The PDF file includes:

• Section S1. Mechanical analysis of the droplet behaviors manipulated by the magnetic-actuated robot
• Section S2. Detailed analysis of the phase diagram
• Section S3. Analysis of factors affecting droplet manipulation behaviors
• Section S4. Principle of the bead surface modification
• Section S5. Analysis of factors influencing the volume of daughter drops
• Section S6. Quantitative evaluation of the mixing efficiency
• Fig. S1. Scheme of the magnetic-actuated robot.
• Fig. S2. Contact angle characterization.
• Fig. S3. Micro-droplet manipulation.
• Fig. S4. Demonstration of the droplet behaviors influenced by D/d and V.
• Fig. S5. Demonstration of the luminol reaction.
• Fig. S6. Demonstrations of the drug delivery using the magnetic-actuated robot.
• Legends for movies S1 to S8

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Other Supplementary Material for this manuscript includes the following:

• Movie S1 (.mov format). Typical behaviors of the droplets manipulated using the magnetic-actuated robot.
• Movie S2 (.mov format). Demonstration of the droplet behaviors influenced by D/d and V.
• Movie S3 (.mov format). Generality demonstration of the magnetic-actuated robot.
• Movie S4 (.mov format). Display of the stepwise acid-based neutralization reactions.
• Movie S5 (.mov format). Display of the luminol reaction.
• Movie S6 (.mov format). Simulation of the calculi removal.
• Movie S7 (.mov format). Simulation of the drug delivery.
• Movie S8 (.mov format). Simulation of the vascular clearance.