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This paper is concerned with the study of contact between free-flying space robots, and the minimization of the impulse at impact. The paper begins with a presentation of a new model of space robots which takes into account external applied forces. Next a contact model which consider both linear and angular motion between contacting systems is presented. Two approaches for trajectory planning in Cartesian space are discussed, and a strategy for achieving both the primary objective of trajectory tracking in Cartesian space and the secondary objective of impact minimization through configuration space planning is presented. The strategy is tested on a 15 degree of freedom space robot and simulation results are presented.