Soft robots promise rich behaviors with minimal hardware by embedding part of the control in the body. We pursue this idea using flexible mechanical metamaterials as a soft embodiment and focus on the design and validation of a dynamic metamaterial platform for underactuated motion generation. We adopt a dynamic model with ligament-level viscous damping, identify its parameters from quasi-static tests, and validate it quantitatively against dynamic experiments. We compare three fabrication routes for the compliant ligaments. We then adopt an inverse-design framework that tunes the geometry so that a single sinusoidal base input produces closed-loop motion at a user-selected target region. Using a hybrid global–local optimization strategy (CMA-ES + MMA) with an angular momentum objective, the framework automatically discovers non-trivial geometries that generate clockwise or counter-clockwise limit cycles from the same reciprocal input. We further demonstrate frequency-based multifunctionality in simulation: a single architecture switches between opposing closed-loop behaviors (CW vs. CCW) when driven at distinct frequencies. Overall, the results position dynamic metamaterials as a viable soft embodiment that shifts complexity from electronics to morphology, a step toward single-actuator, multigait soft robotic matter.

Many robotic applications require moving an end-effector through intricate closed-loop paths for object manipulation or locomotion. Conventionally, rotary-actuated rigid-link mechanisms perform this task successfully. However, several drawbacks, such as wear, play, and assembly difficulties, limit their performance. In high-speed applications, these rigid and often bulky links require high accelerations, leading to high power usage or the need for dynamic balancing, further complicating the mechanism. Rigid mechanisms are not the only ones that generate paths; compliant mechanisms are also widely used. However, compliant hinges cannot undergo complete rotations by definition, making cyclic actuation impossible. As a result, creating closed-loop paths typically requires multiple actuators—one per end-effector degree of freedom—adding to power demands and complexity. In contrast, closed-loop deformations can occur when dynamically actuating a soft body with a single actuator. We can create customizable soft bodies that leverage internal dynamics by structuring this soft body with a mechanical metamaterial made of tessellated compliant cells and designing its internal geometry. This research explores how these dynamics can be harnessed for path generation within mechanical metamaterials. Through multi-objective optimization, we embed reprogrammable control strategies within the metamaterial geometry, enabling adaptive responses to actuation frequency and amplitude for complex behaviors. We validate these designs with tabletop prototypes, building up to a self-propelled, walking prototype—a step toward autonomous robotic metamaterials.