arXiv subjects

Stefano Stramigioli

Publications and source records attributed to Stefano Stramigioli.

At least 19 recordsLinked to original sources

arXiv2026

Symmetric Lyapunov Subcenter Manifolds for Periodic Regulation of Mechanical Systems

Multi-body mechanical systems have rich internal dynamics, whose solutions can be exploited as energy-efficient control targets. Yet, solutions non-trivially depend on system parameters, obscuring feasible properties for use as target trajectories. For periodic regulation tasks in robotics applications, we investigate properties of nonlinear oscillations collected in Lyapunov subcenter manifolds (LSMs) of conservative mechanical systems (CMs). Using a time-symmetry of CMs, it is shown that mild non-resonance conditions guarantee that LSMs exclusively consist of oscillations between two points of zero velocity. The existence of a unique generator is proven, which is a connected, 1D manifold that collects these points of zero velocity for a given LSM. Furthermore, it is shown that an additional spatial symmetry provides LSMs with yet stronger properties of Rosenberg manifolds. Here all oscillations pass through a unique equilibrium configuration, which can be favorable for control applications. These theoretical results are numerically confirmed on two mechanical systems: a double pendulum and a 5-link pendulum.

math.DS↗

arXiv2026

Sensitivity increase of 3D printed, self-sensing, carbon fibers structures with conductive filament matrix due to flexural loading

The excellent structural and piezoresistive properties of continuous carbon fiber make it suitable for both structural and sensing applications. This work studies the use of 3D printed, continuous carbon fiber reinforced beams as self-sensing structures. It is demonstrated how the sensitivity of these carbon fiber strain gauges can be increased irreversibly by means of a pretreatment by pre-stressing the sensors with a large compressive bending load. The increase in the gauge factor is attributed to local progressive fiber failure, due to the combination of the thermal residual stress from the printing process and external loading. The coextrusion of conductive filament around the carbon fibers is demonstrated as a means of improving the reliability, noise and electrical connection of the sensors. A micrograph of the sensor cross section shows that the conductive filament contacts the various carbon fiber bundles. All-in-all, the use of pre-stressing carbon fiber strain gauges in combination with coextrusion of conductive filament hold promises for 3D printed structural sensors with a high sensitivity.

eess.SY↗

arXiv2026

Physical Human-Robot Interaction: A Critical Review of Safety Constraints

This paper aims to provide a clear and rigorous understanding of commonly recognized safety constraints in physical human-robot interaction, particularly regarding ISO/TS 15066. We investigate the derivation of these constraints, critically examine the underlying assumptions, and evaluate their practical implications for system-level safety and performance in industrially relevant scenarios. Key design parameters within safety-critical control architectures are identified, and numerical examples are provided to quantify performance degradation arising from typical approximations and design decisions in manufacturing environments. Within this analysis, the fundamental role of energy in safety assessment is emphasized, providing focused insights into energy-based safety methodologies for collaborative industrial robot systems.

eess.SY↗

arXiv2026

Model order reduction via Lie groups

Lie groups and their actions are ubiquitous in the description of physical systems, and we explore implications in the setting of model order reduction (MOR). We present a novel framework of MOR via Lie groups, called MORLie, in which high-dimensional dynamical systems on manifolds are approximated by low-dimensional dynamical systems on Lie groups. In comparison to other Lie group methods we are able to attack non-equivariant dynamics, which are frequent in practical applications, and we provide new non-intrusive MOR methods based on the presented geometric formulation. We also highlight numerically that MORLie has a lower error bound than the Kolmogorov $N$-width, which limits linear-subspace methods. The method is applied to various examples: 1. MOR of a simplified deforming body modeled by noisy point cloud data following a sheering motion, where MORLie outperforms a naive POD approach in terms of accuracy and dimensionality reduction. 2. Reconstructing liver motion during respiration with data from edge detection in MRI scans, where MORLie reaches performance approaching the state of the art, while reducing the training time from hours on a computing cluster to minutes on a mobile workstation. 3. An analytic example showing that the method of freezing is analytically recovered as a special case, showing the generality of the geometric framework.

