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History of Robotics Research and Development of Japan1989ManipulationPosition Control of a Manipulator with Passive Joints Using Coupled Dynamics

Hirohiko ARAIMechanical Engineering Laboratory, AIST, MITI (currently National Institute of Advanced Industrial Science and Technology)
Susumu TACHIMechanical Engineering Laboratory, AIST, MITI (currently Keio University)
[Abstract] This paper describes a method of controlling the position of a manipulator which is composed of active and passive joints.  The active joints have actuators and position sensors. The passive joints have holding brakes instead of actuators.  While the brakes are released, the passive joints are indirectly controlled by the motion of the active joints using the coupling characteristics of manipulator dynamics. While the brakes are engaged, the passive joints are fixed and the active joints are controlled. The position of the manipulator is controlled by combining these two control modes. This paper describes the basic principle of the control method and the conditions that ensure the controllability of the passive joints. An algorithm for point to point control of the manipulator is also presented. The feasibility of the method is demonstrated by simulation experiments of a manipulator with two degrees of freedom.   [About the paper] This paper was one of the earliest works on underactuated manipulators.  Its basic idea was to utilize the coupled dynamics among the joints and to control the motion of the passive joints using the torque of the active joints.  In the viewpoint of a control technique, it was a primitive form of partial feedback linearization [6] in nonlinear control theory.  The partial dynamics including the state of the passive joints were linearized by nonlinear feedback, under the condition that a part of the inertia matrix representing the coupled dynamics was nonsingular.  Then the state of the passive joints was controlled using the active joint torque as control inputs.  The boundary conditions related to the remained partial dynamics were adjusted using the brakes at the passive joints, and the positioning of the whole manipulator was achieved. Ref. [1, 4] presented experimental verification of the position control by the proposed method.  Ref. [2, 3, 5] combined the manipulator kinematics with this method to extend to the control in the operational coordinate space, and then applied it to path tracking control.  The movie compiled these experimental results. Now it is widely known that some types of underactuated manipulators belong to second-order nonholonomic systems.  It was firstly pointed out in Ref. [7] in 1991.  The concept of nonholonomic system was hardly known in robotics field around 1988-1989 when the author wrote this paper.  It should be noted that the discussion on the controllability in this paper (Section 3) is based on the linear approximation model and hence incomplete in the state of art now.  Considering the nonholonomic characteristics, the number of the joints which are simultaneously controllable is not limited to the number of the active joints, even when no gravity is applied to the joints. Studies on nonholonomic characteristics and nonholonomic control of underactuated manipulators significantly advanced in late 1990s.  Some types of underactuated manipulators are actually controlled without using the brakes at the passive joints, and the controllability is theoretically proved [8-18].  See those references and the review papers [19, 20] for detail.

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Correspondence papers


Hirohiko Arai, and Susumu Tachi:Position Control of a Manipulator with Passive Joints using Coupled Dynamics

Transactions of the SICE, Vol. 25, No. 9, pp. 1012-1017, 1989 (in Japanese).
(Link: https://www.jstage.jst.go.jp/article/sicetr1965/25/9/25_9_1012/_pdf)

H. Arai and S. Tachi:Position Control of a Manipulator with Passive Joints Using Dynamic Coupling

IEEE Trans. on Robotics and Automation, Vol.7, No.4, pp.528-534, 1991.

Related papers


[1] Hirohiko Arai and Susumu Tachi: Dynamic Control of a Manipulator with Passive Joints (Position Control System of a Two-Degree-of-Freedom Manipulator), Transactions of the Japan Society of Mechanical Engineers (C), Vol.57, No.534, pp.619-624, 1991. (In Japanese)

[2] Hirohiko Arai and Susumu Tachi: Dynamic Control of a Manipulator with Passive Joints in an Operational Coordinate Space, Transactions of the Japan Society of Mechanical Engineers (C), Vol.57, No.537, pp.1621-1624, 1991. (In Japanese)

[3] Hirohiko Arai and Susumu Tachi: Path Tracking Control of a Manipulator with Passive Joints, Transactions of the Society of Instrument and Control Engineers, Vol.27, No.7, pp.800-805, 1991. (In Japanese)

[4] H. Arai and S. Tachi: Position Control System of a Two Degree of Freedom Manipulator with a Passive Joint, IEEE Trans. on Industrial Electronics, Vol.38, No.1, pp.15-20, 1991.

[5] H. Arai, K. Tanie and S. Tachi: Dynamic Control of a Manipulator with Passive Joints in Operational Space, IEEE Trans. on Robotics and Automation, Vol.9, No.1, pp.85-93, 1993.

[6] M. W. Spong: The Swing Up Control Problem for the Acrobot, IEEE Control Systems, Vol.15, No.1, pp.49-55, 1995.

