Universal Dimensionless Framework for Morphological Computing in Hyperelastic Stick-Slip Soft Robotic Locomotion

Abstract

Purpose: Soft pneumatic actuators exhibit immense potential as computational reservoirs due to their hyperelasticity and slow fluidic response. However, empirical data-driven learning often obscures the universal scaling laws and physical limits of the underlying mechanics. This paper aims to establish a foundational, physics-based model for unanchored soft stick-slip robots to identify optimal computational regimes and expose the limitations of continuous sparse regression.

Methods: We derive a dimensionally consistent, two-mass hybrid analytical model that reduces a soft stick-slip crawler to its fundamental state variables. The model in tegrates true Coulomb stick-slip friction to capture macroscopic translation and phase transitions without deleting internal restoring forces. Furthermore, we investigate the application of sparse regression (SINDy), including standard and custom non-smooth basis libraries, to recover the governing dynamics.

Results: By identifying the fundamental dimensionless groups, we map the system’s parameter space and demonstrate that the physical reservoir achieves its maximum Memory Capacity exactly at the boundary between stability and chaos. The sparse regression evaluation reveals that standard continuous empirical discovery fails to re cover the discontinuous acceleration spikes generated by the mechanical diode effect, defining a Kinetic Stiffness Limit.

Conclusion: The failure of continuous regression algorithms on stick-slip discontinu ities highlights a severe vulnerability in off-the-shelf empirical modeling. This under scores the necessity of first-principles derivations for hybrid dynamical systems in soft robotics, ensuring that contact-driven phase transitions are mathematically preserved.