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Research Papers

Haptic Assembly Using Skeletal Densities and Fourier Transforms1

[+] Author and Article Information
Morad Behandish

Computational Design Laboratory,
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: m.behandish@engr.uconn.edu

Horea T. Ilieş

Computational Design Laboratory,
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: ilies@engr.uconn.edu

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received July 11, 2015; final manuscript received January 28, 2016; published online March 11, 2016. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 16(2), 021002 (Mar 11, 2016) (11 pages) Paper No: JCISE-15-1223; doi: 10.1115/1.4032696 History: Received July 11, 2015; Revised January 28, 2016

Haptic-assisted virtual assembly and prototyping has seen significant attention over the past two decades. However, in spite of the appealing prospects, its adoption has been slower than expected. We identify the main roadblocks as the inherent geometric complexities faced when assembling objects of arbitrary shape, and the computation time limitation imposed by the notorious 1 kHz haptic refresh rate. We addressed the first problem in a recent work by introducing a generic energy model for geometric guidance and constraints between features of arbitrary shape. In the present work, we address the second challenge by leveraging Fourier transforms to compute the constraint forces and torques. Our new concept of “geometric energy” field is computed automatically from a cross-correlation of “skeletal densities” in the frequency domain, and serves as a generalization of the manually specified virtual fixtures or heuristically identified mating constraints proposed in the literature. The formulation of the energy field as a convolution enables efficient computation using fast Fourier transforms (FFTs) on the graphics processing unit (GPU). We show that our method is effective for low-clearance assembly of objects of arbitrary geometric and syntactic complexity.

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Figures

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Fig. 1

Different configurations (a) are evaluated using a simple gap function (b), and the shape complementarity score function (c), based on overlapping shape skeletons (d), formulated as a cross-correlation of skeletal densities (e)

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Fig. 2

The extent of geometric details captured by the skeletal density distribution is adjustable by the thickness factor σ. (a) σ = 0.25, (b) σ = 0.50, (c) σ = 1.00, and (d) σ = 10.0.

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Fig. 3

Frequency domain representation allows for a systematic means of successive approximation of the energy field. (a) m′ = 42, (b) m′ = 82, (c) m′ = 162, and (d) m′ = 322.

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Fig. 5

The effect of FFT filtering on part SDFs (top) and score variations versus biaxial relative translation (bottom). (a) Assembly, (b) m′ = 43, (c) m′ = 83, (d) m′ = 163, (e) m′ = 323, (f) m′ = 643, and (g) m′ = m = 1283.

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Fig. 6

CPU versus GPU performances for SDF computation

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Fig. 7

CPU versus GPU performances for FFT convolution

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Fig. 4

A nontrivial, zero-clearance assembly pair

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Fig. 8

Performance of a haptic assembly simulation

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