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Research Papers

Redundancy Resolution of Kinematically Redundant Parallel Manipulators Via Differential Dynamic Programing

[+] Author and Article Information
João Cavacanti Santos

Department of Mechanical Engineering,
School of Engineering of São Carlos,
University of São Paulo,
São Carlos 13566-590, SP, Brazil
e-mail: joao.cavalcanti.santos@usp.br

Maíra Martins da Silva

Professor
Department of Mechanical Engineering,
School of Engineering of São Carlos,
University of São Paulo,
São Carlos 13566-590, SP, Brazil
e-mail: mairams@sc.usp.br

1Corresponding author.

Manuscript received December 10, 2016; final manuscript received April 26, 2017; published online May 24, 2017. Assoc. Editor: Marc Gouttefarde.

J. Mechanisms Robotics 9(4), 041016 (May 24, 2017) (9 pages) Paper No: JMR-16-1372; doi: 10.1115/1.4036739 History: Received December 10, 2016; Revised April 26, 2017

Kinematic redundancy may be an efficient way to improve the performance of parallel manipulators. Nevertheless, the inverse kinematic problem of this kind of manipulator presents infinite solutions. The selection of a single kinematic configuration among a set of many possible ones is denoted as redundancy resolution. While several redundancy resolution strategies have been proposed for planning the motion of redundant serial manipulators, suitable proposals for parallel manipulators are seldom. Redundancy resolution can be treated as an optimization problem that can be solved locally or globally. Gradient projection methods have been successfully employed to solve it locally. For global strategies, these methods may be computationally demanding and mathematically complex. The main objective of this work is to exploit the use of differential dynamic programing (DDP) for decreasing the computational demand and mathematical complexity of a global optimization based on the gradient projection method for redundancy resolution. The outcome of the proposed method is the optimal inputs for the active joints for a given trajectory of the end-effector considering the input limitations and different cost functions. Using the proposed method, the performance of a redundant 3PRRR manipulator is investigated numerically and experimentally. The results demonstrate the capability and versatility of the strategy.

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References

Figures

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Fig. 1

3PRRR: the kinematically redundant planar parallel manipulator built at São Carlos School of Engineering at University of São Paulo

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Fig. 2

Schematic representation of a 3PRRR

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Fig. 3

3RRR: (a) nonsingular configuration and (b) singular configuration, which mitigates mechanism rigidity

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Fig. 4

Illustration of persistent interchange between σ2 and σ3

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Fig. 5

The influence of c3 over H3

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Fig. 6

Pick-and-place task: reference poses

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Fig. 7

Numerical results: comparison between the reference and actual poses of the nonredundant manipulator's end-effector under torque disturbance (−0.05 N·m)

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Fig. 8

Experimental results: comparison between (a) the reference final pose and (b) the actual final pose of the nonredundant manipulator under no load disturbance

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Fig. 9

Numerical comparison between the reference and actual pose of the redundant manipulator's end-effector under torque disturbance (−1.30 N·m): (a) the end-effector's orientation and (b) the end-effector's translational positions

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Fig. 10

Experimental comparison between the reference and actual pose of the redundant manipulator's end-effector under no torque disturbance: (a) the end-effector's orientation and (b) the end-effector's translational positions

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Fig. 11

Active revolute joints' currents: (a) 3RRR and (b) 3PRRR

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