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Research Papers

Task Space Impedance Control of the Manipulator Driven Through the Multistage Nonlinear Flexible Transmission

[+] Author and Article Information
Phongsaen Pitakwatchara

Assistant Professor
Department of Mechanical Engineering,
Faculty of Engineering,
Chulalongkorn University,
Bangkok 10330, Thailand
e-mail: phongsaen.p@chula.ac.th

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 20, 2013; final manuscript received August 4, 2014; published online September 10, 2014. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 137(2), 021001 (Sep 10, 2014) (17 pages) Paper No: DS-13-1360; doi: 10.1115/1.4028252 History: Received September 20, 2013; Revised August 04, 2014

This paper addresses the task space impedance control of a robot driven through the multistage nonlinear flexible transmission. The proposed controller uses limited information of the angle and the current of the motors to regulate the end point compliance at the specified set point. In particular, motor angle is employed to estimate the stationary robot link angle and joint velocity in real time. They are then used to constitute the stationary force on the attempt to cancel the robot gravity force and to form the task space interacting force according to the desired impedance characteristics. Motor current is used to infer the transmitted torque to the robot. This torque is fed back to mitigate the effect of the motor inertia from deteriorating the desired impedance. Asymptotic stability of this controller with the flexible joint robot is guaranteed with additional damping. Passivity of the system is also investigated. Simulation and experiments of the proposed control scheme on a two degrees-of-freedom (DOF) cable-pulley driven flexible joint robot model are examined.

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Figures

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Fig. 1

Multidimensional bond graph diagram of the transmission system displaying the interconnection of the lumped elements along the cascading stages. Causality assignments conform to the cable-pulley transmission elastic model ej-1(·).

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Fig. 2

Signal flow diagram illustrating the network of the elastic elements and the subscript notations of the jth-stage transmission system

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Fig. 3

Overall diagram of the task space impedance controller

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Fig. 4

Interpretation of each term in Eq. (53) as the sub areas of the elastic potential/co-PE

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Fig. 5

Feedback interconnection of three subsystems of the nonlinear flexible joint robot controlled system interacting with the passive environment. The system as a whole is passive.

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Fig. 6

A 2DOF multistage cable-pulley driven flexible joint robot. In the figure, the proof mass of 1.0 kg is placed at the link end tip with a vernier height gauge used to measure the position in Y-direction.

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Fig. 7

Winches and pulleys arrangement in the drivetrain unit of the flexible joint robot. Relevant coordinate frames are shown. Left winch#1 is occluded.

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Fig. 8

Detailed bond graph diagram of the 2DOF cable-pulley driven flexible joint robot controlled system. The diagram displays the interconnection of the controller, motor, drivetrain, counterbalance, and robot units. In addition, physical systemlike couplings of the lumped model of the system components ease the understanding of the overall dynamics.

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Fig. 9

Simulation of the flexible robot end tip deflection with the nominal stiffness value of 10 × 103N/m and a set of damping ratios subject to 10 N force in the X- and Y-direction, respectively

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Fig. 10

Deflection responses of the real (left) and simulated (right) robot end tip under 1.0 kg proof mass with the stiffness value of 500 N/m

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Fig. 11

Tracking simulation with the stiffness of 10 × 103N/m subject to the 10 N force applied along the X- (left) and Y- (right) direction

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Fig. 12

Circular path tracking with the stiffness of 500 N/m under the 10 N force applied along the Y-direction for the real (left) and simulated (right) system

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Fig. 13

Current consumption of the simulated system for the regulation task under three different values of the effective motor inertia (150, 200, and 248 g cm2)

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Fig. 14

Current consumption of the real system for the regulation task under three different values of the effective motor inertia (150, 200, and 248 g cm2)

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Fig. 15

Current consumption of the simulated system for the circular tracking task under three different values of the effective motor inertia (170, 200, and 248 g cm2)

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Fig. 16

Current consumption of the real system for the circular tracking task under three different values of the effective motor inertia (170, 200, and 248 g cm2)

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