Welcome to the home page of the Multibody Systems Research Group in the Department of Mathematics and Computer Science at Clark University, Worcester, Massachusetts. We study fundamental mathematical properties and develop efficient algorithms for multibody systems of various types, including kinematic chains and manipulation systems in robotics, braids and knots in topology, proteins in biochemistry, and many more!
Some of the activities reported on this page are supported by the National Science Foundation under Grant No. IIS-0713335.
This page is still under construction. Last update: 08/07/2008.
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This summer Sam Dorsey-Gordon, Dan Menard, James Wilson, Jon Moran and Dylan Glotzer worked on a java program to simulate and animate text files of 5-bar multibody systems. James Wilson and Dylan Glotzer worked on the complex mathmatical formulas that Sam Dorsey-Gordon and Jon Moran converted into java code. Dan Menard worked on parallel applications of the code, overall object-oriented structure and website development. To use the java code for your own 5-bar multibody system as well as learn about the fundamental math behind the code, visit the 5-bar page (not yet available as we wait to submit our paper in early September).
In addition, a program simulating a 6-bar and N-bar cases have begun. Linkages greater than 6-bar are possible, but require 4-dimensional displays.
Between June 25 and 28, 2008, Lee Rudolph attended 2008 Robotics: Science and Systems (RSS 2008) a at ETH in Zurich, Switzerland, to present the paper Simplex-Tree Based Kinematics of Foldable Objects as Multibody Systems Involving Loops by Li Han and Lee Rudolph.
On May 30, 2008, members of our laboratory attended the Fourth Annual New England Manipulation Symposium (NEMS) at Brown University.
In April 2008, the National Science Foundation supplemented its funding for our research on Practical Parametrization and Efficient Motion Planning of Linkage Systems to further support a Research Experience for Undergraduates (REU) program.
On August 18, 2007, the National Science Foundation announced Award 0713335, for research on Practical Parametrization and Efficient Motion Planning of Linkage Systems, with Li Han as Principal Investigator and Lee Rudolph as co-PI. An important feature of the successful proposal is training and involvement of undergraduate students in mathematical and algorithmic aspects of robotics research.
On Friday, April 13, 2007, Li Han presented the paper A unified geometric approach to inverse kinematics of a spatial chain with spherical joints at ICRA 2007 in Rome. At the end of May, Lee Rudolph attended the conference BRAIDS AND THEIR RAMIFICATIONS: Configuration Spaces, Arrangements, Mapping-Class Groups, 3-Manifolds in Cortona, Italy.
In 2006, Li Han and Lee Rudolph attended three robotics conferences and presented two papers on applications of configuration spaces to multibody systems problems in robotics.
Simplex-Tree Based Kinematics of Foldable Objects as Multibody Systems Involving Loops, L. Han and L. Rudolph, to appear in Proceedings of Robotics: Science and Systems 2008.
A unified geometric approach to inverse kinematics of a spatial chain with spherical joints, L. Han and L. Rudolph, Proceedings of ICRA07 (IEEE International Conference on Robotics and Automation, 2007).
Convexly Stratified Deformation Spaces and Efficient Path Planning for Planar Closed Chains with Revolute Joints, L. Han, L. Rudolph, J. Blumenthal, and I. Valodzin (under review by International Journal of Robotics Research).
Inverse kinematics for a serial chain with joints under distance constraints, L. Han and L. Rudolph, in Proceedings of Robotics: Science and Systems II (Gaurav Suhas Sukhatme, ed.), MIT Press (Cambridge, Mass.), 2007, pp. 177-184.
Stratified configuration space and path planning for a planar closed chain with revolute joints, L. Han, L. Rudolph, J. Blumenthal, and I. Valodzin, in Proceedings of WAFR 2006 (Seventh International Workshop on the Algorithmic Foundations of Robotics), Springer-Verlag (to appear, 2007).
A temperature-dependent probabilistic roadmap algorithm for calculating variationally optimized conformational transition pathways, H. Yang, H. Wu, L. Han, and S. Huo, Journal of Chemical Theory and Computation 3 (2007), 17-25.
L. Rudolph, Knot theory of complex plane curves, in Handbook of Knot Theory (ed. W. Menasco and M. Thistlethwaite), Elsevier (2005), Chapter 8, pp. 349-427 (see particularly sections 1.9, ``Configuration spaces''; 2.1-2.6, on braids and braided surfaces largely from the point of view of configuration spaces; and 7.3, a speculation on ``spaces of C-links'').
L. Han, Hybrid Probabilistic Roadmap - Monte Carlo motion planning for closed chain systems with spherical joints, Proc. 2004 IEEE International Conference on Robotics and Automation (ICRA'04), April 2004.
L. Han, Hybrid Probabilistic Roadmap and Monte Carlo methods for biomolecule conformational changes, Eighth Annual International Conference on Research in Computational Molecular Biology (RECOMB04), March 2004.
L. Han and N. M. Amato, A kinematics-based Probabilistic Roadmap Method for closed chain systems, Algorithmic and Computational Robotics - New Directions (Proceedings of WAFR 2000), eds. B. Donald, K. Lynch and D. Rus, June 2000, pp. 233-246.
L. Rudolph, Some Knot theory of complex plane curves, in Noeuds, Tresses, et Singularités (Plans-sur-Bex, 1982) (ed. C. Weber), Monogr. Enseign. Math., 31, Enseignement Math., Geneva (1983), pp. 49-98.