Multi-contact interaction remains a central challenge for precise robotic manipulation. This paper proposes a screw impedance control (SIC) framework based on screw theory that supports intuitive modeling of distributed, non-orthogonal interactions while enabling independent impedance tuning at multiple contact points. To ensure physical realizability, an SIC parameter matrix boundary-constraint algorithm is proposed to confine impedance matrices to the renderable range while preserving the desired multi-contact impedance profile with minimal distortion. We propose a hierarchical iterative strategy for constructing the impedance parameter matrices in multi-priority tasks, regulating impedance coupling effects in multi-contact prioritization. Flexible, task-specific hierarchies are achieved by differentiated coupling term designs. Extensive simulations with a planar robot across diverse multi-contact scenarios demonstrate the effectiveness and robustness of SIC. Hardware experiments were conducted on three representative multi-contact tasks: multi-virtual fixtures in robotic surgery, multi-dowel pin precision assembly, and complex surface polishing in robotic manufacturing. The results indicate that SIC enables precise interaction modulation and substantially improves end-effector interaction performance under multi-contact conditions.
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