A comparison of representations of general spatial screw displacement

Rooney, J.

doi:10.1068/b050045

Cited by 57 publications

(36 citation statements)

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“…Of the various representations of the resulting screw displacement that are possible (Rooney 1978), the most popular among roboticists is the use of homogeneous 4x4 matrices. The concatenation of N such joint-link pairs gives the final transformation that describes the translation and rotation of the end effector relative to the base of the robot.…”

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confidence: 99%

A Perturbation Approach to Robot Calibration

Kirchner

Gurumoorthy

Prinz

1987

The International Journal of Robotics Research

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The forward and reverse solutions of a manipulator with six joints are expanded up to second order in the 24 joint param eters. Assuming that the 24 errors of the 24 joint parameters are independent of the setting of the six controllable joint parameters, if suffices to triangulate the six coordinates (three translational, three rotational) of the end-effector and sub tract the ideal position computed from the forward solution of the ideal error-free robot. This provides 24 equations for 24 unknowns. Calibration compensation consists of correcting the six controllable joint parameters by six controllable ad justments so that the effect of the 24 errors is compensated for.

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confidence: 99%

A Perturbation Approach to Robot Calibration

Kirchner

Gurumoorthy

Prinz

1987

The International Journal of Robotics Research

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“…Screw motions can be used to describe rigid body motions. Already as early as 1830 Chasles proved that every rigid body motion can be realized by a rotation around an axis combined with a translation parallel to that axis, see also [25,30]. This is called a screw motion.…”

Section: Rigid Motions In Conformal Geometricmentioning

confidence: 99%

“…Fortunately, there are other algebraic embeddings which result in linearization with respects to points or other entities. While so far either point or line based transformations for rigid displacements have been distinguished [30], we will introduce in this paper a third category which is based on spheres, see Section 3.3.…”

Section: Rotations and Translations In The Euclideanmentioning

confidence: 99%

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Pose Estimation in Conformal Geometric Algebra Part II: Real-Time Pose Estimation Using Extended Feature Concepts

Rosenhahn

Sommer

2005

J Math Imaging Vis

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Abstract. 2D-3D pose estimation means to estimate the relative position and orientation of a 3D object with respect to a reference camera system. This work has its main focus on the theoretical foundations of the 2D-3D pose estimation problem: We discuss the involved mathematical spaces and their interaction within higher order entities. To cope with the pose problem (how to compare 2D projective image features with 3D Euclidean object features), the principle we propose is to reconstruct image features (e.g. points or lines) to one dimensional higher entities (e.g. 3D projection rays or 3D reconstructed planes) and express constraints in the 3D space. It turns out that the stratification hierarchy [11] introduced by Faugeras is involved in the scenario. But since the stratification hierarchy is based on pure point concepts a new algebraic embedding is required when dealing with higher order entities. The conformal geometric algebra (CGA) [24] is well suited to solve this problem, since it subsumes the involved mathematical spaces. Operators are defined to switch entities between the algebras of the conformal space and its Euclidean and projective subspaces. This leads to another interpretation of the stratification hierarchy, which is not restricted to be based solely on point concepts. This work summarizes the theoretical foundations needed to deal with the pose problem. Therefore it contains mainly basics of Euclidean, projective and conformal geometry. Since especially conformal geometry is not well known in computer science, we recapitulate the mathematical concepts in some detail. We believe that this geometric model is useful also for many other computer vision tasks and has been ignored so far. Applications of these foundations are presented in Part II [36].

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“…In fact, any line in the space is solely determined by its own position and direction [21,22]. If merely using the direction information for registration, the geometry constraint of registration model is not strong enough.…”

Section: Introductionmentioning

confidence: 99%

Registration of Urban Aerial Image and LiDAR Based on Line Vectors

et al. 2017

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Abstract:In a traditional registration of a single aerial image with airborne light detection and ranging (LiDAR) data using linear features that regard line direction as a control or linear features as constraints in the solution, lacking the constraint of linear position leads to the error propagation of the adjustment model. To solve this problem, this paper presents a line vector-based registration mode (LVR) in which image rays and LiDAR lines are expressed by a line vector that integrates the line direction and the line position. A registration equation of line vector is set up by coplanar imaging rays and corresponding control lines. Three types of datasets consisting of synthetic, theInternational Society for Photogrammetry and Remote Sensing (ISPRS) test project, and real aerial data are used. A group of progressive experiments is undertaken to evaluate the robustness of the LVR. Experimental results demonstrate that the integrated line direction and the line position contributes a great deal to the theoretical and real accuracies of the unknowns, as well as the stability of the adjustment model. This paper provides a new suggestion that, for a single image and LiDAR data, registration in urban areas can be accomplished by accommodating rich line features.

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A comparison of representations of general spatial screw displacement

Cited by 57 publications

References 0 publications

A Perturbation Approach to Robot Calibration

A Perturbation Approach to Robot Calibration

Pose Estimation in Conformal Geometric Algebra Part II: Real-Time Pose Estimation Using Extended Feature Concepts

Registration of Urban Aerial Image and LiDAR Based on Line Vectors

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