arXiv subjects

Antonio Franchi

Publications and source records attributed to Antonio Franchi.

At least 37 records · Page 2Linked to original sources

arXiv2026

A Geometric Task-Space Port-Hamiltonian Formulation for Redundant Manipulators

We present a novel geometric port-Hamiltonian formulation of redundant manipulators performing a differential kinematic task $η=J(q)\dot{q}$, where $q$ is a point on the configuration manifold, $η$ is a velocity-like task space variable, and $J(q)$ is a linear map representing the task, for example the classical analytic or geometric manipulator Jacobian matrix. The proposed model emerges from a change of coordinates from canonical Hamiltonian dynamics, and splits the standard Hamiltonian momentum variable into a task-space momentum variable and a null-space momentum variable. Properties of this model and relation to Lagrangian formulations present in the literature are highlighted. Finally, we apply the proposed model in an \textit{Interconnection and Damping Assignment Passivity-Based Control} (IDA-PBC) design to stabilize and shape the impedance of a 7-DOF Emika Panda robot in simulation.

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arXiv2026

STL-Based Motion Planning and Uncertainty-Aware Risk Analysis for Human-Robot Collaboration with a Multi-Rotor Aerial Vehicle

This paper presents a motion planning and risk analysis framework for enhancing human-robot collaboration with a Multi-Rotor Aerial Vehicle. The proposed method employs Signal Temporal Logic to encode key mission objectives, including safety, temporal requirements, and human preferences, with particular emphasis on ergonomics and comfort. An optimization-based planner generates dynamically feasible trajectories while explicitly accounting for the vehicle's nonlinear dynamics and actuation constraints. To address the resulting non-convex and non-smooth optimization problem, smooth robustness approximations and gradient-based techniques are adopted. In addition, an uncertainty-aware risk analysis is introduced to quantify the likelihood of specification violations under human-pose uncertainty. A robustness-aware event-triggered replanning strategy further enables online recovery from disturbances and unforeseen events by preserving safety margins during execution. The framework is validated through MATLAB and Gazebo simulations on an object handover task inspired by power line maintenance scenarios. Results demonstrate the ability of the proposed method to achieve safe, efficient, and resilient human-robot collaboration under realistic operating conditions.

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arXiv2026

Cyclic Nullspace Coordination: Perpetual Flight of Aerial Carriers for Static Suspension

This work demonstrates that the non-stop flights of three or more carriers are compatible with holding a constant pose of a cable-suspended load. It also presents an algorithm for generating the carriers' coordinated non-stop trajectories. The proposed method builds upon two pillars: (1) the choice of n special linearly independent directions of internal forces within the 3n-6-dimensional nullspace of the grasp matrix of the load, chosen as the edges of a Hamiltonian cycle on the graph that connects the cable attachment points on the load. Adjacent pairs of directions are used to generate n forces evolving on distinct 2D affine subspaces, despite the attachment points being generically in 3D; (2) the construction of elliptical trajectories within these subspaces by mapping, through appropriate graph coloring, each edge of the Hamiltonian cycle to a periodic coordinate while ensuring that no adjacent coordinates exhibit simultaneous zero derivatives. Combined with conditions for load statics and attachment point positions, these choices ensure that each of the n force trajectories projects onto the corresponding cable constraint sphere with non-zero tangential velocity, enabling perpetual motion of the carriers while the load is still. The work provides a scalable constructive design for any n greater than or equal to 3 with tuning guidelines, quantifies sensitivity and single-carrier failures, and provides a fixed-wing-compatible planner that preserves load statics under speed/bank/flight-path constraints. The theoretical findings are validated through simulations and laboratory experiments with quadrotor UAVs.

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arXiv2026

A Comparative Study of INDI and NDI with Nonlinear Disturbance Observer for Aerial Robotics

This work presents a simulation-based comparative robustness analysis of Incremental Nonlinear Dynamic Inversion (INDI) and Nonlinear Dynamic Inversion augmented with a nonlinear disturbance observer (NDI+NDO) for fully actuated aerial robots. A systematic simulation campaign across representative operating scenarios is conducted, where we compare tracking performance, robustness, control effort, under parametric variations, external disturbances, and measurement noise. Results show that INDI demonstrates stronger robustness in several model-mismatch and combined-stress cases, while NDI+NDO primarily matches nominal performance but exhibits greater sensitivity under several non-ideal conditions. These findings provide practical guidance on the relative strengths and limitations of incremental and observer-based inversion strategies for aerial robotic applications.

