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Research Papers

Stiffness Analysis and Control of a Stewart Platform-Based Manipulator With Decoupled Sensor–Actuator Locations for Ultrahigh Accuracy Positioning Under Large External Loads

[+] Author and Article Information
Boyin Ding

School of Mechanical Engineering,
University of Adelaide,
Adelaide, SA 5005, Australia
e-mail: boyin.ding@adelaide.edu.au

Benjamin S. Cazzolato, Steven Grainger

School of Mechanical Engineering,
University of Adelaide,
Adelaide, SA 5005, Australia

Richard M. Stanley

Biomechanics and Implants Research Group,
Medical Device Research Institute
and School of Computer Science,
Engineering and Mathematics,
Flinders University,
Bedford Park, SA 5042, Australia

John J. Costi

Biomechanics and Implants Research Group,
Medical Device Research Institute
and School of Computer Science,
Engineering and Mathematics,
Flinders University,
Bedford Park, SA 5042, Australia
e-mail: john.costi@flinders.edu.au

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 23, 2013; final manuscript received June 25, 2014; published online August 8, 2014. Assoc. Editor: Nariman Sepehri.

J. Dyn. Sys., Meas., Control 136(6), 061008 (Aug 08, 2014) (12 pages) Paper No: DS-13-1064; doi: 10.1115/1.4027945 History: Received January 23, 2013; Revised June 25, 2014

Robot frame compliance has a large negative effect on the global accuracy of the system when large external forces/torques are exerted. This phenomenon is particularly problematic in applications where the robot is required to achieve ultrahigh (micron level) accuracy under very large external loads, e.g., in biomechanical testing and high precision machining. To ensure the positioning accuracy of the robot in these applications, the authors proposed a novel Stewart platform-based manipulator with decoupled sensor–actuator locations. The unique mechanism has the sensor locations fully decoupled from the actuator locations for the purpose of passively compensating for the load frame compliance, as a result improving the effective stiffness of the manipulator in six degrees of freedom (6DOF). In this paper, the stiffness of the proposed manipulator is quantified via a simplified method, which combines both an analytical model (robot kinematics error model) and a numerical model [finite element analysis (FEA) model] in the analysis. This method can be used to design systems with specific stiffness requirements. In the control aspect, the noncollocated positions of the sensors and actuators lead to a suboptimal control structure, which is addressed in the paper using a simple Jacobian-based decoupling method under both kinematics- and dynamics-based control. Simulation results demonstrate that the proposed manipulator configuration has an effective stiffness that is increased by a factor of greater than 15 compared to a general design. Experimental results show that the Jacobian-based decoupling method effectively increases the dynamic tracking performance of the manipulator by 25% on average over a conventional method.

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Figures

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Fig. 1

Left images: Inventor model showing the upper and lower decoupled sensor–actuator locations of the Stewart platform-based manipulator. Right image: Inventor model of the entire Stewart platform-based manipulator.

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Fig. 2

Schematic showing the kinematic model of the manipulator

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Fig. 3

Schematic showing the lateral section of the manipulator with attached coordinate systems

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Fig. 4

Block diagram showing the kinematics-based control scheme

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Fig. 5

Block diagram showing the decoupled PID control algorithm

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Fig. 6

Loading and boundary conditions on the platform assembly ([tTθT] = [0 0 500 mm 0 0 0],[FeTMeT] = [0 0 20,000 N 0 0 0])

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Fig. 7

Loading and boundary conditions on the supporting frame ([tTθT] = [0 0 500 mm 0 0 0],[FeTMeT] = [0 0 20,000 N 0 0 0])

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Fig. 8

Deformations of the platform assembly ([tTθT]= [0 0 500 mm 0 0 0],[FeTMeT] = [0 0 20,000 N 0 0 0])

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Fig. 9

Deformations of the supporting frame ([tTθT]= [0 0 500 mm 0 0 0],[FeTMeT] = [0 0 20,000 N 0 0 0])

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Fig. 10

Photograph of the assembled manipulator testing a polymer specimen

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Fig. 11

Schematics showing the control hardware configuration and communication between hardware elements

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Fig. 12

Set-points for six leg controllers in the form of absolute leg lengths in mm

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Fig. 13

Tracking errors on three translations at specimen COR under kinematics-based control

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Fig. 14

Tracking errors on three rotations at specimen COR under kinematics-based control

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