arXiv subjects

Leonardo Colombo

Publications and source records attributed to Leonardo Colombo.

At least 19 recordsLinked to original sources

arXiv2026

Feasibility and Singularity in High-Order Safety-Critical Control for Quadrotor UAVs

We study high-order safety-critical control of quadrotor teams under bounded inputs and pairwise collision-avoidance constraints. Squared-distance barriers may lose thrust effectiveness when the relative displacement is orthogonal to the available thrust directions, while nonsingular constraints may still be jointly infeasible under shared bounds. We characterize both phenomena through pairwise effectiveness and aggregate feasibility measures. A torque-aware dynamic extension exposes attitude torques in a fourth-order barrier and prevents the extended-input row from vanishing under positive thrust. Gaussian processes directly learn the fourth-order HOCBF residual, providing robust margins without differentiating unknown perturbations. Under residual-bound and persistent-feasibility assumptions, the resulting QP guarantees collision avoidance and recovers the nominal input whenever it satisfies the robust safety and actuator constraints.

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arXiv2026

Lindblad Quantum Dynamics as Euler-Poincaré Reduction on Adjoint-Coupled Semidirect Products

We present a geometric and variational derivation of the Gorini--Kossakowski--Sudarshan--Lindblad equation from Euler--Poincar'e reduction on an adjoint--coupled semidirect product (ACSP). In this construction a Lie group $G$ acts on $V=\mathfrak{g}^{\oplus m}$ by the adjoint representation together with a second, adjointly compatible action whose failure to commute defines an adjoint torsion $K(ξ,v)$. This torsion generates a canonical quadratic curvature operator on $\mathfrak{g}^*$ that survives reduction and yields a metric double--bracket term. For $G=SU(n)$ the reduced Euler--Poincar'e equation reproduces exactly the GKSL generator: the Hamiltonian part arises from the coadjoint action, while the dissipator $-\tfracγ{2}[L,[L,ρ]]$ appears as the torsion--induced metric component of an ACSP bracket. We prove a characterization theorem showing that any quadratic $SU(n)$--equivariant operator generated by torsion factorizes into a Lindblad double commutator; a uniqueness theorem establishing that, under natural structural assumptions, the only admissible dissipator is the Lindblad form; and an orbit--contraction theorem showing strict contraction toward the commutant of the Lindblad operators. For $SU(2)$ and $SU(3)$ the ACSP geometry yields explicit Bloch equations for representative dissipative channels. We also show that the ACSP bracket fits into a metriplectic and contact--geometric framework in which the Lindblad term is the metric component and the Reeb part of a contact Hamiltonian flow. In this picture, decoherence is a curvature--induced contraction generated by Euler--Poincar'e reduction rather than a phenomenological input.

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arXiv2026

Stable Walking for Bipedal Locomotion under Foot-Slip via Virtual Nonholonomic Constraints

Foot slip is a major source of instability in bipedal locomotion on low-friction or uncertain terrain. Standard control approaches typically assume no-slip contact and therefore degrade when slip occurs. We propose a control framework that explicitly incorporates slip into the locomotion model through virtual nonholonomic constraints, which regulate the tangential stance-foot velocity while remaining compatible with the virtual holonomic constraints used to generate the walking gait. The resulting closed-loop system is formulated as a hybrid dynamical system with continuous swing dynamics and discrete impact events. A nonlinear feedback law enforces both classes of constraints and yields a slip-compatible hybrid zero dynamics manifold for the reduced-order locomotion dynamics. Stability of periodic walking gaits is characterized through the associated Poincaré map, and numerical results illustrate stabilization under slip conditions.

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arXiv2026

Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure

This paper develops a bridge between bi-Hamiltonian structures of Poisson--Lie type, contact Hamiltonian dynamics, and the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) formalism for open quantum systems. On the classical side, we consider bi-Hamiltonian systems defined by a Poisson pencil with non-trivial invariants. Using an exact symplectic realization, these invariants are lifted and projected onto a contact manifold, yielding a completely integrable contact Hamiltonian system and a Jacobi-commutative algebra of observables. On the quantum side, we introduce a class of contact-compatible Lindblad generators: GKSL evolutions whose dissipative part preserves a commutative $C^\ast$-subalgebra generated by the quantizations of the classical dissipated quantities, and whose Hamiltonian part admits an Egorov-type semiclassical limit to the contact dynamics. This construction provides a mathematical mechanism compatible with the semiclassical limit for pure dephasing, compatible with integrability and contact dissipation. An explicit Poisson--Lie pencil, inspired by deformed Euler top models, is developed as a fully worked-out example illustrating the resulting bi-Lindblad structure and its semiclassical behavior.

