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Marcello Romano

Publications and source records attributed to Marcello Romano.

11 recordsLinked to original sources
arXiv2026

Coupling Tensor Trains with Graph of Convex Sets: Effective Compression, Exploration, and Planning in the C-Space

We present TANGO (Tensor ANd Graph Optimization), a novel motion planning framework that integrates tensor-based compression with structured graph optimization to enable efficient and scalable trajectory generation. While optimization-based planners such as the Graph of Convex Sets (GCS) offer powerful tools for generating smooth, optimal trajectories, they typically rely on a predefined convex characterization of the high-dimensional configuration space-a requirement that is often intractable for general robotic tasks. TANGO builds further by using Tensor Train decomposition to approximate the feasible configuration space in a compressed form, enabling rapid discovery and estimation of task-relevant regions. These regions are then embedded into a GCS-like structure, allowing for geometry-aware motion planning that respects both system constraints and environmental complexity. By coupling tensor-based compression with structured graph reasoning, TANGO enables efficient, geometry-aware motion planning and lays the groundwork for more expressive and scalable representations of configuration space in future robotic systems. Rigorous simulation studies on planar and real robots reinforce our claims of effective compression and higher quality trajectories.

cs.RO↗
arXiv2025

(Super)$\,$Gravity from Positivity

We investigate whether the effective theory for isolated, massive, and weakly interacting spin-$3/2$ particles is compatible with causality and unitarity-i.e., the positivity of scattering amplitudes. We find no solution to positivity constraints, except when gravitons are also present and couple in a (nearly) supersymmetric way. Gravity is thus bootstrapped from $S$-matrix consistency conditions for the longitudinal and transverse polarizations of massive spin-$3/2$ states. For two such particles forming a $U(1)$-charged state, a (gravi)photon gauging the symmetry is also required, with couplings characteristic of supergravity and consistent with both the no global symmetry and weak gravity conjectures. We further explore the EFT-hedron associated with the longitudinal polarizations, the Goldstinos, through novel $t$-$u$ symmetric dispersion relations. We identify the extremal UV models that lie at the corners of the allowed parameter space, recovering familiar models of supersymmetry breaking and uncovering new ones.

hep-th↗
arXiv2025

On the spin-orbit problem for highly elliptical orbits and recursive excitation

Examining the spin-orbit coupling effects for highly elliptical orbits is relevant to the mission design and operation of cislunar space assets, such as the Lunar Gateway. In high-eccentricity orbits, the gravity-gradient moment is here modelled as an instantaneous excitation at each periapsis passage. By approximating the gravity-gradient moment through Dirac pulses, we derive a recursive discrete map describing the rotational state of the satellite at the periapsis passage. Thanks to the recursive map, we are able to find the initial attitude corresponding to an unbounded growth of angular velocity, and to identify initial conditions whose evolution is such that the pulses have the same sign (in-phase condition) or the alternate sign (counterphase condition) at successive periapsis passages. In the recursive map, we perform the numerical analysis up to ten periapsis passages. In order to justify the introduction of the discrete map, we compare the results of the discrete map with those found in the spin-orbit problem. Because of numerical errors due to the high eccentricity, we restrict the investigation up to three periapsis passages in the spin-orbit problem. Moreover, we apply the Fast Lyapunov Indicators method to draw the phase portrait and detect the initial conditions fulfilling the counterphase condition.

