Harnessing Discrete Differential Geometry: A Virtual Playground for the Bilayer Soft Robotics

Robotics is the science of designing and constructing machines capable of movement, perception, and cognition to assist humans in performing various tasks. Inspired by living organisms, using soft matter in robot design has gained significant attention in recent decades. The inherent compliance of soft bodies allows them to adapt to complex environments, enabling innovative applications in fields such as healthcare, agriculture, and the food industry [1-10]. Given the potential of soft robots, various functional materials, such as liquid crystal elastomers, pneumatic actuators, and light-driven systems, have been explored as actuators due to their ability to deform in response to diverse external stimuli. However, the intrinsic compliance and nonlinearity of soft materials pose significant challenges in achieving precise and effective deformation control, which limits their practical effectiveness in real-world applications. A widely adopted approach to addressing this challenge is using bilayer structures in soft robot design. Inspired by natural phenomena such as the opening of pea pods, a bilayer structure consists of two layers--an top and a bottom layer--adhered at their interface [11], as illustrated in Figure 1A. When one layer undergoes expansion, a mismatch strain arises at the interface.