Automatic determination of possible velocity and applicable force of frictionless objects in contact from a geometric model

Kirukawa, H.; Matsui, Toshihiro; Takase, Kunikatsu

doi:10.1109/70.294206

Cited by 34 publications

(18 citation statements)

References 16 publications

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“…Formulate the equation of feasible infinitesimal displacement using the method (Hirukawa et al (1994)) 3. Calculate the optimum configuration by removing the redundant displacement that is derived from the non-linear optimization.…”

Section: Vision Error Correction Using Contact Relationsmentioning

confidence: 99%

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Stereo Vision and Its Application to Robotic Manipulation

Takamatsu¹

2011

Advances in Stereo Vision

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Section: Vision Error Correction Using Contact Relationsmentioning

confidence: 99%

“…Hirukawa et al proposed a method for introducing the constraint on the contact relation between two polynomial objects (Hirukawa et al (1994)). They proved that the infinitesimal displacement that maintains the contact relation can be formulated as Eq.…”

Section: Vision Error Correction Using Contact Relationsmentioning

confidence: 99%

Stereo Vision and Its Application to Robotic Manipulation

Takamatsu¹

2011

Advances in Stereo Vision

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“…Also, since the used boolean expressions are valid for general polyhedra, no concavities have to be decomposed into convex parts. Thus, our algorithm is a simpler alternative to the one presented in [10].…”

Section: Discussionmentioning

confidence: 99%

“…In [10], Hirulmwa et al presented a technique for automatically deriving the possible velocities and applicable forces bet ween two polyhedra in contact. Their basic idea is to find separating planes between two neighborhoods of the contact points and use them to represent the possible motions of the moving object in terms of a system of homogeneous linear inequalities, which they efficiently solve.…”

Section: Related Workmentioning

confidence: 99%

A simple characterization of the infinitesimal motions separating general polyhedra in contact

Staffetti

Ros²,

Thomas³

Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C)

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We present a simple local geometric characterization of the configuration space of two polyhedra in coratact that provides a representation of all infinitesimal motions that separate them. The considered polyhedra are general in the sense that they possibly have nonconvex faces and arbitrary number of holes.The approach presented herein has two main advantages over former ones: (a) it only relies on the classical basic contacts between polyhedra, i.e. the vertexface and edge-edge contacts; and (b) it does not require the local decomposition of non-convem"ties into convex parts. IntroductionThis paper presents an algorithm for computing the infinitesimal motions separating two polyhedra A4 and S in contact, seen as a moving body and a static environment, respectively.The algorithm is complete, in the sense that it finds all feasible motions, and conceptually simpler than previous approaches.Our algorithm mainly operates in the 6-dimensional configuration space of &f, i.e. SO(3) x w. First, it considers the C-surfaces associated with the basic contacts at a configuration X.. Then, it computes the arrangement of tangent hyperplanes to these surfaces in X., obtaining all 6-dimensional convex cones it induces in !R6. Finally, the output is a classification of each of these cones into occupied or free, depending on whether the configurations it contains correspond to intersecting or separated polyhedra. This classification is efficiently attained by evaluating simple boolean expressions that depend on the geometric configurations of the basic contacts. The problem at hand arises in the assembly partitioning problem given a collection of polyhedral parts in contact, is there some infinitesimal motion that rigidly removes some subset of the parts from the rest? A negative answer means that the parts cannot be assembled by a sequence of rigid motions that fit them together. A positive answer, with the possible directions of motion, does not provide a plan on how to disassemble the parts, since the subsets need to be separated completely -and not only infinitesimally. However, this constitutes a very useful information for an assembly sequence planner [20].The paper is structured as follows. Section 2 summarizes the contributions of this work and its connections with previous research in the field. Section 3 introduces several basic concepts needed throughout the paper. Afterwards, section 4 gives a general description of the algorithm, which is followed by explanations on the role of non-effective contacts (section 5), and details on the main geometric constructions: the computation of tangent hyperplanes (section 6) and the construction of the resulting plane arrangement (section 7). The characterization of free and occupied cones follows in section 8. Finally, section 9 gives the conclusions and points that deserve further attention. Related workMany different approaches to the motion planning and related problems have been presented over the years. A common topic of many of them is Configuration Space, the spa...

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“…This can be done efficiently and robustly using the Oriented Bounding Box trees [2] and extending the concept of the separating plane [3], but it is not described here since it is out of the scope of this paper. From the infinitesimal translation and rotation, the contact force and torque are computed based on a nonlinear spring-damper model as follows.…”

Section: Finding the Contact Forcementioning

confidence: 99%