Computation reuse for rigid-body dynamics

13 years 10 months ago

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— The accelerations of and forces among contacting rigid bodies may be computed by formulating the dynamics equations and contact constraints as a complementarity problem [1]. Dantzig’s algorithm, when applicable, will ﬁnd a solution to the linear complementarity problem corresponding to an assembly with n contacts in O(n) major cycles. Can the dynamics of an assembly be computed more quickly if the dynamics of a subassembly are already known? This paper shows that Dantzig’s algorithm will ﬁnd a solution in O(n − k) major cycles if the algorithm is initialized with a solution to the dynamics problem for a subassembly with k internal contacts. We apply this observation to two robotics problems: dynamic simulation and assembly sequence planning. In dynamic simulation, the positions of several bodies might remain ﬁxed during a sequence of frames. We compute the dynamics of this motionless subset (which might not be motionless when considered in isolation), and use the result...

Anne Loomis, Devin J. Balkcom

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