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arXiv2026

Lie Group Formulation of Recursive Dynamics Algorithms of Higher Order for Floating-Base Robots

In this paper, we describe procedures for computing higher-order time derivatives of the Lie-group Newton-Euler, Articulated-Body Inertia, and hybrid dynamics algorithms for floating-base trees, where the base configuration evolves on SE(3) and the attached mechanism is an open kinematic tree with configuration on the (n1+n2)-dimensional manifold T^{n1} \times R^{n2}, using spatial representation of twists. After presenting the algorithms, we collect the resulting recursions into closed-form equations of motion, identifying an admissible Coriolis matrix satisfying the passivity property, and showing that the articulated inertia tensor remains unchanged across all time derivatives. We then apply the developed methods to a 12-DoF aerial manipulator to derive analytical expressions for its geometric forward and inverse dynamics along with their first time derivatives whereas the numerical simulations successfully evaluate these dynamics up to fifth order. Finally, to demonstrate their practical utility, we benchmark the proposed extensions and show that, in the considered tests, their computational cost scales quadratically with the derivative order, whereas the automatic-differentiation baseline exhibits exponential scaling.

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arXiv2026

Trajectory control of a suspended load with non-stopping flying carriers

This work presents the first closed-loop control framework for cooperative payload transportation with non-stopping flying carriers. The proposed method includes a feedback wrench-controller that actively regulates the load's pose by computing the wrench required for tracking its desired pose trajectory. Building upon grasp-matrix formulation and internal force redundancy, an optimization layer dynamically shapes internal-force parameters to guarantee persistent carrier motion, while not altering the desired load wrench. The desired non-stopping carrier's trajectories are computed using the system's kinematics and desired cable forces. Numerical simulations demonstrate that the method successfully prevents the carriers from stopping, while achieving a successful tracking of the desired load trajectory.

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arXiv2026

Sensitivity-Based Tube NMPC for Cooperative Aerial Structures Under Parametric Uncertainty

This paper presents a sensitivity-based tube Nonlinear Model Predictive Control (NMPC) framework for cooperative aerial chains under bounded parametric uncertainty. We consider a planar two-vehicle chain connected by rigid links, modeled with input-rate actuation to enforce slew-rate and magnitude limits on thrust and torque. Robustness to uncertainty in link mass, length, and inertia is achieved by propagating first-order parametric state sensitivities along the horizon and using them to compute online constraint-tightening margins. We robustify an inter-link separation constraint, implemented via a smooth cosine embedding, and thrust-magnitude bounds. The method is implemented in MATLAB and evaluated with boundary-hugging maneuvers and Monte-Carlo uncertainty sampling. Results show improved constraint margins under uncertainty with tracking performance comparable to nominal NMPC.

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arXiv2026

Geometric Inverse Flight Dynamics on SO(3) and Application to Tethered Fixed-Wing Aircraft

We present a robotics-oriented, coordinate-free formulation of inverse flight dynamics for fixed-wing aircraft on SO(3). Translational force balance is written in the world frame and rotational dynamics in the body frame; aerodynamic directions (drag, lift, side) are defined geometrically, avoiding local attitude coordinates. Enforcing coordinated flight (no sideslip), we derive a closed-form trajectory-to-input map yielding the attitude, angular velocity, and thrust-angle-of-attack pair, and we recover the aerodynamic moment coefficients component-wise. Applying such a map to tethered flight on spherical parallels, we obtain analytic expressions for the required bank angle and identify a specific zero-bank locus where the tether tension exactly balances centrifugal effects, highlighting the decoupling between aerodynamic coordination and the apparent gravity vector. Under a simple lift/drag law, the minimal-thrust angle of attack admits a closed form. These pointwise quasi-steady inversion solutions become steady-flight trim when the trajectory and rotational dynamics are time-invariant. The framework bridges inverse simulation in aeronautics with geometric modeling in robotics, providing a rigorous building block for trajectory design and feasibility checks.

