Alternate forms of the operational space inertia matrix for the dynamic simulation of complex robot systems

This paper extends the concept of the traditional operational space inertia matrix (OSIM) for single robots with single external contacts to systems of multiple robots with multiple concurrent contacts (both internal and external). Alternate forms of the OSIM are presented, including the cross-point operational space inertia matrix used for robots with multiple external contacts. Three new forms of the OSIM are also presented for robots with multiple contacts where one or more of these are formed by internal closed loops. In addition to their value in system modelling, these new forms of the OSIM enable the efficient modular dynamic simulation of systems of multiple robots with complex topologies. This application of the OSIM is also discussed here, along with a practical example that illustrates the use of its various forms. Issues of computational complexity are addressed as well.