Computation reuse for rigid-body dynamics

— 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...

• Type: Conference
• Year: 2006
• Where: IROS
• Authors: Anne Loomis, Devin J. Balkcom
• Keywords: Complementarity Problem, IROS 2006, Linear Complementarity Problem, Major Cycles, Robotics