This paper proposes a kinematic obstacle avoidance algorithm for Space hyper-redundant manipulators, and its basic idea is to use a static and a dynamic curve to constrain the macroshape of the manipulators simultaneously. The static curve is constructed based on a traditional rapidly exploring random tree algorithm, and a backbone curve is utilized as the dynamic curve. For these two curves, two novel shape control methods are proposed to accomplish the shape constraining process. Finally, we verify the reliability and effectiveness of our algorithm through simulations. © The Author(s), 2021. Published by Cambridge University Press.