arXiv subjects

Eron Ristich

Publications and source records attributed to Eron Ristich.

4 recordsLinked to original sources

arXiv2026

Real-Time Shape Control of Multi-Segment Soft Robotic Arms Using Koopman Operators with Global and Local Observables

Multi-segment soft robotic arms can continuously reconfigure their body shapes for safe interaction, but tip control alone is insufficient for constrained-space tasks. Therefore, shape control is a more important task for multi-segment soft arms than tip control, but remains challenging due to the high dimensionality and nonlinear dynamics of continuum deformation. In existing work, shape control accuracy is defined by the error in the global frame (global shape error). For multi-segment soft arms, using only global shape error as the control objective is insufficient, as segment coupling, gravity-induced loading, and inertial effects become more significant. This difficulty increases with the number of segments. In this paper, we present a Koopman-based model predictive control framework that combines global and local observables, enabling real-time shape control on multi-segment soft robotic arms. The framework is evaluated through numerical and physical experiments. Numerical experiments demonstrate the scalability of the proposed controller by achieving shape control on robots with up to 10 independently actuated segments. The physical experiments demonstrate that the controller is capable of (1) real-time shape control of 3- and 5-segment robotic arms with tip speeds up to 0.6 m/s, (2) robust tracking without retraining, including distal payloads up to 400~g and recovery from a 7~N lateral disturbance, and (3) the potential for future inspection applications through a confined-space demonstration. These results demonstrate that the proposed framework enables dynamic, scalable, and accurate real-time shape control on multi-segment soft robotic arms.

cs.RO↗

arXiv2026

On the Nonexistence of Continuous Immersions for Discrete-time Systems

Understanding when linear immersions of nonlinear dynamical systems exist is important since such immersions allow us to leverage the rich tools of linear system theory to analyze nonlinear dynamics. Recently, Liu et al. (2023) showed that continuous-time dynamical systems that admit countably many but more than one omega-limit sets cannot be immersed into finite dimensional linear systems with a one-to-one and continuous mapping. In this paper, we extend these results to discrete-time dynamics and show that similar obstructions exist also in discrete time. We further consider a generalization involving alpha-limit sets. Several examples are provided to demonstrate the results.

eess.SY↗

arXiv2025

Shape control of simulated multi-segment continuum robots via Koopman operators with per-segment projection

Soft continuum robots can allow for biocompatible yet compliant motions, such as the ability of octopus arms to swim, crawl, and manipulate objects. However, current state-of-the-art continuum robots can only achieve real-time task-space control (i.e., tip control) but not whole-shape control, mainly due to the high computational cost from its infinite degrees of freedom. In this paper, we present a data-driven Koopman operator-based approach for the shape control of simulated multi-segment tendon-driven soft continuum robots with the Kirchhoff rod model. Using data collected from these simulated soft robots, we conduct a per-segment projection scheme on the state of the robots allowing for the identification of control-affine Koopman models that are an order of magnitude more accurate than without the projection scheme. Using these learned Koopman models, we use a linear model predictive control (MPC) to control the robots to a collection of target shapes of varying complexity. Our method realizes computationally efficient closed-loop control, and demonstrates the feasibility of real-time shape control for soft robots. We envision this work can pave the way for practical shape control of soft continuum robots.

cs.RO↗

arXiv2025

Physics-informed Split Koopman Operators for Data-efficient Soft Robotic Simulation

Koopman operator theory provides a powerful data-driven technique for modeling nonlinear dynamical systems in a linear framework, in comparison to computationally expensive and highly nonlinear physics-based simulations. However, Koopman operator-based models for soft robots are very high dimensional and require considerable amounts of data to properly resolve. Inspired by physics-informed techniques from machine learning, we present a novel physics-informed Koopman operator identification method that improves simulation accuracy for small dataset sizes. Through Strang splitting, the method takes advantage of both continuous and discrete Koopman operator approximation to obtain information both from trajectory and phase space data. The method is validated on a tendon-driven soft robotic arm, showing orders of magnitude improvement over standard methods in terms of the shape error. We envision this method can significantly reduce the data requirement of Koopman operators for systems with partially known physical models, and thus reduce the cost of obtaining data.

cs.RO↗