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

Hirohiko ARAI	Mechanical Engineering Laboratory, AIST, MITI (currently National Institute of Advanced Industrial Science and Technology)
Susumu TACHI	Mechanical 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.

記事はありません。

Related Article