astro-ph.EP↗
arXiv2024

Continuous-Spin Particles, On Shell

We study on-shell scattering amplitudes for continuous-spin particles (CSPs). Poincar\'e invariance, little-group $ISO(2)$ covariance, analyticity, and on-shell factorisation (unitarity) impose stringent conditions on these amplitudes. We solve them by realizing a non-trivial representation for all little-group generators on the space of functions of bi-spinors. The three-point amplitudes are uniquely determined by matching their high-energy limit to that of definite-helicity (ordinary) massless particles. Four-point amplitudes are then bootstrapped using consistency conditions, allowing us to analyze the theory in a very transparent way, without relying on any off-shell Lagrangian formulation. We present several examples that highlight the main features of the resulting scattering amplitudes. We discuss CSP's amplitudes as a new infrared deformation of ordinary massless amplitudes, which is controlled by the scale of the Pauli-Lubanski vector squared, as opposed to the familiar mass deformation. Finally, we explore under which conditions it is possible to relax some assumptions, such as strict on-shell factorisation, analyticity, or others. In particular, we also investigate how continuous-spin particles may couple to gravity and electromagnetism, in a loose version of $S$-matrix principles.

hep-th↗
arXiv2024

A novel strategy to prove chiral symmetry breaking in QCD-like theories

We demonstrate that chiral symmetry breaking occurs in the confining regime of QCD-like theories with $N_c$ colors and $N_f$ flavors. Our proof is based on a novel strategy, called `downlifting', by which solutions of the 't Hooft anomaly matching and persistent mass conditions for a theory with $N_f-1$ flavors are constructed from those of a theory with $N_f$ flavors, while $N_c$ is fixed. By induction, chiral symmetry breaking is proven for any $N_f\geq p_{min}$ in the confining regime, where $p_{min}$ is the smallest prime factor of $N_c$. The proof can be extended to $N_f <p_{min}$ under the additional assumption on the absence of phase transitions when quark masses are sent to infinity. Our results do not rely on assumptions on the spectrum of massless bound states other than the fact that they are color-singlet hadrons.

hep-th↗
arXiv2022

On the Proof of Chiral Symmetry Breaking from Anomaly Matching in QCD-like Theories

We critically reconsider the argument based on 't Hooft anomaly matching that aims at proving chiral symmetry breaking in confining four-dimensional QCD-like theories with $N_c>2$ colors and $N_f$ flavors. The main line of reasoning relies on a property of the solutions of the anomaly matching and persistent mass equations called $N_f$-independence. In previous works, the validity of $N_f$-independence was assumed based on qualitative arguments, but it was never proven rigorously. We provide a detailed proof and clarify under which (dynamical) conditions it holds. Our results are valid for a generic spectrum of massless composite fermions including baryons and exotics.

hep-th↗
arXiv2018

A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints

A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven to converge to a locally optimal solution. Assuming that the first convex problem in the sequence is feasible, these properties are obtained by convexifying the non-convex cost and inequality constraints with inner-convex approximations. Additionally, a computationally efficient method is introduced to obtain inner-convex approximations based on Taylor series expansions. These Taylor-based inner-convex approximations provide the overall algorithm with a quadratic rate of convergence. The proposed method is capable of solving problems of practical interest in real-time. This is illustrated with a numerical simulation of an aerial vehicle trajectory optimization problem on commercial-of-the-shelf embedded computers.

math.OC↗
arXiv2018

An Offline-Sampling SMPC Framework with Application to Automated Space Maneuvers

In this paper, a sampling-based Stochastic Model Predictive Control algorithm is proposed for discrete-time linear systems subject to both parametric uncertainties and additive disturbances. One of the main drivers for the development of the proposed control strategy is the need of real-time implementability of guidance and control strategies for automated rendezvous and proximity operations between spacecraft. The paper presents considers the validation of the proposed control algorithm on an experimental testbed, showing how it may indeed be implemented in a realistic framework. Parametric uncertainties due to the mass variations during operations, linearization errors, and disturbances due to external space environment are simultaneously considered. The approach enables to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided, and under mild assumptions, asymptotic stability in probability of the origin can be established. The offline sampling approach in the control design phase is shown to reduce the computational cost, which usually constitutes the main limit for the adoption of Stochastic Model Predictive Control schemes, especially for low-cost on-board hardware. These characteristics are demonstrated both through simulations and by means of experimental results.

eess.SY↗
arXiv2012

Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.

physics.class-ph↗
arXiv2012

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.

physics.class-ph↗