This work introduces a novel methodology for the development of interpretable reduced-order dynamic models specifically tailored for jumping quadruped robots. Leveraging Symbolic Regression combined with autoencoder neural networks, the framework autonomously derives symbolic equations from data and fundamental physics principles capturing the complex dynamics of jumping actions with high fidelity. This approach significantly reduces model complexity while enhancing interpretability, facilitating deeper insights for legged robotic applications. The efficacy and accuracy of the proposed models are validated through comprehensive experimental studies, marking a substantial advancement in the design of agile and efficient legged robots. This research demonstrates the outperformance of a learned 2D model compared to existing template models such as the ASLIP. Also, an analysis of the dimensionality of the learned model is conducted showing the overarching tradeoff between accuracy and complexity. The method is validated on different simulated quadrupeds and an actual hardware robot.

In recent years, soft robots have become a focal point of research due to their ability to mimic natural movements and adapt to unstructured settings. However, their inherent flexibility poses significant challenges, particularly in the areas of modelling and control. While data-driven methods can model soft robot behavior without explicit physical models, they require extensive data and lack interpretability. On the other hand, physics-based low-dimensional models have relied heavily on expert knowledge and intuition, sometimes leading to models that are either too simple and inaccurate, or excessively high-dimensional.

This thesis introduces an end-to-end methodology for automatically identifying low-dimensional kinematic and dynamic models of planar continuum soft robots using image data. Based on the Piecewise Constant Strain (PCS) parametrization, the proposed approach determines an efficient segmentation for the soft robot to approximate its configuration. Afterward, a model identification strategy is employed to obtain a dynamic model that contains only the most essential strains. This model is formulated in the standard Euler-Lagrange framework, facilitating the integration with conventional model-based control schemes. The methodology is validated through simulations involving various planar soft manipulators and in the presence of noise, demonstrating its capability to generate accurate and computationally efficient models. This work provides a fast and practical tool to help the modelling and control of continuum soft robots, highlighting the potential for future applications in more complex actuation systems and real-world soft robots.