Operational Space Dynamics of a Space Robot and Computational Efficient Algorithm

On-orbit servicing space robot is one of the challenging applications in space robotic field. Main task of the on-orbit space robot involves the tracking, the grasping and the positioning of a target. The dynamics in operational space is useful to achieve such tasks in Cartesian space. The operational space dynamics is a formulation of the dynamics of a complex branching redundant mechanism in task or operational points. Khatib proposed the formulation of a serial robot manipulator system on ground in (Khatib, 1987). Russakow et. al. modified it for a branching manipulator system in (Russakow et al., 1995). Chang and Khatib introduced efficient algorithms for this formulation, especially for operational space inertia matrix in (Chang & Khatib, 1999; 2000). The operational space dynamics of the space robot is more complex than that of the groundbased manipulator system since the base-satellite is inertially free. However, by virtue of no fixed-base, the space robot is invertible in its modeling and arbitrary operational points to control can be chosen in a computational efficientmanner. Bymaking use of this unique characteristic, we firstly propose an algorithm of the dynamics of a single operational point in the space robot system. Then, by using the concept of the articulated-body algorithm(Featherstone, 1987), we propose a recursive computation of the dynamics of multi-operational points in the space robot. The numerical simulations are carried out using a two-arm space robot shown in Fig. 1. This chapter is organized as follows. Section 2 describes basic dynamic equations of freeflying and free-floating space robots. Section 3 derives the operational space formulation of both types of space robots. Section 4 briefly introduces spatial notation to represent complex robot kinematics and dynamics, which is used for the derivation of the proposed algorithms. Section 5 describes recursive algorithms of the generalized Jacobian matrix(Xu & Kanade, 1993), that is a Jacobian matrix including dynamical coupling between the base body and the robot arm. Section 6 proposes computational efficient algorithms of the operational space dynamics. Section 7 shows the simulation example of the proposed algorithms. Section 8 summarizes the conclusions.