Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2402.07038

Nonlinear Modes as a Tool for Comparing the Mathematical Structure of Dynamic Models of Soft Robots

Pietro Pustina·Davide Calzolari·Alin Albu-Schäffer·Alessandro De Luca·Cosimo Della Santina
View original source ↗Read source document ↗Export metadata ↓

Abstract

Continuum soft robots are nonlinear mechanical systems with theoretically infinite degrees of freedom (DoFs) that exhibit complex behaviors. Achieving motor intelligence under dynamic conditions necessitates the development of control-oriented reduced-order models (ROMs), which employ as few DoFs as possible while still accurately capturing the core characteristics of the theoretically infinite-dimensional dynamics. However, there is no quantitative way to measure if the ROM of a soft robot has succeeded in this task. In other fields, like structural dynamics or flexible link robotics, linear normal modes are routinely used to this end. Yet, this theory is not applicable to soft robots due to their nonlinearities. In this work, we propose to use the recent nonlinear extension in modal theory -- called eigenmanifolds -- as a means to evaluate control-oriented models for soft robots and compare them. To achieve this, we propose three similarity metrics relying on the projection of the nonlinear modes of the system into a task space of interest. We use this approach to compare quantitatively, for the first time, ROMs of increasing order generated under the piecewise constant curvature (PCC) hypothesis with a high-dimensional finite element (FE)-like model of a soft arm. Results show that by increasing the order of the discretization, the eigenmanifolds of the PCC model converge to those of the FE model.

Explore related subjects

cs.RO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Pietro Pustina, Davide Calzolari, Alin Albu-Schäffer, Alessandro De Luca, Cosimo Della Santina. 2024-02-10. Nonlinear Modes as a Tool for Comparing the Mathematical Structure of Dynamic Models of Soft Robots. https://arxiv.org/abs/2402.07038

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

J-PARSE: Jacobian-based Projection Algorithm for Resolving Singularities Effectively in Inverse Kinematic Control of Serial Manipulators

J-PARSE is an algorithm for smooth first-order inverse kinematic control of a serial manipulator near kinematic singularities. The commanded end-effector velocity is interpreted component-wise, according to the available mobility in each dimension of the task space. First, a substitute ''Safety'' Jacobian matrix is created, keeping the aspect ratio of the manipulability ellipsoid above a threshold value. The desired velocity is then projected onto non-singular and singular directions, and the latter projection scaled down by a factor informed by the altered mobility. A right-inverse of the non-singular Safety Jacobian is applied to the modified command. In the absence of joint limits and collisions, this ensures safe transition into and out of low-mobility configurations, guaranteeing locally stable reaching behavior towards target poses within, on the boundary of, and outside the workspace. The behavior is further guaranteed to be locally asymptotically stable if the starting and target configurations are not exactly singular, even if they are nearly singular. Velocity control with J-PARSE is benchmarked against approaches from the literature, illustrating its use of a single tuning parameter to simultaneously achieve high reaching accuracy and stable behavior. Applications in teleoperation, servoing, and learning are demonstrated. Videos and code are available at https://jparse-manip.github.io/.

cs.RO↗
arXiv2026

Spatiotemporal Calibration of Doppler Velocity Logs for Underwater Robots

The calibration of extrinsic parameters and clock offsets between sensors for high-accuracy performance in underwater SLAM systems remains insufficiently explored. Existing methods for Doppler Velocity Log (DVL) calibration are either constrained to specific sensor configurations or rely on oversimplified assumptions, and none jointly estimate translational extrinsics and time offsets. We propose a Unified Iterative Calibration (UIC) framework for general DVL sensor setups, formulated as a Maximum A Posteriori (MAP) estimation with a Gaussian Process (GP) motion prior for high-fidelity motion interpolation. UIC alternates between efficient GP-based motion state updates and gradient-based calibration variable updates, supported by a provably statistically consistent sequential initialization scheme. The proposed UIC can be applied to IMU, cameras and other modalities as co-sensors. We release an open-source DVL-camera calibration toolbox. Beyond underwater applications, several aspects of UIC-such as the integration of GP priors for MAP-based calibration and the design of provably reliable initialization procedures-are broadly applicable to other multi-sensor calibration problems. Finally, simulations and real-world tests validate our approach.

cs.RO↗
arXiv2026

HazardArena: Evaluating Semantic Safety in Vision-Language-Action Models

Vision-Language-Action (VLA) models inherit rich world knowledge from vision-language backbones and acquire executable skills via action demonstrations. However, existing evaluations largely focus on action execution success, leaving action policies loosely coupled with visual-linguistic semantics. This decoupling exposes a systematic vulnerability whereby correct action execution may induce unsafe outcomes under semantic risk. To expose this vulnerability, we introduce HazardArena, a benchmark designed to evaluate semantic safety in VLAs under controlled yet risk-bearing contexts. HazardArena is constructed from safe/unsafe twin scenarios that share matched objects, layouts, and action requirements, differing only in the semantic context that determines whether an action is unsafe. We find that VLA models trained exclusively on safe scenarios often fail to behave safely when evaluated in their corresponding unsafe counterparts. HazardArena includes over 2,000 assets and 40 risk-sensitive tasks spanning 7 real-world risk categories grounded in established robotic safety standards. To mitigate this vulnerability, we propose a training-free Safety Option Layer that constrains action execution using semantic attributes or a vision-language judge, substantially reducing unsafe behaviors with minimal impact on task performance. We hope that HazardArena highlights the need to rethink how semantic safety is evaluated and enforced in VLAs as they scale toward real-world deployment. Code released at https://github.com/HazardArena-Team/HazardArena ; updated code availability information.

cs.RO↗