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Small-scale robots have the potential to impact many areas of medicine and manufacturing including targeted drug delivery, telemetry and micromanipulation. This paper develops an algorithmic framework for regulating external magnetic fields to induce motion in millimeter-scale robots in a viscous liquid, to simulate the physics of swimming at the micrometer scale. Our approach for planning motions for these swimmers is based on tools from geometric mechanics that provide a novel means to design periodic changes in the physical shape of a robot that propels it in a desired direction. Using these tools, we are able to derive new motion primitives for generating locomotion in these swimmers. We use these primitives for optimizing swimming efficiency as a function of its internal magnetization and describe a principled approach to encode the best magnetization distribu- tions in the swimmers. We validate this procedure experimentally and conclude by implementing these newly computed motion primitives on several magnetic swimmer prototypes that include two-link and three-link swimmers.