Cyber-physical systems (CPS) consist of computational nodes tightly integrated with their physical environments. Such systems often exhibit repetitive or periodic behaviors, for example, orchestrated leg movements in a robotic dog. Other examples include multi-finger manipulators, traffic flow control, and chemical plants. Synthesis of such periodic behaviors is a challenging problem since computation quickly becomes intractable as system complexity increases. This project will alleviate such computational challenges and ensure that synthesized motions are robust against uncertainties in the system model and in its environment, as well as external disturbances. The technical approach builds upon recent advancements in contraction theory and will extend this theory to cover hybrid behaviors (i.e., behaviors that have both a continuous-time evolutions and instantaneous discrete jumps). The work will focus on providing interpretable and scalable guarantees of contraction, which in turn will ensure robustness of behaviors. This methodology will leverage the natural dynamics of the system and decrease the required energy consumption for stabilization. The project is decomposed into three separate contributions: (1) the development of a theoretical foundation of contraction in hybrid systems to approximate regions of attraction for contact rich CPS; (2) the design of computation-aware algorithms for efficient computation of the regions of attraction for practical motion synthesis; and (3) the experimental validation of the entire framework on various contact-rich mechanical CPS, including bipedal and multi-fingered robots. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.