Hydrosoft: Non-Holonomic Hydroelastic Models for Compliant Tactile Manipulation

Tactile sensors have long been valued for their perceptual capabilities, offering rich insights into the otherwise hidden interface between the robot and grasped objects. Yet their inherent compliance -- a key driver of force-rich interactions -- remains underexplored. The central challenge is to capture the complex, nonlinear dynamics introduced by these passive-compliant elements. Here, we present a computationally efficient non-holonomic hydroelastic model that accurately models path-dependent contact force distributions and dynamic surface area variations. Our insight is to extend the object's state space, explicitly incorporating the distributed forces generated by the compliant sensor. Our differentiable formulation not only accounts for path-dependent behavior but also enables gradient-based trajectory optimization, seamlessly integrating with high-resolution tactile feedback. We demonstrate the effectiveness of our approach across a range of simulated and real-world experiments and highlight the importance of modeling the path dependence of sensor dynamics.