Parallel robots based on Handed Shearing Auxetics (HSAs) can implement complex motions using standard electric motors while maintaining the complete softness of the structure, thanks to specifically designed architected metamaterials. However, their control is especially challenging due to varying and coupled stiffness, shearing, non-affine terms in the actuation model, and underactuation. In this paper, we present a model-based control strategy for planar HSA robots enabling regulation in task space. We formulate equations of motion, show that they admit a collocated form, and design a P-satI-D feedback controller with compensation for elastic and gravitational forces. We experimentally identify and verify the proposed control strategy in closed loop.
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