Parallel O(log N) Algorithm for Dynamics Simulation of Humanoid Robots

This paper presents a new formulation the forward dynamics algorithm called assembly-disassembly algorithm (ADA) developed by the authors. The algorithm has the complexity of O(N) for serial computation and O(log N) for parallel computation on O(N) processors, which is comparable to the current fastet algorithms such as articulated-body algorithm (ABA) and divide-and-conquer algorithm (DCA), both proposed by Featherstone. However, it was difficult to figure out the essential differences of ADA and other two algorithms because they are based on different concepts. We reformulated ADA by applying the concept of articulated-body inertia (ABI) which is used in both ABA and DCA. The new formulation enables more rigorous comparison of the three algorithms and clarifies the difference of the underlying equations and efficiency. We also provide some implementation results including computation time, accuracy, and a simulation example

[1]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .

[2]  Katsu Yamane.  Simulating and Generating Motions of Human Figures (Springer Tracts in Advanced Robotics, V. 9) , 2004 .

[3]  Roy Featherstone,et al.  A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n)) Calculation of Rigid-Body Dynamics. Part 1: Basic Algorithm , 1999, Int. J. Robotics Res..

[4]  E. Haug,et al.  A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems , 1987 .

[5]  Roy Featherstone,et al.  A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n)) Calculation of Rigid-Body Dynamics. Part 2: Trees, Loops, and Accuracy , 1999, Int. J. Robotics Res..

[6]  David Baraff,et al.  Linear-time dynamics using Lagrange multipliers , 1996, SIGGRAPH.

[7]  Katsu Yamane,et al.  Stable penalty-based model of frictional contacts , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[8]  D. E. Rosenthal.  An Order n Formulation for Robotic Ststems , 1990 .

[9]  Amir Fijany,et al.  A technique for analyzing constrained rigid-body systems, and its application to the constraint force algorithm , 1999, IEEE Trans. Robotics Autom..

[10]  Edward J. Haug,et al.  A Recursive Formation for Constrained Mechanical Systems Dynamics: Part I, Open Loop Systems , 1987 .

[11]  Katsu Yamane,et al.  O(N) forward dynamics computation of open kinematic chains based on the principle of virtual work , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[12]  Katsu Yamane,et al.  Simulating and Generating Motions of Human Figures , 2004, Springer Tracts in Advanced Robotics.

[13]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .

[14]  Amir Fijany,et al.  Parallel O(log N) algorithms for computation of manipulator forward dynamics , 1994, IEEE Trans. Robotics Autom..

[15]  Yoshihiko Nakamura,et al.  Efficient parallel dynamics computation of human figures , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[16]  David E. Orin,et al.  Kinematic and kinetic analysis of open-chain linkages utilizing Newton-Euler methods , 1979 .

[17]  Kurt S. Anderson,et al.  Highly Parallelizable Low-Order Dynamics Simulation Algorithm for Multi-Rigid-Body Systems , 2000 .