Research Papers

Controllability Ellipsoid to Evaluate the Performance of Mobile Manipulators for Manufacturing Tasks

[+] Author and Article Information
Stephen L. Canfield

Department of Mechanical Engineering,
Tennessee Technological University,
Cookeville, TN 38505
e-mail: SCanfield@tntech.edu

Reabetswe M. Nkhumise

Department of Mechanical Engineering,
Tennessee Technological University,
Cookeville, TN 38505

1Corresponding author.

Manuscript received December 14, 2016; final manuscript received September 8, 2017; published online October 12, 2017. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 9(6), 061013 (Oct 12, 2017) (10 pages) Paper No: JMR-16-1374; doi: 10.1115/1.4038007 History: Received December 14, 2016; Revised September 08, 2017

This paper develops an approach to evaluate a state-space controller design for mobile manipulators using a geometric representation of the system response in tool space. The method evaluates the robot system dynamics with a control scheme and the resulting response is called the controllability ellipsoid (CE), a tool space representation of the system’s motion response given a unit input. The CE can be compared with a corresponding geometric representation of the required motion task (called the motion polyhedron) and evaluated using a quantitative measure of the degree to which the task is satisfied. The traditional control design approach views the system response in the time domain. Alternatively, the proposed CE views the system response in the domain of the input variables. In order to complete the task, the CE must fully contain the motion polyhedron. The optimal robot arrangement would minimize the total area of the CE while fully containing the motion polyhedron. This is comparable to minimizing the power requirements of robot design when applying a uniform scale to all inputs. It will be shown that changing the control parameters changes the eccentricity and orientation of the CE, implying a preferred set of control parameters to minimize the design motor power. When viewed in the time domain, the control parameters can be selected to achieve desired stability and time response. When coupled with existing control design methods, the CE approach can yield robot designs that are stable, responsive, and minimize the input power requirements.

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Fig. 2

Weld patterns with corresponding motion and APs

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Fig. 1

Trapezoidal weld path

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Fig. 11

Poles of NCD, ICD

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Fig. 12

Time response of NCD (solid), ICD (dashed)

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Fig. 8

CE versus AP of square weld pattern for Xs=[0,0,0.2094,0.25,0,0,0]T, md∈[0.28,0.63] and α∈[40 deg,170 deg]

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Fig. 9

CE versus AP of trapezoidal weld pattern for Xs=[0,0,0,0.25,0,0,0]T, md∈[0.45,0.78] and α∈[52 deg,92 deg]

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Fig. 10

CE versus AP of trapezoidal weld pattern for Xs=[0,0,0.2094,0.25,0,0,0]T, md∈[0.67,0.23] and α∈[42 deg,154 deg]

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Fig. 4

Dynamic comparisons: CE versus AP for trapezoidal pattern

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Fig. 5

Manipulability ellipsoids versus motion polygon of square weld pattern, with mk=0.508 and α=144 deg (orientation of the ellipsoid’s major axis) for Xs=[0000.25000]T

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Fig. 6

Manipulability ellipsoids versus motion polygon of trapezoidal weld pattern, with mk=0.057 and α=144 deg (orientation of the ellipsoid’s major axis) for Xs=[0000.25000]T

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Fig. 7

CE versus AP of square weld pattern for Xs=[0,0,0,0.25,0,0,0]T, md∈[0.37,0.90] and α∈[53 deg,101 deg]

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Fig. 13

CE versus AP, unscaled ((a) left), scaled ((b) right) 1.26 scaling for improved versus 2.9 scaling for nominal



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