[7] G. Oriolo and Y. Nakamura: Free-Joint Manipulators: Motion Control under Second-Order Nonholonomic Constraints, Proc. IEEE/RSJ Int. Workshop on Intelligent Robots and Systems (IROS'91), pp.1248-1253, 1991.

[8] Y. Nakamura, R. Iwamoto, and K. Yoshimoto: Control of Nonholonomic Mechanisms with Drift, Journal of Robotic Society of Japan, Vol.13, No.6, pp.830-837, 1995. (In Japanese)

[9] Y. Nakamura, M. Koinuma and T. Suzuki: Chaotic Behavior and Nonlinear Control of a Two-joint Planar Arm with a Free Joint - Control of Nonholonomic Mechanisms with Drift -, Journal of Robotic Society of Japan, Vol.14, No.4, pp.602-611, 1996. (In Japanese)

[10] Hirohiko Arai: Controllability of a 3-DOF Manipulator with a Passive Joint under a Nonholonomic Constraint Journal of Robotic Society of Japan, Vol.14, No.5, pp.751-758, 1996. (In Japanese)

[11] Hirohiko Arai, Kazuo Tanie and Naoji Shiroma: Feedback Control of a 3-Axis Planar Manipulator with a Passive Joint under a Nonholonomic Constraint, Journal of the Robotics Society of Japan, Vol.15, No.6, pp.943-952, 1997. (In Japanese)

[12] K. Kobayashi, J. Imura and T. Yoshikawa: Nonholonomic Control of 3-D. O. F. Manipulator with a Free Joint, Transactions of the Society of Instrument and Control Engineers, Vol.33, No.8, pp.799-804, 1997. (In Japanese)

[13] Y. Nakamura and T. Suzuki: Behavior Analysis and Control by Amplitude Modulation of Nonholonomic Mechanical Systems via the Averaging Method - Positioning Control of Planar 2R Free-Joint Manipulators -, Vol.16, No.3, pp.407-416, 1998. (In Japanese)

[14] Hirohiko Arai, Kazuo Tanie and Naoji Shiroma: Time-scaling Control of an Underactuated Manipulator, Journal of the Robotics Society of Japan, Vol.16, No.4, pp.561-568, 1998. (In Japanese)

[15] K. Kobayashi, J. Imura and T. Yoshikawa: Controllability of a 4-D.O.F. Planar Manipulator with Two Unactuated Joints, Journal of the Robotics Society of Japan, Vol.17, No.6, pp.811-817, 1999. (In Japanese)

[16] K. Kobayashi, J. Imura and T. Yoshikawa: Controllability of Planar Manipulators with One Unactuated Joint, Journal of the Robotics Society of Japan, Vol.17, No.8, pp.1167-1172, 1999. (In Japanese)

[17] T. Yoshikawa, K. Kobayashi and T. Watanabe: Design of a Desirable Trajectory and Convergent Control for 3 - D.O.F Manipulator with a Nonholonomic Constraint, Journal of the Robotics Society of Japan, Vol.18, No.4, pp.584-589, 2000. (In Japanese)

[18] T. Suzuki, W. Miyoshi and Y. Nakamura: Control of Nonholonomic Free Joint Manipulators, Journal of the Robotics Society of Japan, Vol.19, No.4, pp.499-509, 2001. (In Japanese)

[19] Hirohiko Arai: Control of Second-order Nonholonomic Systems, Journal of the Society of Instrument and Control Engineers, Vol.36, No.6, pp.404-410, 1997. (In Japanese)

[20] Hirohiko Arai: Nonholonomic Control of Underactuated Manipulators, Systems, Control and Information, Vol.43, No.10, pp.553-560, 1999. (In Japanese)


[Patents]
H. Arai and S. Tachi: Japan Patent No. 1,806,579, Dec. 10, 1993.

H. Arai and S. Tachi: Japan Patent No. 1,928,062, May 12, 1995.

H. Arai and S. Tachi: Manipulator and Control Method, United States Patent No.4,928,047, May 22, 1990.

[Links]
Dr. Hirohiko Arai, Low-Formability-Materials Processing Group, Advanced Manufacturing Research Institute, National Institute of Advanced Industrial Science and Technology
http://staff.aist.go.jp/h.arai/uam_e.html

Prof. Takahiro Suzuki, The Institute of Industrial Science, The University of Tokyo
http://www.iis.u-tokyo.ac.jp/~suzukitk/index-j.html

Prof. Keigo Kobayashi, Department of Systems Design and Informatics, Kyushu Institute of Technology
http://www.kklab.ces.kyutech.ac.jp/~kobayasi/

DIAG Robotics Laboratory, Universita' di Roma "La Sapienza" (Prof. A. De Luca, Prof. G. Oriolo)
http://www.dis.uniroma1.it/~labrob/index.html

Neuroscience and Robotics Laboratory, Northwestern University (Prof. Kevin M. Lynch)
http://nxr.northwestern.edu/

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