Abstract
The generalized inertia matrix and its inverse are used extensively in robotics applications. While construction of the inertia matrix requires Θ(n 2) time, inverting it traditionally employs algorithms running in time O(n 3). We describe an algorithm that reduces the asymptotic time complexity of this operation to the theoretical minimum: Θ(n 2). We also present simple modifications that reduce the number of arithmetic operations (and thereby the running time). We compare our approach against fast Cholesky factorization both theoretically (using number of arithmetic operations) and empirically (using running times). We demonstrate our method to dynamically simulate a highly articulated robot undergoing contact, yielding an order of magnitude decrease in running time over existing methods.
Keywords
- Arithmetic Operation
- Inertia Matrix
- Cholesky Factorization
- Robot Dynamic
- Global Frame
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References
Khatib, O.: A unified approach to motion and force control of robot manipulators: The operational space formulation. IEEE Journal on Robotics and Automation 3(1), 43–53 (1987)
Walker, M.W., Orin, D.E.: Efficient dynamic computer simulation of robotic mechanisms. ASME J. Dynamic Systems, Measurement, and Control 104, 205–211 (1982)
Featherstone, R.: Robot Dynamics Algorithms. Kluwer (1987)
Hollerbach, J.M.: A recursive lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity. IEEE Trans. Systems, Man, and Cybernetics SMC-10(11), 730–736 (1980)
Featherstone, R.: The calculation of robot dynamics using articulated body inertias. Intl. J. Robotics Research 2(1), 13–30 (1983)
Featherstone, R.: Rigid Body Dynamics Algorithms. Springer (2008)
Featherstone, R., Orin, D.: Robot dynamics: Equations and algorithms. In: Proc. of IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA (April 2000)
Featherstone, R.: Efficient factorization of the joint space inertia matrix for branched kinematic trees. Intl. J. Robotics Research 24(6), 487–500 (2005)
Baraff, D.: Linear-time dynamics using lagrange multipliers. In: Proc. of Computer Graphics, New Orleans, LA (August 1996)
Drumwright, E., Shell, D.A.: Modeling contact friction and joint friction in dynamic robotic simulation using the principle of maximum dissipation. In: Proc. of Workshop on the Algorithmic Foundations of Robotics, WAFR (2010)
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© 2012 Springer-Verlag Berlin Heidelberg
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Drumwright, E. (2012). Fast Dynamic Simulation of Highly Articulated Robots with Contact via Θ(n 2) Time Dense Generalized Inertia Matrix Inversion. In: Noda, I., Ando, N., Brugali, D., Kuffner, J.J. (eds) Simulation, Modeling, and Programming for Autonomous Robots. SIMPAR 2012. Lecture Notes in Computer Science(), vol 7628. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34327-8_9
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DOI: https://doi.org/10.1007/978-3-642-34327-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34326-1
Online ISBN: 978-3-642-34327-8
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