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arXiv2026

Safety-Critical Control for Quadrotor UAVs via Decentralized Navigation Functions

We study safety-critical control for teams of quadrotor UAVs driven by decentralized navigation functions under learned model uncertainty. These functions generate fully actuated translational reference forces, while quadrotors can only produce thrust along their body-fixed vertical axes. We construct a thrust-attitude implementation of the induced navigation forces and quantify its error with respect to the fully actuated reference dynamics. An aggregated robust HOCBF-QP safety filter minimally modifies the nominal thrusts while guaranteeing pairwise collision avoidance with high probability.

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arXiv2026

Discrete-time generalized canonical transformations for non-autonomous systems

A dynamical system is said to be \emph{non-autonomous} when the differential equations describing its evolution depends explicitly on time. Among the various geometric approaches to investigate such systems, the cosymplectic formulation provides a natural framework that extends symplectic geometry to time-dependent Hamiltonians systems. However, preserving the associated geometric structures under numerical discretization remains a challenging problem: standard integrators, such as explicit Euler schemes, generally fail to conserve the cosymplectic volume or the underlying Poisson structure. In this work we propose a geometric method for the discretization of non-autonomous Hamiltonian systems based on \emph{generalized canonical transformations}. The approach constructs a symplectomorphism on the extended phase space $T^*(Q \times \mathbb{R})$ whose projection onto $T^*Q \times \mathbb{R}$ defines a structure-preserving discrete flow. We show that this formulation guarantees the preservation of key invariants, including the volume form, the Poisson bracket, and the symplectic structure on each time fiber.

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arXiv2026

Contact Tulczyjew Geometry for Continuous and Discrete Dissipative Dynamics on Skew Algebroids

We develop a contact Tulczyjew formalism for dissipative dynamics on skew algebroids. Starting from the Tulczyjew morphism of an skew algebroid, we identify its contact extension in a local line-bundle trivialization. The local representative is obtained by adding to the ordinary Tulczyjew morphism the Euler vector field contribution on $E^*$. This gives an intrinsic explanation of the contact term appearing in the local contact Tulczyjew morphism. For a contact generating object, the construction produces an implicit dissipative dynamics on the contact phase side. In local coordinates, the matching condition gives the Euler-Lagrange-Herglotz equations on the skew algebroid. In the hyperregular case, the corresponding contact Hamiltonian equations are recovered by Legendre transformation. We also develop the discrete counterpart of the construction. After fixing a discrete admissibility relation, a discrete contact generating object defines a discrete contact Tulczyjew relation on the contact phase space. Discrete Herglotz extremals are obtained by matching consecutive contact momenta, with the usual conormal interpretation in the constrained case. In the regular tangent-bundle case, this recovers standard contact variational integrators, while in the singular or skew algebroid setting the same construction remains meaningful as an implicit discrete relation rather than an a priori update map.

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arXiv2026

Stabilizing Role of Uninformed Participants in Collective Decision Making

For groups without strict hierarchy, collective decisions often emerge through compromise. We develop a second-order network model of collective decision-making using a dissipative Hamiltonian formulation, in which informed agents introduce preferred directions while uninformed participants contribute only direction-free dissipation. We show that under low conflict, the model admits a locally unique, exponentially stable compromise state. Using a structured modular network we further show that as conflict increases the local compromise branch terminates through a saddle-node fold rather than through a smooth mean-field symmetry-breaking transition. Modular polarized states persist on branches that are locally separated from the compromise branch. Direction-free dissipation does not shift the static structural threshold, but it delays escape from the saddle-node ghost and pushes the observable onset of polarization to larger conflicts. Our work identifies a dissipation-mediated mechanism, complementary to connectivity-based accounts, through which uninformed participants stabilize collective behavior in biological and engineered swarms.

