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196
The calculation of robot dynamics using articulatedbody inertias
 Int J. Robot. Res
, 1983
"... This paper describes a new method for calculating the acceleration of a robot in response to given actuator forces. The method is applicable to openloop kinematic chains containing revolute and prismatic joints. The algorithm is based on recursive formulas involving quantities called articulatedbo ..."
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Cited by 110 (4 self)
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This paper describes a new method for calculating the acceleration of a robot in response to given actuator forces. The method is applicable to openloop kinematic chains containing revolute and prismatic joints. The algorithm is based on recursive formulas involving quantities called articulatedbody inertias, which represent the inertia properties of collections of rigid bodies connected together by joints allowing constrained relative motion between the bodies. A new, matrixbased notation is introduced to represent articulatedbody inertias and other spatial quantities. This notation is used to develop the algorithm, and results in a compact representation of the equations. The new algorithm has a computational requirement that varies linearly with the number of joints,
SelfCalibration from Image Triplets
, 1996
"... We describe a method for determining affine and metric calibration of a camera with unchanging internal parameters undergoing planar motion. It is shown that affine calibration is recovered uniquely, and metric calibration up to a two fold ambiguity. The novel ..."
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Cited by 109 (18 self)
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We describe a method for determining affine and metric calibration of a camera with unchanging internal parameters undergoing planar motion. It is shown that affine calibration is recovered uniquely, and metric calibration up to a two fold ambiguity. The novel
On Computing FourFinger Equilibrium and ForceClosure Grasps of Polyhedral Objects
 International Journal of Robotics Research
, 1996
"... : This paper addresses the problem of computing stable grasps of threedimensional polyhedral objects. We consider the case of a hand equipped with four hard fingers and assume point contact with friction. We prove new necessary and sufficient conditions for equilibrium and force closure, and presen ..."
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Cited by 99 (6 self)
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: This paper addresses the problem of computing stable grasps of threedimensional polyhedral objects. We consider the case of a hand equipped with four hard fingers and assume point contact with friction. We prove new necessary and sufficient conditions for equilibrium and force closure, and present a geometric characterization of all possible types of fourfinger equilibrium grasps. We then focus on concurrent grasps, for which the lines of action of the four contact forces all intersect in a point. In this case, the equilibrium conditions are linear in the unknown grasp parameters, which reduces the problem of computing the stable grasp regions in configuration space to the problem of constructing the eightdimensional projection of an elevendimensional polytope. We present two projection methods: the first one uses a simple Gaussian elimination approach, while the second one relies on a novel outputsensitive contourtracking algorithm. Finally, we use linear optimization within t...
Metric calibration of a stereo rig
 In Proc. IEEE Workshop on Representation of Visual Scenes
, 1995
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On Geometric Assembly Planning
, 1992
"... This dissertation addresses the problem of generating feasible assembly sequences for a mechanical product from a geometric model of the product. An operation specifies a motion to bring two subassemblies together to make a larger subassembly. An assembly sequence is a sequence of operations that co ..."
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Cited by 81 (13 self)
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This dissertation addresses the problem of generating feasible assembly sequences for a mechanical product from a geometric model of the product. An operation specifies a motion to bring two subassemblies together to make a larger subassembly. An assembly sequence is a sequence of operations that construct the product from the individual parts. I introduce the nondirectional blocking graph, a succinct characterization of the blocking relationships between parts in an assembly. I describe efficient algorithms to identify removable subassemblies by constructing and analyzing the NDBG. For an assembly A of n parts and m partpart contacts equivalent to k contact points, a subassembly that can translate a small distance from the rest of A can be identified in O(mk 2 ) time. When rotations are allowed as well, the time bound is O(mk 5 ). Both algorithms are extended to find connected subassemblies in the same time bounds. All free subassemblies can be identified in outputdependent ...
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
, 2001
"... In engineering and applied mathematics, polynomial systems arise whose solution sets contain components of different dimensions and multiplicities. In this article we present algorithms, based on homotopy continuation, that compute much of the geometric information contained in the primary decomposi ..."
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Cited by 76 (36 self)
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In engineering and applied mathematics, polynomial systems arise whose solution sets contain components of different dimensions and multiplicities. In this article we present algorithms, based on homotopy continuation, that compute much of the geometric information contained in the primary decomposition of the solution set. In particular, ignoring multiplicities, our algorithms lay out the decomposition of the set of solutions into irreducible components, by finding, at each dimension, generic points on each component. As byproducts, the computation also determines the degree of each component and an upper bound on itsmultiplicity. The bound issharp (i.e., equal to one) for reduced components. The algorithms make essential use of generic projection and interpolation, and can, if desired, describe each irreducible component precisely as the common zeroesof a finite number of polynomials.
Geometric Skinning with Approximate Dual Quaternion Blending
, 2008
"... Skinning of skeletally deformable models is extensively used for realtime animation of characters, creatures and similar objects. The standard solution, linear blend skinning, has some serious drawbacks that require artist intervention. Therefore, a number of alternatives have been proposed in re ..."
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Cited by 56 (3 self)
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Skinning of skeletally deformable models is extensively used for realtime animation of characters, creatures and similar objects. The standard solution, linear blend skinning, has some serious drawbacks that require artist intervention. Therefore, a number of alternatives have been proposed in recent years. All of them successfully combat some of the artifacts, but none challenge the simplicity and efficiency of linear blend skinning. As a result, linear blend skinning is still the number one choice for the majority of developers. In this paper, we present a novel skinning algorithm based on linear combination of dual quaternions. Even though our proposed method is approximate, it does not exhibit any of the artifacts inherent in previous methods and still permits an efficient GPU implementation. Upgrading an existing animation system from linear to dual quaternion skinning is very easy and has a relatively minor impact on runtime performance.
3D motion estimation, understanding and prediction from noisy image sequences
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 1987
"... AbstractThis paper presents an approach to understanding general 3D motion of a rigid body from image sequences. Based on dynamics, a locally constant angular momentum (LCAM) model is introduced. The model is local in the sense that it is applied to a limited number of image frames at a time. Spec ..."
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Cited by 50 (2 self)
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AbstractThis paper presents an approach to understanding general 3D motion of a rigid body from image sequences. Based on dynamics, a locally constant angular momentum (LCAM) model is introduced. The model is local in the sense that it is applied to a limited number of image frames at a time. Specifically, the model constrains the motion, over a local frame subsequence, to be a superposition of precession and translation. Thus, the instantaneous rotation axis of the object is allowed to change through the subsequence. The trajectory of the rotation center is approximated by a vector polynomial. The parameters of the model evolve in time so that they can adapt to long term changes in motion characteristics. The nature and parameters of short term motion can be estimated continuously with the goal of understanding motion through the image sequence. The estimation algorithm presented in this paper is linear, i.e., the algorithm consists of solving simultaneous linear equations. Based on the assumption that the motion is smooth, object positions and motion in the near future can be predicted, and short missing subsequences can be recovered. Noise smoothing is achieved by overdetermination and a leastsquares criterion. The framework is flexible in the sense that it allows both overdetermination in number of feature points and the number of image frames. The number of frames from which the model is derived can be varied according to the complexity of motion and the noise level so as to obtain stable and good estimates of parameters over the entire image sequence. Simulation results are given for noisy synthetic data and images taken of a model airplane. Index TermsComputer vision, dynamic model, image sequence analysis, motion, motion estimation, motion prediction, motion understanding. I.