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Research Papers

A Synergistic Optimal Design for Trajectory Tracking of Underactuated Manipulators

[+] Author and Article Information
Guaraci Bastos, Jr.

Mechanical Engineering Department,
Federal University of Pernambuco,
Av. Prof. Moraes Rego 1235,
Recife-PE 50670-901, Brazil
e-mail: guarajr.bastos@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 17, 2017; final manuscript received September 13, 2018; published online October 29, 2018. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 141(2), 021015 (Oct 29, 2018) (9 pages) Paper No: DS-17-1031; doi: 10.1115/1.4041530 History: Received January 17, 2017; Revised September 13, 2018

An integrated and general methodology is required to define an ideal relation between input controls and structural parameters of a system in trajectory tracking problems. For underactuated manipulators, a synergistic optimal design should be able to reduce elastic deformations, mass of the structure, and actuation forces. The key advantage of such integrated approach is the capability to search in a feasible design space, to account for many dynamic couplings in an early design stage, and to avoid simplifying assumptions which would induce to suboptimal design. Particularly, some advances considering underactuated manipulators are the possibility to treat nonminimum phase systems, then lighter structures could be selected, since bounded and smoother solution can be generated. A synergistic consideration, in order to find the desired requirements and realize the specified task through an optimal control problem, is in evidence, where a generalization of an inverse dynamics problem is defined. A planar underactuated manipulator is considered for the methodology application.

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Figures

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Fig. 1

Underactuated manipulator: scheme and motion

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Fig. 2

Integrated design—initial guess (i) 130 time steps

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Fig. 3

Integrated design—initial guess (ii) 130 time steps

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Fig. 4

Final objective function values related to the case 1, for a variety of initial values of type p0 = (0.05, c0, 0.25)T

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Fig. 5

Inverse dynamics comparison—passive joint motion

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Fig. 6

Inverse dynamics comparison—feedforward controls

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