Maximilian Stölzle

Maximilian Stölzle, Cosimo Della Santina

Even though a variety of methods have been proposed in the literature, efficient and effective latent-space control (i.e., control in a learned low-dimensional space) of physical systems remains an open challenge. We argue that a promising avenue is to leverage powerful and well-understood closed-form strategies from control theory literature in combination with learned dynamics, such as potential-energy shaping. We identify three fundamental shortcomings in existing latent-space models that have so far prevented this powerful combination: (i) they lack the mathematical structure of a physical system, (ii) they do not inherently conserve the stability properties of the real systems, (iii) these methods do not have an invertible mapping between input and latent-space forcing. This work proposes a novel Coupled Oscillator Network (CON) model that simultaneously tackles all these issues. More specifically, (i) we show analytically that CON is a Lagrangian system - i.e., it possesses well-defined potential and kinetic energy terms. Then, (ii) we provide formal proof of global Input-to-State stability using Lyapunov arguments. Moving to the experimental side, we demonstrate that CON reaches SoA performance when learning complex nonlinear dynamics of mechanical systems directly from images. An additional methodological innovation contributing to achieving this third goal is an approximated closed-form solution for efficient integration of network dynamics, which eases efficient training. We tackle (iii) by approximating the forcing-to-input mapping with a decoder that is trained to reconstruct the input based on the encoded latent space force. Finally, we show how these properties enable latent-space control. We use an integral-saturated PID with potential force compensation and demonstrate high-quality performance on a soft robot using raw pixels as the only feedback information.

Ricardo Valadas, Maximilian Stölzle, Jingyue Liu et al.

Obtaining dynamic models of continuum soft robots is central to the analysis and control of soft robots, and researchers have devoted much attention to the challenge of proposing both data-driven and first-principle solutions. Both avenues have, however, shown their limitations; the former lacks structure and performs poorly outside training data, while the latter requires significant simplifications and extensive expert knowledge to be used in practice. This paper introduces a streamlined method for learning low-dimensional, physics-based models that are both accurate and easy to interpret. We start with an algorithm that uses image data (i.e., shape evolutions) to determine the minimal necessary segments for describing a soft robot's movement. Following this, we apply a dynamic regression and strain sparsification algorithm to identify relevant strains and define the model's dynamics. We validate our approach through simulations with various planar soft manipulators, comparing its performance against other learning strategies, showing that our models are both computationally efficient and 25x more accurate on out-of-training distribution inputs. Finally, we demonstrate that thanks to the capability of the method of generating physically compatible models, the learned models can be straightforwardly combined with model-based control policies.

Gioele Buriani, Jingyue Liu, Maximilian Stölzle et al.

Reduced-order models are essential for motion planning and control of quadruped robots, as they simplify complex dynamics while preserving critical behaviors. This paper introduces a novel methodology for deriving such interpretable dynamic models, specifically for jumping. We capture the high-dimensional, nonlinear jumping dynamics in a low-dimensional latent space by proposing a learning architecture combining Sparse Identification of Nonlinear Dynamics (SINDy) with physical structural priors on the jump dynamics. Our approach demonstrates superior accuracy to the traditional actuated Spring-loaded Inverted Pendulum (aSLIP) model and is validated through simulation and hardware experiments across different jumping strategies.

Maximilian Stölzle, T. Konstantin Rusch, Zach J. Patterson et al. · eth-zurich

Learning from demonstration provides a sample-efficient approach to acquiring complex behaviors, enabling robots to move robustly, compliantly, and with fluidity. In this context, Dynamic Motion Primitives offer built - in stability and robustness to disturbances but often struggle to capture complex periodic behaviors. Moreover, they are limited in their ability to interpolate between different tasks. These shortcomings substantially narrow their applicability, excluding a wide class of practically meaningful tasks such as locomotion and rhythmic tool use. In this work, we introduce Orbitally Stable Motion Primitives (OSMPs) - a framework that combines a learned diffeomorphic encoder with a supercritical Hopf bifurcation in latent space, enabling the accurate acquisition of periodic motions from demonstrations while ensuring formal guarantees of orbital stability and transverse contraction. Furthermore, by conditioning the bijective encoder on the task, we enable a single learned policy to represent multiple motion objectives, yielding consistent zero-shot generalization to unseen motion objectives within the training distribution. We validate the proposed approach through extensive simulation and real-world experiments across a diverse range of robotic platforms - from collaborative arms and soft manipulators to a bio-inspired rigid-soft turtle robot - demonstrating its versatility and effectiveness in consistently outperforming state-of-the-art baselines such as diffusion policies, among others.

Maximilian Stölzle, Takahiro Miki, Levin Gerdes et al.

Accurate and complete terrain maps enhance the awareness of autonomous robots and enable safe and optimal path planning. Rocks and topography often create occlusions and lead to missing elevation information in the Digital Elevation Map (DEM). Currently, these occluded areas are either fully avoided during motion planning or the missing values in the elevation map are filled-in using traditional interpolation, diffusion or patch-matching techniques. These methods cannot leverage the high-level terrain characteristics and the geometric constraints of line of sight we humans use intuitively to predict occluded areas. We introduce a self-supervised learning approach capable of training on real-world data without a need for ground-truth information to reconstruct the occluded areas in the DEMs. We accomplish this by adding artificial occlusion to the incomplete elevation maps constructed on a real robot by performing ray casting. We first evaluate a supervised learning approach on synthetic data for which we have the full ground-truth available and subsequently move to several real-world datasets. These real-world datasets were recorded during exploration of both structured and unstructured terrain with a legged robot, and additionally in a planetary scenario on Lunar analogue terrain. We state a significant improvement compared to the baseline methods both on synthetic terrain and for the real-world datasets. Our neural network is able to run in real-time on both CPU and GPU with suitable sampling rates for autonomous ground robots. We motivate the applicability of reconstructing occlusion in elevation maps with preliminary motion planning experiments.