math.NA↗

arXiv2025

Lossless optimal transient control for rigid bodies in 3D space

In this letter, we propose a control scheme for rigid bodies designed to optimise transient behaviors. The search space for the optimal control input is parameterized to yield a passive, specifically lossless, nonlinear feedback controller. As a result, it can be combined with other stabilizing controllers without compromising the stability of the closed-loop system. The controller commands torques generating fictitious gyroscopic effects characteristics of 3D rotational rigid body motions, and as such does not inject nor extract kinetic energy from the system. We validate the controller in simulation using a model predictive control (MPC) scheme, successfully combining stability and performance in a stabilization task with obstacle avoidance constraints.

eess.SY↗

arXiv2025

The effect of control barrier functions on energy transfers in controlled physical systems

Using a port-Hamiltonian formalism, we show the qualitative and quantitative effect of safety-critical control implemented with control barrier functions (CBFs) on the power balance of controlled physical systems. The presented results will provide novel tools to design CBFs inducing desired energetic behaviors of the closed-loop system, including nontrivial damping injection effects and non-passive control actions, effectively injecting energy in the system in a controlled manner. Simulations validate the stated results.

eess.SY↗

arXiv2025

Hybrid Schrödinger-Liouville and projective dynamics

Quantum dynamics provides the arguably most fundamental example of hybrid dynamics: As long as no measurement takes place, the system state is governed by the Schrödinger-Liouville differential equation, which is however interrupted and replaced by projective dynamics at times when measurements take place. We show how this alternatingly continuous and projective evolution can be cast in form of one single differential equation for a refined state space manifold and thus be made amenable to standard port-theoretic analysis and control techniques.

quant-ph↗

arXiv2025

Finite element hybridization of port-Hamiltonian systems

In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation phenomena. To this aim, a dual field mixed Galerkin discretization is introduced, in which one variable is approximated via conforming finite element spaces, whereas the second is completely local. This scheme is equivalent to the second order mixed Galerkin formulation and retains a discrete power balance and discrete conservation laws. The mixed formulation is also equivalent to the hybrid formulation. The hybrid system can be efficiently solved using a static condensation procedure in discrete time. The size reduction achieved thanks to the hybridization is greater than the one obtained for the Hodge Laplacian as one field is completely discarded. Numerical experiments on the 3D wave and Maxwell equations show the convergence of the method and the size reduction achieved by the hybridization.

math.NA↗

arXiv2024

Optimal Potential Shaping on SE(3) via Neural ODEs on Lie Groups

This work presents a novel approach for the optimization of dynamic systems on finite-dimensional Lie groups. We rephrase dynamic systems as so-called neural ordinary differential equations (neural ODEs), and formulate the optimization problem on Lie groups. A gradient descent optimization algorithm is presented to tackle the optimization numerically. Our algorithm is scalable, and applicable to any finite dimensional Lie group, including matrix Lie groups. By representing the system at the Lie algebra level, we reduce the computational cost of the gradient computation. In an extensive example, optimal potential energy shaping for control of a rigid body is treated. The optimal control problem is phrased as an optimization of a neural ODE on the Lie group SE(3), and the controller is iteratively optimized. The final controller is validated on a state-regulation task.

math.OC↗

arXiv2024

Anatomical Region Recognition and Real-time Bone Tracking Methods by Dynamically Decoding A-Mode Ultrasound Signals

