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In this work, we propose a dynamical system based strategy for establishing a stable contact with convex shaped surfaces during non-contact/contact scenarios. A contact is called stable if the impact occurs only once and the robot remains in contact with the surface after the impact. Realizing a stable contact is particularly challenging as the contact leaves a very short time-window for the robot to react properly to the impact force. In this paper, we propose a strategy consisting of locally modulating the robot’s motion in a way that it aligns with the surface before making the contact. We show theoretically and empirically that by using the modulation framework, the contact is stable and the robot stays in contact with the surface after the first impact.