EFFICIENT DYNAMIC SIMULATION OOF MULTIPLE MANIPULATOR SYSTEMS WITH SINGULAR CONFIGURATIONS

The paper presents an efficient algorithm for the simulation of a syst em of m manipulators each having N degrees of freedom that are graspin g a common object. Algorithms for such a system have been previously d eveloped by others. In [1], an O(mN) algorithm is presented that does not fully consider the case when one or more of the manipulators are i n singular configurations. However, it is stated in [2] that the algor ithm has an O(mN)+O(m3) computational complexity when one or more of t he chains are singular. This results because the size of the system of equations to be solved grows linearly with the number of chains in th e system [3]. The algorithm presented in this paper significantly redu ces the size of the system of equations to be solved to one that grows linearly with the number of singular chains, s, and achieves an O(mN) +O(s3) complexity. In addition to this result, efficient O(mN) algorit hms are also presented for special cases where only one or two chains are in singular configurations. These are particularly useful because it is common to deal with systems consisting of only a few manipulator s grasping a common object, and even with more manipulators, it is unl ikely that many of them will be singular simultaneously. Finally, by a pplying the algorithm developed for the case of two singularities to a dual-arm system, an algorithm results that requires fewer computation s than that of existing methods, and has the added benefit of being ro bust in the presence of singular manipulators.