For the free-flying space robots, normally, the total momenta of the robot are written to obtain the desired kinematic model. In this paper, an approach based on the concept of the Primary Body (PB) is presented to derive a set of
generalized expressions for the total momenta of the free-flying space robots, consisting of a serial manipulator mounted on a free-base, e.g., a satellite. The generalized expressions help in deciding upon a suitable model. Thus, the choice of the satellite as the PB leads to the definition of the well-known Generalized Jacobian Matrix, which is important when the motion of the satellite and the end-effector are to be calculated together. However, to control the end-effector only, the concept of PB suggests that the end-effector, in contrary to the satellite, should be selected as the PB that will give more efficient algorithm.
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