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37
STRANDS: Interactive Simulation of Thin Solids using Cosserat Models
 EUROGRAPHICS 2002
, 2002
"... STRANDS are thin elastic solids that are visually well approximated as smooth curves, and yet possess essential physical behaviors characteristic of solid objects such as twisting. Common examples in computer graphics include: sutures, catheters, and tendons in surgical simulation; hairs, ropes, a ..."
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Cited by 70 (4 self)
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STRANDS are thin elastic solids that are visually well approximated as smooth curves, and yet possess essential physical behaviors characteristic of solid objects such as twisting. Common examples in computer graphics include: sutures, catheters, and tendons in surgical simulation; hairs, ropes, and vegetation in animation. Physical models based on spring meshes or 3D finite elements for such thin solids are either inaccurate or inefficient for interactive simulation. In this paper we show that models based on the Cosserat theory of elastic rods are very well suited for interactive simulation of these objects. The physical model reduces to a system of spatial ordinary differential equations that can be solved efficiently for typical boundary conditions. The model handles the important geometric nonlinearity due to large changes in shape. We introduce Cosserattype physical models, describe efficient numerical methods for interactive simulation of these models, and implementation results.
Enumerating the NonIsomorphic Assembly Configurations of Modular Robotic Systems
 the International Journal of Robotics Research
"... A "modular" robotic system consists of joint and link modules that can be assembled in a variety of configurations to meet different or changing task requirements. However, due to typical symmetries in module design, different assembly configurations may lead to robotic structures which ar ..."
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Cited by 29 (1 self)
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A "modular" robotic system consists of joint and link modules that can be assembled in a variety of configurations to meet different or changing task requirements. However, due to typical symmetries in module design, different assembly configurations may lead to robotic structures which are kinematically identical, or isomorphic. This paper considers how to enumerate the nonisomorphic assembly configurations of a modular robotic system. We introduce an Assembly Incidence Matrix (AIM) to represent a modular robot assembly configuration. Then we use symmetries of the module geometry and graph isomorphisms to define an equivalence relation on the AIMs. Equivalent AIMs represent isomorphic robot assembly configurations. Based on this equivalence relation, we propose an algorithm to generate nonisomorphic assembly configurations of an nlink treelike robot with different joint and link module types. Examples demonstrate that this method is a significant improvement over a brute force enu...
A recursive multibody dynamics and sensitivity algorithm for branched kinematic chains
 ASME J. of Dynamic Systems Meas. and Control
, 2001
"... In this work an efficient dynamics algorithm is developed, which is applicable to a wide range of multibody systems, including underactuated systems, branched or treetopology systems, robots, and walking machines. The dynamics algorithm is differentiated with respect to the input parameters in orde ..."
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Cited by 11 (3 self)
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In this work an efficient dynamics algorithm is developed, which is applicable to a wide range of multibody systems, including underactuated systems, branched or treetopology systems, robots, and walking machines. The dynamics algorithm is differentiated with respect to the input parameters in order to form sensitivity equations. The algorithm makes use of techniques and notation from the theory of Lie groups and Lie algebras, which is reviewed briefly. One of the strengths of our formulation is the ability to easily differentiate the dynamics algorithm with respect to parameters of interest. We demonstrate one important use of our dynamics and sensitivity algorithms by using them to solve difficult optimal control problems for underactuated systems. The algorithms in this paper have been implemented in a software package named Cstorm (Computer simulation tool for the optimization of robot manipulators), which runs from within Matlab and Simulink. It can be downloaded from the website
Numerical inverse kinematics for modular reconfigurable robots
 Proceedings of IEEE Conf. Robotics & Automation
, 1998
"... Abstract — Inverse kinematics solutions of a reconfigurabie robot system built upon a collection of standardized components is dificult to obtain because of its varying configuration. This paper addresses the formulation of a generic numerical inverse kinematics model and automatic generation of the ..."
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Cited by 9 (6 self)
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Abstract — Inverse kinematics solutions of a reconfigurabie robot system built upon a collection of standardized components is dificult to obtain because of its varying configuration. This paper addresses the formulation of a generic numerical inverse kinematics model and automatic generation of the model for arbitrary robot geometry including serial type and branching type geometry. Both revolute and prismatic types of joints are considered. The inverse kinematics is obtained through the di@erential kinematics equations based on the Productofexponential (POE) formulas. The NewtonRaphson iteration method is employed for solution. The automated model generation is accomplished through the introduction of Assembly Incidence Matrix (AIM) representation of a modular robot assembly configuration and the related accessibility matrix and path matrix. Examples of the inverse kinematics solutions for different types of modular robots are given to demonstrate the applicability and effectiveness of the proposed algorithm. 1
Projective Rotations applied to a PanTilt Stereo Head
 In Proc. of Intl. Conf. on Computer Vision and Pattern Recognition (CVPR’ 1999), volume II
, 1999
"... A nonmetric pantilt stereohead consists of a weakly calibrated stereo rig mounted on a pantilt mechanism. It is called nonmetric since neither the kinematics of the mechanism, nor camera calibration are required. The Lie group of "projective rotations" homographies of projective spac ..."
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Cited by 7 (3 self)
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A nonmetric pantilt stereohead consists of a weakly calibrated stereo rig mounted on a pantilt mechanism. It is called nonmetric since neither the kinematics of the mechanism, nor camera calibration are required. The Lie group of "projective rotations" homographies of projective space corresponding to pure rotations  is an original formalism to model the geometry of such a pantilt system. A Rodrigues alike formula as well as a minimal parameterization of projective rotations are introduced.
Kinematic sets for realtime robust articulated object tracking
 IMAGE AND VISION COMPUTING
, 2007
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