A dynamics formulation of general constrained robots

Abstract

The complexity of a standard compact-in-form Lagrangian dynamical expression is proportional to the fourth power of the number of degrees of freedom (DOF) of a robotic system. This fact challenges both simulation and control of robots with hyper degrees of freedom. In this paper, a systematic approach for deriving the dynamical expression of so-called general constrained robots is proposed. This proposed approach has two main features. First, it uses the subsystem dynamics such as the dynamics of joints and rigid links to construct the dynamical expression of the entire robotic system in a closed form. The complexity of the resulted dynamic expression is linearly proportional to the number of DOF of a robotic system. Second, it extends the standard dynamical form and properties of the conventional single-arm constrained robots to a class of more general robotic systems including the coordinated multiple-arm robotic systems. Three spaces, namely the general joint space, the general task space, and the extended subsystems space, are connected through corresponding velocity/force mapping matrices.