arXiv subjects

Roshan S. Kaundinya

Publications and source records attributed to Roshan S. Kaundinya.

7 recordsLinked to original sources

arXiv2026

Orientation Control of Soft Robots via Adiabatic Spectral Submanifolds

Soft robots are commonly sought for safety-critical interactions in delicate environments, where accurate position and orientation control is imperative. Model predictive control (MPC) offers a solution, but it requires a model of the robot's infinite-dimensional nonlinear dynamics that is at once accurate and computationally cheap. Recent theory on adiabatic spectral submanifolds (aSSMs) and their applications to soft robots provide data-driven model-reduction methods to construct such models. Here, we extend these methods to identify aSSMs from enlarged observable datasets and upgrade the currently available aSSM-MPC schemes. Evaluated on a high-fidelity finite-element simulation of a pressure-actuated soft arm, our controller reduces position and orientation tracking error by more than 60% compared to existing data-driven baselines.

cs.RO↗

arXiv2026

Data-Driven Soft Robot Control via Adiabatic Spectral Submanifolds

The mechanical complexity of soft robots creates significant challenges for their model-based control. Specifically, linear data-driven models have struggled to control soft robots on complex, spatially extended paths that explore regions with significant nonlinear behavior. To account for these nonlinearities, we develop here a model-predictive control strategy based on the recent theory of adiabatic spectral submanifolds (aSSMs). This theory is applicable because the internal vibrations of heavily overdamped robots decay at a speed that is much faster than the desired speed of the robot along its intended path. In that case, low-dimensional attracting invariant manifolds (aSSMs) emanate from the path and carry the dominant dynamics of the robot. Aided by this recent theory, we devise an aSSM-based model-predictive control scheme purely from data. We demonstrate the effectiveness of our data-driven model in tracking dynamic trajectories across diverse tasks. We validate on high-fidelity, high-dimensional finite-element models of a soft trunk robot and Cosserat-rod-based elastic soft arms, with additional experiments confirming robust performance even in the presence of experimental noise. Notably, we find that five- or six-dimensional aSSM-reduced models outperform the tracking performance of other data-driven modeling methods by a factor up to 10 across all closed-loop control tasks.

cs.RO↗

arXiv2026

Learning Actuator-Aware Spectral Submanifolds for Precise Control of Continuum Robots

Continuum robots exhibit high-dimensional, nonlinear dynamics which are often coupled with their actuation mechanism. Spectral submanifold (SSM) reduction has emerged as a leading method for reducing high-dimensional nonlinear dynamical systems to low-dimensional invariant manifolds. Our proposed control-augmented SSMs (caSSMs) extend this methodology by explicitly incorporating control inputs into the state representation, enabling these models to capture nonlinear state-input couplings. Training these models relies solely on controlled decay trajectories of the actuator-augmented state, thereby removing the additional actuation-calibration step commonly needed by prior SSM-for-control methods. We learn a compact caSSM model for a tendon-driven trunk robot, enabling real-time control and reducing open-loop prediction error by 40% compared to existing methods. In closed-loop experiments with model predictive control (MPC), caSSM reduces tracking error by 52%, demonstrating improved performance against Koopman and SSM based MPC and practical deployability on hardware continuum robots.

cs.RO↗

arXiv2026

Predicting Generalized Steady States in Aperiodically Forced Mechanical Systems

The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical algorithm that yields explicit and arbitrarily refinable approximations for GSSs without the need for an initial convergence period. This is to be contrasted with a direct numerical integration of the system, whose convergence is hard to assess or is even undefined for short, transient forcing. When at least the linear part of the equations of motion is known, our GSS algorithm outperforms available data-driven neural-network-based techniques for predicting forced response in structural dynamics problems. In a fully equation-driven setting, our GSS computations are shown to be faster than a direct numerical integration of forced nonlinear finite-element models of beams and shells.

math.DS↗

arXiv2025

Taming High-Dimensional Dynamics: Learning Optimal Projections onto Spectral Submanifolds

High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on orthogonal projections, a simplification that may lead to large prediction errors. In this work, we derive optimality of fiber-aligned projections onto spectral submanifolds, preserving the nonlinear geometric structure and minimizing long-term prediction error. We propose a data-driven procedure to learn these projections from trajectories and demonstrate its effectiveness through a 180-dimensional robotic system. Our reduced-order models achieve up to fivefold improvement in trajectory tracking accuracy under model predictive control compared to the state of the art.

eess.SY↗

arXiv2024

Nonlinear Model Reduction to Random Spectral Submanifolds in Random Vibrations

Dynamical systems in engineering and physics are often subject to irregular excitations that are best modeled as random. Monte Carlo simulations are routinely performed on such random models to obtain statistics on their long-term response. Such simulations, however, are prohibitively expensive and time consuming for high-dimensional nonlinear systems. Here we propose to decrease this numerical burden significantly by reducing the full system to very low-dimensional, attracting, random invariant manifolds in its phase space and performing the Monte Carlo simulations on that reduced dynamical system. The random spectral submanifolds (SSMs) we construct for this purpose generalize the concept of SSMs from deterministic systems under uniformly bounded random forcing. We illustrate the accuracy and speed of random SSM reduction by computing the SSM-reduced power spectral density of the randomly forced mechanical systems that range from simple oscillator chains to finite-element models of beams and plates.

math.DS↗

arXiv2024

Nonlinear Model Reduction to Temporally Aperiodic Spectral Submanifolds

We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and control problems. The time-dependent SSMs we construct under these assumptions are normally hyperbolic and hence will persist for larger forcing and faster time dependence that are beyond the reach of our precise existence theory. For this reason, we also derive formal asymptotic expansions that, under explicitly verifiable nonresonance conditions, approximate SSMs and their aperiodic anchor trajectories accurately for stronger, faster or even temporally discontinuous forcing. Reducing the dynamical system to these persisting SSMs provides a mathematically justified model reduction technique for non-autonomous physical systems whose time dependance is moderate either in magnitude or speed. We illustrate the existence, persistence and computation of temporally aperiodic SSMs in mechanical examples under chaotic forcing.

math.DS↗