Accurate bone tracking is crucial for kinematic analysis in orthopedic surgery and prosthetic robotics. Traditional methods (e.g., skin markers) are subject to soft tissue artifacts, and the bone pins used in surgery introduce the risk of additional trauma and infection. For electromyography (EMG), its inability to directly measure joint angles requires complex algorithms for kinematic estimation. To address these issues, A-mode ultrasound-based tracking has been proposed as a non-invasive and safe alternative. However, this approach suffers from limited accuracy in peak detection when processing received ultrasound signals. To build a precise and real-time bone tracking approach, this paper introduces a deep learning-based method for anatomical region recognition and bone tracking using A-mode ultrasound signals, specifically focused on the knee joint. The algorithm is capable of simultaneously performing bone tracking and identifying the anatomical region where the A-mode ultrasound transducer is placed. It contains the fully connection between all encoding and decoding layers of the cascaded U-Nets to focus only on the signal region that is most likely to have the bone peak, thus pinpointing the exact location of the peak and classifying the anatomical region of the signal. The experiment showed a 97% accuracy in the classification of the anatomical regions and a precision of around 0.5$\pm$1mm under dynamic tracking conditions for various anatomical areas surrounding the knee joint. In general, this approach shows great potential beyond the traditional method, in terms of the accuracy achieved and the recognition of the anatomical region where the ultrasound has been attached as an additional functionality.

eess.SP↗

arXiv2024

The port-Hamiltonian structure of continuum mechanics

In this paper we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems. Leveraging Dirac structures, instead of symplectic or Poisson structures, this formalism allows the incorporation of energy exchange within the spatial domain or through its boundary, which allows for a more comprehensive description of continuum mechanics. Building upon our recent work in describing nonlinear elasticity using exterior calculus and bundle-valued differential forms, this paper focuses on the systematic derivation of port-Hamiltonian models for solid and fluid mechanics in the material, spatial, and convective representations using Hamiltonian reduction theory. This paper also discusses constitutive relations for stress within this framework including hyper-elasticity, for both finite- and infinite-strains, as well as viscous fluid flow governed by the Navier-Stokes equations.

math-ph↗

arXiv2024

Deep Learning based acoustic measurement approach for robotic applications on orthopedics

In Total Knee Replacement Arthroplasty (TKA), surgical robotics can provide image-guided navigation to fit implants with high precision. Its tracking approach highly relies on inserting bone pins into the bones tracked by the optical tracking system. This is normally done by invasive, radiative manners (implantable markers and CT scans), which introduce unnecessary trauma and prolong the preparation time for patients. To tackle this issue, ultrasound-based bone tracking could offer an alternative. In this study, we proposed a novel deep learning structure to improve the accuracy of bone tracking by an A-mode ultrasound (US). We first obtained a set of ultrasound dataset from the cadaver experiment, where the ground truth locations of bones were calculated using bone pins. These data were used to train the proposed CasAtt-UNet to predict bone location automatically and robustly. The ground truth bone locations and those locations of US were recorded simultaneously. Therefore, we could label bone peaks in the raw US signals. As a result, our method achieved sub millimeter precision across all eight bone areas with the only exception of one channel in the ankle. This method enables the robust measurement of lower extremity bone positions from 1D raw ultrasound signals. It shows great potential to apply A-mode ultrasound in orthopedic surgery from safe, convenient, and efficient perspectives.

eess.SP↗

arXiv2024

Learning passive policies with virtual energy tanks in robotics

Within a robotic context, we merge the techniques of passivity-based control (PBC) and reinforcement learning (RL) with the goal of eliminating some of their reciprocal weaknesses, as well as inducing novel promising features in the resulting framework. We frame our contribution in a scenario where PBC is implemented by means of virtual energy tanks, a control technique developed to achieve closed-loop passivity for any arbitrary control input. Albeit the latter result is heavily used, we discuss why its practical application at its current stage remains rather limited, which makes contact with the highly debated claim that passivity-based techniques are associated with a loss of performance. The use of RL allows us to learn a control policy that can be passivized using the energy tank architecture, combining the versatility of learning approaches and the system theoretic properties which can be inferred due to the energy tanks. Simulations show the validity of the approach, as well as novel interesting research directions in energy-aware robotics.

