Efficient dynamic simulation of multiple manipulator systems with singular configurations

The paper presents an efficient algorithm for the simulation of a system of m manipulators each having N degrees of freedom that are grasping a common object. Algorithms for such a system have been previously developed by others. In Lilly and Orin (1989), an O(mN) algorithm is presented that does not fully consider the case when one or more of the manipulators are in singular configurations. However, it is stated in Rodriguez, Jain, and Kreutz-Delgado (1989) that the algorithm has an O(mN)+O(m³) computational complexity when one or more of the chains are singular. This results because the size of the system of equations to be solved grows linearly with the number of chains in the system. The algorithm presented in this paper significantly reduces 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) algorithms 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 manipulators grasping a common object, and even with more manipulators, it is unlikely that many of them will be singular simultaneously. Finally, by applying the algorithm developed for the case of two singularities to a dual-arm system, an algorithm results that requires fewer computations than that of existing methods, and has the added benefit of being robust in the presence of singular manipulators