Lie groups approach to space robots kinematics modelling

In this article we would like to present a geometric approach to model the velocity-level behaviour of the free-floating space manipulator system. Namely we will incorporate some concepts from the theory of Lie groups which have already proved useful in the kinematic and dynamic modelling of fixed-base manipulators. The treatment presented in this article allows obtaining general and coordinate-free kinematic expressions which relate Cartesian velocities of rigid bodies with joint-space velocities. Moreover due to the exponential map and product of exponentials formula we were able to obtain closed form expressions for derivatives of system’s equations with respect to the joint angles.