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Abstract

A modular robotic system consists of standardized joint and link units that can be assembled into various kinematic configurations for different types of tasks. For the control and simulation of such a system, manual derivation of the kinematic and dynamic models, as well as the error model for kinematic calibration, require tremendous effort, because the models constantly change as the robot geometry is altered after module reconfiguration. This paper presents a framework to facilitate the model-generation procedure for the control and simulation of the modular robot system. A graph technique, termed kinematic graphs and realized through assembly incidence matrices (AIM), is introduced to represent the module-assembly sequence and robot geometry. The kinematics and dynamics are formulated based on a local representation of the theory of Lie groups and Lie algebras. The automatic model-generation procedure starts with a given assembly graph of the modular robot. Kinematic, dynamic, and error models of the robot are then established, based on the local representations and iterative graph-traversing algorithms. This approach can be applied to a modular robot with both serial and branch-type geometries, and arbitrary degrees of freedom. Furthermore, the AIM of the robot naturally leads to solving the task-oriented optimal configuration problem in modular robots. There is no need to maintain a huge library of robot models, and the footprint of the overall software system can be reduced.

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References

Ambrose, R. O. 1995. Interactive robot joint design, analysis, and prototyping. IEEE Intl. Conf on Robot. and Automat.. Washington, DC: IEEE , pp. 2119-2124.

Benhabib, B., Zak, G., and Lipton, M. G. 1989. A generalized kinematic modeling method for modular robots . J Robot. Sys. 6(5): 545-571 .

Chen, I.-M. 1994. Theory and applications of modular reconfigurable robotic systems. Ph.D. thesis, Division of Engineering and Applied Science, California Institute of Technology.

Chen, I.-M. 1996. On optimal configuration of modular reconfigurable robots . lnt. Conj. Control, Automation, Robot., and Vision, Singapore, pp. 1855-1859 .

Chen, I.-M., and Burdick, J. W. 1993. Enumerating nonisomorphic assembly configurations of modular robotic systems. IEEE/RSJ Intl. Conf on Intell. Robots and Sys. Washington, DC: IEEE , pp. 1985-1992.

Chen, I.-M., and Burdick, J. W. 1995. Determining taskoptimal modular robot-assembly configurations. IEEE Intl. Conf on Robot. and Automat. Washington, DC: IEEE , pp. 132-137.

Chen, I.-M., and Yang, G. 1996. Configuration-independent kinematics for modular robots. IEEE Intl. Conf. on Robot. and Automat. Washington, DC: IEEE , pp. 1440-1445.

Chen, I.-M., and Yang, G. 1997. Kinematic calibration of modular reconfigurable robots using product-ofexponentials formula . J. Robot. Sys. 14(11): 807-821 .

Cohen, R., Lipton, M. G., Dai, M. Q., and Benhabib, B. 1992. Conceptual design of a modular robot . ASME J. Mechanical Design 114: 117-125 .

10.

Cormen, T., Leiserson, C., and Rivest, R. 1990. Introduction to Algorithms. Cambridge, MA: MIT Press .

11.

Deo, N. 1974. Graph Theory with Applications to Engineering and Computer Science. New York: Prentice Hall .

12.

Dobrjanskyj, L., and Freudenstein, F. 1967. Some applications of graph theory to the structural analysis of mechanisms . ASME J. Eng. Industry 89: 153-158 .

13.

Featherstone, R. 1987. Robot Dynamics Algorithms. Holland: Kluwer Academic .

14.

Fukuda, T., and Nakagawa, S. 1988. Dynamically reconfigurable robotic system. IEEE Intl. Conf. on Robot. and Automat. Los Alamitos, CA: IEEE , pp. 1581-1586.

15.

Hollerbach, J. M. 1980. A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics-formulation complexity . IEEE Trans. Sys. Man Cybernet. 10: 730-736 .

16.

Kelmar, L., and Khosla, P. 1988. Automatic generation of kinematics for a reconfigurable modular manipulator system. IEEE Intl. Conf. on Robot. and Automat. Los Alamitos, CA: IEEE , pp. 663-668.

17.

Khosla, P. K., Neuman, C., and Prinz, F. 1985. An algorithm for seam-tracking applications . Intl. J Robot. Res. 4(1): 27-41 .

18.

Michalewicz, Z. 1994. Genetic Algorithms + Data Structures = Evolution Programs, 2ed. Berlin: Springer-Verlag .

19.

Murray, R., Li, Z., and Sastry, S. 1994. A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC Press .

20.

Paredis, C. J. J., Brown, Casciola, Moody, and Khosla. 1995. A rapidly deployable manipulator system. Intl. Workshop on Some Critical Issues in Robotics, pp. 175-185, Singapore .

21.

Paredis, C. J. J., and Khosla, P. K. 1995. Design of modular fault-tolerant manipulators. In Goldberg, K. (ed.) Algorithmic Foundations of Robotics. Wellesley, MA: A. K. Peters , pp. 371-383.

22.

Park, F. C., and Bobrow, J. E. 1994 (San Diego, CA). A recursive algorithm for robot dynamics using Lie groups. Proc. of the IEEE Conf. on Robot. and Automat. Washington, DC: IEEE , pp. 1535-1540.

23.

Park, F. C., Bobrow, J. E., and Ploen, S. R. 1995. A Liegroup formulation of robot dynamics . Intl. J. Robot. Res. 14(6): 609-618 .

24.

Rodriguze, G., Jain, A., and Kreutz-Delgado, K. 1991. A spatial operator algebra for manipulator modeling and control . Intl. Robot. Res. 10(4): 371-381 .

25.

Schmitz, D., Khosla, P. K., and Kanade, T. 1988. The CMU reconfigurable modular manipulator system. Technical Report CMU-RI-TR-88-7, Robotics Institute, Carnegie Mellon University .

26.

Wurst, K. H. 1986. The conception and construction of a modular robot system . Proc. of the 16th Intl. Symp. on Industrial Robot. (ISIR), pp. 37-44 .

27.

Yang, G., Chen, I.-M., and Kang, I.-G. 1998. Numerical inverse kinematics for modular reconfigurable robots. Technical Report TR-MPE-NTU-06-98-0 1, School of Mechanical and Production Engineering, Nanyang Technological University, Singapore .

Kernel for Modular Robot Applications: Automatic Modeling Techniques

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