Research Papers

Peg-in-Hole Revisited: A Generic Force Model for Haptic Assembly

[+] 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

A short version of this article was presented at the ASME IDETC/CIE'2014 Conferences, DOI: 10.1115/DETC2014-35290.Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received December 2, 2014; final manuscript received May 22, 2015; published online August 20, 2015. Assoc. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 15(4), 041004 (Aug 20, 2015) (11 pages) Paper No: JCISE-14-1443; doi: 10.1115/1.4030749 History: Received December 02, 2014

The development of a generic and effective force model for semi-automatic or manual virtual assembly with haptic support is not a trivial task, especially when the assembly constraints involve complex features of arbitrary shape. The primary challenge lies in a proper formulation of the guidance forces and torques that effectively assist the user in the exploration of the virtual environment (VE), from repulsing collisions to attracting proper contact. The secondary difficulty is that of efficient implementation that maintains the standard 1 kHz haptic refresh rate. We propose a purely geometric model for an artificial energy field that favors spatial relations leading to proper assembly, differentiated to obtain forces and torques for general motions. The energy function is expressed in terms of a cross-correlation of shape-dependent affinity fields, precomputed offline separately for each object. We test the effectiveness of the method using familiar peg-in-hole examples. We show that the proposed technique unifies the two phases of free motion and precise insertion into a single interaction mode and provides a generic model to replace the ad hoc mating constraints or virtual fixtures, with no restrictive assumption on the types of the involved assembly features.

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Grahic Jump Location
Fig. 1

Assembly features captured by skeletal branches ((a) and (b)), which replace the virtual fixtures for assembly (c). The implicit skeletal density distribution ((d) and (e)) provides a robust substitute to facilitate measuring the overlap (f).

Grahic Jump Location
Fig. 2

The affinity computation is decomposed into two steps: a projection in Eq. (1) that characterizes the distance distribution as observed from the query point, followed by applying the kernel in Eq. (2).

Grahic Jump Location
Fig. 3

Possible spatial relations and the corresponding interactions. The generic virtual fixtures practically restrict the DOF if the stiffness properties (i.e., second-order partial derivatives of EG at the energy well) are large enough.

Grahic Jump Location
Fig. 4

Three peg-in-hole assemblies (a), their SDFs (imaginary-parts) ((b) and (c)), and their spatial overlap (real-part) (d)

Grahic Jump Location
Fig. 5

The shape complementarity score variations versus biaxial relative translation of the peg with respect to the hole

Grahic Jump Location
Fig. 6

The geometric energy variations versus uniaxial relative translation and rotation of the peg with respect to the hole

Grahic Jump Location
Fig. 7

Haptic force feedback versus time, for collision test (a)–(c) and snap test (d)–(f) for peg-in-hole examples in Fig. 4



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