cs.RO↗

arXiv2023

Exp[licit]-A Robot modeling Software based on Exponential Maps

$ $Deriving a robot's equation of motion typically requires placing multiple coordinate frames, commonly using the Denavit-Hartenberg convention to express the kinematic and dynamic relationships between segments. This paper presents an alternative using the differential geometric method of Exponential Maps, which reduces the number of coordinate frame choices to two. The traditional and differential geometric methods are compared, and the conceptual and practical differences are detailed. The open-source software, Exp[licit], based on the differential geometric method, is introduced. It is intended for use by researchers and engineers with basic knowledge of geometry and robotics. Code snippets and an example application are provided to demonstrate the benefits of the differential geometric method and assist users to get started with the software.

cs.RO↗

arXiv2023

Intrinsic nonlinear elasticity: An exterior calculus formulation

In this paper we formulate the theory of nonlinear elasticity in a geometrically intrinsic manner using exterior calculus and bundle-valued differential forms. We represent kinematics variables, such as velocity and rate-of-strain, as intensive vector-valued forms while kinetics variables, such as stress and momentum, as extensive covector-valued pseudo-forms. We treat the spatial, material and convective representations of the motion and show how to geometrically convert from one representation to the other. Furthermore, we show the equivalence of our exterior calculus formulation to standard formulations in the literature based on tensor calculus. In addition, we highlight two types of structures underlying the theory. First, the principle bundle structure relating the space of embeddings to the space of Riemannian metrics on the body, and how the latter represents an intrinsic space of deformations. Second, the de Rham complex structure relating the spaces of bundle-valued forms to each other.

math-ph↗

arXiv2022

Discovering Efficient Periodic Behaviours in Mechanical Systems via Neural Approximators

It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the system. The classification of these periodic behaviours and their geometric characterisation are in an on-going secular debate, which recently led to the so-called eigenmanifold theory. The eigenmanifold characterises nonlinear oscillations as a generalisation of linear eigenspaces. With the motivation of performing periodic tasks efficiently, we use tools coming from this theory to construct an optimization problem aimed at inducing desired closed-loop oscillations through a state feedback law. We solve the constructed optimization problem via gradient-descent methods involving neural networks. Extensive simulations show the validity of the approach.

math.OC↗

arXiv2022

On the use of energy tanks for robotic systems

In this document we describe and discuss energy tanks, a control algorithm which has gained popularity inside the robotics and control community over the last years. This article has the threefold scope of i) introducing to the reader the topic in a simple yet precise way, starting with a throughout description of the energy-aware framework, where energy tanks find their genesis; ii) summarising the range of applications of energy tanks, including an original reflection about different formulations of those; iii) discussing limits and future challenges involving energy tanks and energy-aware control in general.

eess.SY↗

arXiv2022

The Principle Bundle Structure of Continuum Mechanics

In this paper it is shown that the structure of the configuration space of any continua is what is called in differential geometry a {\it principle bundle} \cite{Frankel2011ThePhysics}. A principal bundle is a structure in which all points of the manifold (each configuration in this case) can be naturally projected to a manifold called the {\it base manifold}, which in our case represents pure deformations. All configurations projecting to the same point on the base manifold (same deformation) are called fibers. Each of these fibers is then isomorphic to the Lie group $\mathfrak{se(3)}$ representing pure rigid body motions. Furthermore, it is possible to define what is called a connection and this allows to split any continua motion in a rigid body sub-motion and a deformable one in a completely coordinate free way. As a consequence of that it is then possible to properly define a pure deformation space on which an elastic energy can be defined. This will be shown using screw theory \cite{Ball:1900}, which is vastly used in the analysis of rigid body mechanisms but is not normally used to analyse continua. Beside the just mentioned result, screw theory will also be used to relate concepts like helicity and enstrophy to screw theory concepts.

physics.flu-dyn↗