Abstract
We introduce a novel hierarchical model to partition a kinematic system into a set of nested subsystems. This is framed in a mixed real/virtual context, where some joints and links may exist in simulation only. We then use this capability to build a precise form of kinematic abstraction, where a potentially complex subsystem can be virtually replaced by a simpler “interface.” Hierarchy and abstraction are interesting because they can help manage complexity in large (100+ DoF) mixed real/virtual mechanisms. We prove that checking if an abstraction is proper is PSPACE-hard, but show that even improper abstractions can be useful. Topological algorithms are presented for decomposing a hierarchical or abstracted kinematic system into subsystems that can be treated in isolation, thus speeding up kinematic computations. We demonstrate on a simulation of a hybrid serial/parallel modular tower with over 100 revolute joints.
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References
M. A. Vona. Virtual articulation and kinematic abstraction in robotics. PhD thesis, EECS, Massachusetts Institute of Technology (2009).
E. Davis. Approximation and abstraction in solid object kinematics. Technical Report TR1995-706, New York University, Department of Computer Science (1995).
K. E. Zanganeh and J. Angeles. A formalism for the analysis and design of modular kinematic structures. The International Journal of Robotics Research, 17(7), 720–730 (1998).
R. L. Williams and J. B. Mayhew. Control of truss-based manipulators using virtual serial models. In The 1996 ASME Design Eng. Tech. Conf. and Comp. in Eng. Conf. (1996).
A. B. Kempe. On a general method of describing plane curves of the nth degree by linkwork. Proceedings of the London Mathematical Society, 7, 213–216 (1876).
R. Connelly and E. D. Demaine. Geometry and topology of polygonal linkages. In Goodman, J. E. and OŔourke, J., (Eds.), CRC Handbook of Discrete and Computational Geometry, 2nd ed. CRC Press, pp. 197–218 (2004).
J. Hopcroft, D. Joseph, and S. Whitesides. Movement problems for 2-dimensional linkages. SIAM Journal of Computing, 14, 315–333 (1985).
P. Baerlocher and R. Boulic. An inverse kinematics architecture enforcing an arbitrary number of strict priority levels. The Visual Computer, 20, 402–417 (2004).
C. Welman. Inverse kinematics and geometric constraints for articulated figure manipulation. Master`s Thesis, Simon Fraser University (1993).
R. Tarjan. Depth-first search and linear graph algorithms. SIAM J. Comp., 1, 146–160 (1972).
C. Detweiler, M. Vona, K. Kotay, and D. Rus. Hierarchical control for self-assembling mobile trusses with passive and active links. In IEEE International Conference on Robotics and Automation, pp. 1483–1490 (2006).
G. S. Chirikjian and J. W. Burdick. The kinematics of hyper-redundant robot locomotion. IEEE Transactions on Robotics and Automation, 11(6), 781–793 (1995).
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Vona, M. (2010). Hierarchical Decomposition and Kinematic Abstraction with Virtual Articulations. In: Lenarcic, J., Stanisic, M. (eds) Advances in Robot Kinematics: Motion in Man and Machine. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9262-5_4
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DOI: https://doi.org/10.1007/978-90-481-9262-5_4
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