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arXiv2026

Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance

It was shown in \cite{bloch2000optimal} that an optimal control formulation for incompressible ideal fluid flow yields Euler's equations. In this paper, we consider a variational obstacle-avoidance formulation for incompressible ideal flows by introducing a barrier-type potential in the associated optimal control functional. This leads to \textit{modified Euler equations for an inviscid fluid}, in which the barrier term acts on the Lagrangian configuration and appears in the Eulerian description as a shift in the effective pressure. We also present a numerical illustration of the reduced Eulerian dynamics, showing that the barrier term induces a localized deformation of the flow near the obstacle region, consistent with its role as an obstacle-avoidance penalization.

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arXiv2026

Robust Geometric Control of Catenary Robots under Unstructured Force Uncertainties

This paper considers the robust control of a catenary robot composed of two quadrotors connected by an inextensible cable. The system is modeled on $SE(3)$, with the cable treated as a geometric subsystem induced by the UAV configuration rather than as an independent dynamical element. The catenary shape determines configuration-dependent forces that couple the translational dynamics of the vehicles. We propose a geometric tracking controller for the relative configuration of the agents and analyze its robustness with respect to unstructured uncertainties in the catenary-induced forces. The main theoretical result establishes local input-to-state stability of the closed-loop tracking errors. In particular, we obtain asymptotic convergence in the nominal case and an explicit ultimate bound for the tracking errors under bounded catenary-force perturbations.

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arXiv2026

Data-Driven Boundary Control of Distributed Port-Hamiltonian Systems

Distributed Port-Hamiltonian (dPHS) theory provides a powerful framework for modeling physical systems governed by partial differential equations and has enabled a broad class of boundary control methodologies. Their effectiveness, however, relies heavily on the availability of accurate system models, which may be difficult to obtain in the presence of nonlinear and partially unknown dynamics. To address this challenge, we combine Gaussian Process distributed Port-Hamiltonian system (GP-dPHS) learning with boundary control by interconnection. The GP-dPHS model is used to infer the unknown Hamiltonian structure from data, while its posterior uncertainty is incorporated into an energy-based robustness analysis. This yields probabilistic conditions under which the closed-loop trajectories remain bounded despite model mismatch. The method is illustrated on a simulated shallow water system.

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arXiv2026

Dissipation-assisted stabilization of periodic orbits via actuated exterior impacts in hybrid mechanical systems with symmetry

Impulsive mechanical systems exhibit discontinuous jumps in their state, and when such jumps are triggered by spatial events, the geometry of the impact surface carries information about the controllability of the hybrid dynamics. For mechanical systems defined on principal $G$-bundles, two qualitatively distinct types of impacts arise: interior impacts, associated with events on the shape space, and exterior impacts, associated with events on the fibers. A key distinction is that interior impacts preserve the mechanical connection, whereas exterior impacts generally do not. In this paper, we exploit this distinction by allowing actuation through exterior impacts. We study the pendulum-on-a-cart system, derive controlled reset laws induced by moving-wall impacts, and analyze the resulting periodic motions. Our results show that reset action alone does not provide a convincing stabilizing regime, whereas the addition of dissipation in the continuous flow yields exponentially stable periodic behavior for suitable feedback gains.

eess.SY↗

arXiv2026

Structure-Preserving Learning of Nonholonomic Dynamics

Data-driven modeling is playing an increasing role in robotics and control, yet standard learning methods typically ignore the geometric structure of nonholonomic systems. As a consequence, the learned dynamics may violate the nonholonomic constraints and produce physically inconsistent motions. In this paper, we introduce a structure-preserving Gaussian process (GP) framework for learning nonholonomic dynamics. Our main ingredient is a nonholonomic matrix-valued kernel that incorporates the constraint distribution directly into the GP prior. This construction ensures that the learned vector field satisfies the nonholonomic constraints for all inputs. We show that the proposed kernel is positive semidefinite, characterize its associated reproducing kernel Hilbert space as a space of admissible vector fields, and prove that the resulting estimator admits a coordinate representation adapted to the constraint distribution. We also establish the consistency of the learned model. Numerical simulations on a vertical rolling disk illustrate the effectiveness of the proposed approach.

