Spatial rational motions based on rational frenet-serret curves

Ravani, Reza; Meghdari, Ali

doi:10.1109/icsmc.2004.1401233

Cited by 7 publications

(3 citation statements)

References 12 publications

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“…In this paper we discuss a special class of rational motions called Rational Frenet-Serret (RF) (Ravani and Meghdari, 2004a;Ravani and Meghdari, 2004b) and apply this type of rational motions to robot trajectory planning. In application requiring control of the orientation of a rigid body, as its center of mass executes a given path, alignment of body's principal axes with the Frenet-Serret frame at each point appear to be the solution.…”

Section: Introductionmentioning

confidence: 99%

Velocity Distribution Profile for Robot Arm Motion Using Rational Frenet–Serret Curves

Ravani¹,

Meghdari²

2006

Informatica

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The aim of this paper is to demonstrate that the techniques of Computer Aided Geometric Design such as spatial rational curves and surfaces could be applied to Kinematics, Computer Animation and Robotics. For this purpose we represent a method which utilizes a special class of rational curves called Rational Frenet-Serret (RF) curves for robot trajectory planning. RF curves distinguished by the property that the motion of their Frenet-Serret frame is rational. We describe an algorithm for interpolation of positions by a rational Frenet-Serret motion. Further more we present an algorithm for tracking the constructed RF motion to achieve the desired velocity distribution profile of robot arm.

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Section: Introductionmentioning

confidence: 99%

Velocity Distribution Profile for Robot Arm Motion Using Rational Frenet–Serret Curves

Ravani¹,

Meghdari²

2006

Informatica

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“…The only difference is that the orientation of the body is required to follow the Bishop frame to the curve. This type of motion has been advocated by several authors over the years for different applications in robotics and computer aided design, see for example [16,25,26].…”

Section: Bishop Motionsmentioning

confidence: 99%

Persistent rigid-body motions and study’s “Ribaucour” problem

Selig

Carricato

2016

J. Geom.

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Abstract. In this work we show that the concept of a one-parameter persistent rigid-body motion is a slight generalisation of a class of motions called Ribaucour motions by Study. This allows a simple description of these motions in terms of their axode surfaces. We then investigate other special rigid-body motions, and ask if these can be persistent. The special motions studied are line-symmetric motions and motions generated by the moving frame adapted to a smooth curve. We are able to find geometric conditions for the special motions to be persistent and, in most cases, we can describe the axode surfaces in some detail. In particular, this work reveals some subtle connections between persistent rigid-body motions and the classical differential geometry of curves and ruled surfaces.Mathematics Subject Classification. Primary 53A17; Secondary 53A04, 53A25.

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“…The motion associated with the Bishop frame of a curve has been suggested by several workers for different applications. 1,6,7 Notice that any regular curve will define a Frenet-Serret or Bishop motion for a rigid body.…”

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confidence: 99%

Characterisation of Frenet–Serret and Bishop motions with applications to needle steering

Selig

2013

Robotica

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Frenet-Serret and Bishop rigid-body motions have many potential applications in robotics, graphics and computer aided design. In order to study these motions new characterisations in terms of their velocity twists are derived. This is extended to general motions based on any moving frame to a space curve. Further it is shown that any such general moving frame motion is the product of a Frenet-Serret motion with a rotation about the tangent vector.These ideas are applied to a simple model of needle steering. A simple kinematic model of the path of the needle is derived. It is then shown that this leads to Frenet-Serret motions of the needle tip but with constant curvature. Finally some remarks about curves with constant curvature are made.

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Spatial rational motions based on rational frenet-serret curves

Cited by 7 publications

References 12 publications

Velocity Distribution Profile for Robot Arm Motion Using Rational Frenet–Serret Curves

Velocity Distribution Profile for Robot Arm Motion Using Rational Frenet–Serret Curves

Persistent rigid-body motions and study’s “Ribaucour” problem

Characterisation of Frenet–Serret and Bishop motions with applications to needle steering

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