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In this paper, we propose a novel framework, passive set-position modulation (PSPM), which enables us to connect a (continuous-time) robot's position to a sequence of slowly updating/sparse (discrete-time) set-position signal via the simple (yet frequently used in practice) spring coupling with damping injection, while enforcing passivity of the closed-loop robotic system. The PSPM modulates the original set-position signal in such a way that the modulated signal is as close to the original signal as possible (i.e., maximum information recovery for better performance), yet only to the extent permissible by the available energy in the system (i.e., passivity constraints). We present its algorithm and theoretically show its passivity and performance. We also show how this PSPM can be applied for two applications, with some experimental results: Internet teleoperation with varying delay and packet loss; and haptics with slow and variable-rate data update.