eess.SY↗

arXiv2026

Observer-Based Estimation and Hydrostatic Inertia Modeling for Cooperative Transport of Variable-Inertia Loads with Quadrotors

We address load-parameter estimation in cooperative aerial transport with time-varying mass and inertia, as in fluid-carrying payloads. Using an intrinsic manifold model of the multi-quadrotor-load dynamics, we combine a geometric tracking controller with an observer for parameter identification. We estimate mass from measurable kinematics and commanded forces, and handle variable inertia via an inertia surrogate that reproduces the load's rotational dynamics for control and state propagation. Instead of real-time identification of the true inertia tensor, driven by high-dimensional internal fluid motion, we leverage known tank geometry and fluid-mechanical structure to pre-compute inertia tensors and update them through a lookup table indexed by fill level and attitude. The surrogate is justified via the incompressible Navier-Stokes equations in the translating/rotating load frame: when effective forcing is gravity-dominated (i.e., translational/rotational accelerations and especially jerk are limited), the fluid approaches hydrostatic equilibrium and the free surface is well approximated by a plane orthogonal to the body-frame gravity direction.

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arXiv2026

Virtual Constraint for a Quadrotor UAV Enforcing a Body-Axis Pointing Direction

We propose a geometric control framework on $SE(3)$ for quadrotors that enforces pointing-driven missions without completing a full attitude reference. The mission is encoded through virtual constraints defining a task manifold and an associated set of admissible velocities, and invariance is achieved by a feedback law obtained from a linear system in selected inputs. Under a transversality condition with the effective actuation distribution, the invariance-enforcing input is uniquely defined, yielding a constructive control law and, for relevant tasks, closed-form expressions. We further derive a local off-manifold stabilization extension. As a case study, we lock a body axis to a prescribed line-of-sight direction while maintaining fixed altitude.

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arXiv2026

Learning-Based Geometric Leader-Follower Control for Cooperative Rigid-Payload Transport with Aerial Manipulators

This paper presents a learning-based tracking control framework for cooperative transport of a rigid payload by multiple aerial manipulators under rigid grasp constraints. A unified geometric model is developed, yielding a coupled agent--payload differential--algebraic system that explicitly captures contact wrenches, payload dynamics, and internal force redundancy. A leader--follower architecture is adopted in which a designated leader generates a desired payload wrench based on geometric tracking errors, while the remaining agents realize this wrench through constraint-consistent force allocation. Unknown disturbances and modeling uncertainties are compensated using Gaussian Process (GP) regression. High-probability bounds on the learning error are explicitly incorporated into the control design, combining GP feedforward compensation with geometric feedback. Lyapunov analysis establishes uniform ultimate boundedness of the payload tracking errors with high probability, with an ultimate bound that scales with the GP predictive uncertainty.

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arXiv2026

Aggressiveness-Aware Learning-based Control of Quadrotor UAVs with Safety Guarantees

This paper presents an aggressiveness-aware control framework for quadrotor UAVs that integrates learning-based oracles to mitigate the effects of unknown disturbances. Starting from a nominal tracking controller on $\mathrm{SE}(3)$, unmodeled generalized forces and moments are estimated using a learning-based oracle and compensated in the control inputs. An aggressiveness-aware gain scheduling mechanism adapts the feedback gains based on probabilistic model-error bounds, enabling reduced feedback-induced aggressiveness while guaranteeing a prescribed practical exponential tracking performance. The proposed approach makes explicit the trade-off between model accuracy, robustness, and control aggressiveness, and provides a principled way to exploit learning for safer and less aggressive quadrotor maneuvers.

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arXiv2026

Quantum Riemannian Cubics with Obstacle Avoidance for Quantum Geometric Model Predictive Control

We propose a geometric model predictive control framework for quantum systems subject to smoothness and state constraints. By formulating quantum state evolution intrinsically on the projective Hilbert space, we penalize covariant accelerations to generate smooth trajectories in the form of Riemannian cubics, while incorporating state-dependent constraints through potential functions. A structure-preserving variational discretization enables receding-horizon implementation, and a Lyapunov-type stability result is established for the closed-loop system. The approach is illustrated on the Bloch sphere for a two-level quantum system, providing a viable pathway toward predictive feedback control of constrained quantum dynamics.

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