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Advances in additive manufacturing techniques have enabled the creation of stimuli-responsive materials with designed three-dimensional (3D) architectures. Unlike biological systems in which functions such as sensing, actuation, and control are closely integrated, few architected materials have comparable system complexity. We report a design and manufacturing route to create a class of robotic metamaterials capable of motion with multiple degrees of freedom, amplification of strain in a prescribed direction in response to an electric field (and vice versa), and thus, programmed motions with self-sensing and feedback control. These robotic metamaterials consist of networks of piezoelectric, conductive, and structural elements interwoven into a designed 3D lattice. The resulting architected materials function as proprioceptive microrobots that actively sense and move.