Robust dexterity requires the ability to cause and reason about deformation. In real-world environments, robots must routinely interact with deformable objects such as cables, dough, textiles, and hair, in which deformation is part of the object’s state. Soft robots, in turn, are built from compliant materials in which deformation is not a by-product of interaction but the agent’s primary mechanism of action. In both settings, purely analytical models may struggle with real-world complexity, while unconstrained end-to-end policy learning demands prohibitive data and offers little interpretability where failures are costly and often irreversible. This thesis pursues a middle path of mechanics-informed priors that enable robust manipulation skill learning, retaining the physical structure of analytical models while capturing complex robot behavior through learning.

The dissertation builds this perspective progressively. We first establish the core formalisms in continuum mechanics, geometric regularization, and soft-body simulation that ground the subsequent contributions. Building on these tools, we show that mesh priors with geometric regularization support shape estimation and goal-conditioned control of deformable objects under occlusion and contact uncertainty. A key insight is that the same underlying methods extend naturally to the robot body itself, so we apply identical geometric learning approaches to soft robot proprioception and show that one perspective can span both deformable objects and soft robots. With deformation now captured across objects and robots, we leverage it as a useful intermediate representation for kinesthetic teaching and policy learning, enabling dexterous manipulation. Deformation, however, is produced and regulated by contact, so the final part reasons about contact explicitly in complementary forms, namely as force distributions for transferring human manipulation skills across an embodiment mismatch, as continuous slip vectors for reactive grasp control, and as an explicit contact-and-slip intermediate representation that bridges real-world tactile signals with simulation-trained policies.

Together, these contributions build toward the perspective that mechanics-informed deformation and contact representations are principled complements to general robot policy learning frameworks, supporting perception, skill acquisition, and control across soft objects, soft robots, and human-to-robot skill transfer.