2075-2080
25 Nakano Y.,Fujie M.,Hosada Y.. Hitachi’s Robot Hand. Robotics Age. Vol.6,No.7,Jul.1984:18-20
26 G. Hirzinger, M. Ficsher, B. Brunner. Advances in Robotics: The DLR Experience. The International Journal of Robotics Research. 1999, 18(1):1064~1087
27 J. Butterfass, M. Grebenstein, H. Liu, G. Hirzingerr. DLR-Hand II: Next Generation of a Dextrous Robot Hand. Proceedings of the 2001 IEEE International Conference on Robotics and Automation. 2001:109~114
28陈铁鸣,王连明.机械设计.哈尔滨工业大学出版社.2004.
29 D. Lawrence. Impedance Control Stability Properties in Common Implementations. Proceedings of the IEEE International Conference on Robotics and Automation. 1988: 1185~1192.
30刘伊威,姜力.机器人灵巧手手指耦合传动机构的研制.机械传动. 2004, 28(6):1-2
31谢宗武. HIT-1机器人灵巧手及其柔顺控制的研究.哈尔滨工业大学博士论文. 2003
32和平.基于物体阻抗的机器人灵巧手控制.哈尔滨工业大学博士论文. 2004
33杨磊.基于指尖传感器的DLR/HIT机器人灵巧手阻抗控制的研究.哈尔滨工业大学博士论文. 2005
34 R.M.Marry. Control Primitive for Robot Systems. IEEE Trans. On Sys.Man.Cyb.. 1992,22(1):183-193
35殷跃红,尉忠信,朱剑英.机器人柔顺控制研究. 1998,20(3): 232~240.
36李杰,韦庆,常文森,张彭.基于阻抗的自适应力跟踪方法.机器人. 1999, 21(1): 23~29.
37 T. Yoshikawa. Force Control of Robot Manipulators, Proceedings of the 2000 IEEE International Conference on Robotics & Automation, San Francisco, CA, April, 2000:1026~1031
38 Maples J.A, Becker J.J. Experiments in Force Control of Robotic Manipulators. Proc. IEEE Conf. on Robotics &Automat ion, 1986.
39 H. Liu, J. Butterfass, M. Grebenstein, G. Hirzinger. DLR Multisensory Articulated Hand I and II. Proceedings of the 2001 International Workshop on Bio-Robotics & Teleoperation, Beijing, China. 2001, 76~83.
40 H.Kazerooni. Robust Non-linear Impedance Control for robot manipulators. Proceedings of the IEEE International Conference on Robotics andAutomation. 1987: 741~750
41 H. Kazerooni. On the Robot Compliant Motion Control. Transactions of the ASME Journal of Dynamic Systems Measurement and Control. 1989, 111: 416~423
42 Claudio Melchiorri,Gabriele Vassura. Implementation of Whole-Hand Manipulation Capability in the UB Hand System Design. Advanced Robotics. 1995,9(5):547-560
43 Homayoun Seraji, Richard Collaugh. Adaptive force-based impedance control. Proceedings of the 1993 IEEE/RSJ International Conference Intelligent Robots and Systems, Yokonama, Japan. 1993: 1537 ~ 1544
44 S.Haidacher, G. Hirzinger. Estimating Finger Contact Location and Object Pose from Contact Measurements in 3-D Grasping. Proceedings of the 2003 IEEE International Conference on Robotics & Automation. Taipei, Taiwan. 2003: 1805~1810
45 Ziren Lu, Andrew A. Goldenberg. Robust Impedance Control and Force Regulation: Theory and Experiments. The International Journal of Robotics Research. 1995, 14(3): 226~254
46郑勇.六自由度关节型机器人自适应力控制的研究.哈尔滨工业大学工学博士学位论文.1995
47 H.Liu, G. Hizinger. Joint Torque Based Cartesian Impedance Control for the DLR Hand. International Comference on Advanced Intelligent Mechatronics. Atlanta, USA,Septemper19-23, 1999:695~700
48 Astr?m K.J., H?gglund T.. Automatic Tuning of PID Controllers. Instrument Society of America, Research Triangle Park, NC, 1994
49杨汝清等.智能控制工程.上海交通大学出版社,2001:181~201
50 M.H. Raibert and J.J. Craig. Hybrid Position/Force Control of Manipulator. Trans. ASME, J. DSMC, 1981,103(2):126~133
51 C.H. An and J.M. Hollerbach. The Role of Dynamic Models in Cartesian Force Control of Manipulators. International Journal of Robotics Research, 1989, 8(4):51~72
52 J.K. Salisbury. Active Stiffness Control of a Manipulator in Cartesian Coordinates. Proc. 19th IEEE Conf. on Decision and Control. 1980: 984~992
53 N. Hogan. Impedance Control of Robotic Manipulator: An Approach to Manipulation: Part I-Theory; Part II-Implementation; Part III-Applications. ASME J. Dynamic Systems, Measurement, and Control, 1985, 7(1):1~24
54 Markenscoff X., Ni L., and Papadimitriou C. H., The geometry of grasping. the International Journal of Robotics Research, 1990, 9(1): 61–74