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arXiv2026

Muscle Coactivation in the Sky: Geometry and Pareto Optimality of Energy vs. Aerodynamic Promptness and Multirotors as Variable Stiffness Actuators

In robotics and biomechanics, trading metabolic cost for kinematic readiness is a well-established principle. This paper formalizes this concept for aerial multirotors through the introduction of aerodynamic promptness -- a dynamic metric analogous to dynamic manipulability in robotics. By formulating redundancy resolution as a geometric multi-objective optimization along task fibers, we rigorously characterize the topological trade-off between energy consumption and promptness. We demonstrate that this interplay is fundamentally governed by fiber geometry. Cooperative actuation regime yields compact fibers with bounded, compatible Pareto fronts. Conversely, antagonistic actuation regime unlocks unbounded fibers, enabling aerodynamic co-contraction that drives promptness to hardware limits at the expense of flight endurance. We establish a structural isomorphism between aerodynamic co-contraction and biologically inspired variable stiffness actuators, introducing a dynamic ``flying muscle'' paradigm. Ultimately, this framework transitions multirotor allocation from heuristic energy minimization to principled, geometry-aware Pareto navigation, laying foundational theory for the design and control of highly agile aerial platforms.

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arXiv2026

Global Geometry of Orthogonal Foliations of Signed-Quadratic Systems

This work formalizes the differential topology of redundancy resolution for systems governed by signed-quadratic actuation maps. By analyzing the minimally redundant case, the global topology of the continuous fiber bundle defining the nonlinear actuation null-space is established. The distribution orthogonal to these fibers is proven to be globally integrable and governed by an exact logarithmic potential field. This field foliates the actuator space, inducing a structural stratification of all orthants into transverse layers whose combinatorial sizes follow a strictly binomial progression. Within these layers, adjacent orthants are continuously connected via lower-dimensional strata termed reciprocal hinges, while the layers themselves are separated by boundary hyperplanes, or portals, that act as global sections of the fibers. This partition formally distinguishes extremal and transitional layers, which exhibit fundamentally distinct fiber topologies and foliation properties. Exploiting this geometric framework, we prove that the orthogonal manifolds within the extremal orthants form a global diffeomorphism to the entire unbounded task space. This establishes the theoretical existence of globally smooth right-inverses that permanently confine the system to a single orthant, guaranteeing the absolute avoidance of kinematic singularities. While motivated by the physical actuation maps of multirotor and marine vehicles, the results provide a strictly foundational topological classification of signed-quadratic surjective systems.

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arXiv2026

The Geometry of Coordinated Trajectories for Non-stop Flying Carriers Holding a Cable-Suspended Load

This work considers the problem of using multiple aerial carriers to hold a cable-suspended load while remaining in periodic motion at all times. Using a novel differential geometric perspective, it is shown that the problem may be recast as that of finding an immersion of the unit circle into the smooth manifold of admissible configurations. Additionally, this manifold is shown to be path connected under a mild assumption on the attachment points of the carriers to the load. Based on these ideas, a family of simple linear solutions to the original problems is presented that overcomes the constraints of alternative solutions previously proposed in the literature. Simulation results demonstrate the flexibility of the theory in identifying suitable solutions.

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arXiv2026

Autonomous Aerial Non-Destructive Testing: Ultrasound Inspection with a Commercial Quadrotor in an Unstructured Environment

This work presents an integrated control and software architecture that enables arguably the first fully autonomous, contact-based non-destructive testing (NDT) using a commercial multirotor originally restricted to remotely-piloted operations. To allow autonomous operation with an off-the-shelf platform, we developed a real-time framework that interfaces directly with its onboard sensor suite. The architecture features a multi-rate control scheme: low-level control is executed at 200 Hz, force estimation at 100 Hz, while an admittance filter and trajectory planner operate at 50 Hz, ultimately supplying acceleration and yaw rate commands to the internal flight controller. We validate the system through physical experiments on a Flyability Elios 3 quadrotor equipped with an ultrasound payload. Relying exclusively on onboard sensing, the vehicle successfully performs autonomous NDT measurements within an unstructured, industrial-like environment. This work demonstrates the viability of retrofitting off-the-shelf platforms for autonomous physical interaction, paving the way for safe, contact-based inspection of hazardous and confined infrastructure.

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arXiv2026

Switching Among Feedback-Linearizing Output Sets (Melds): Dwell-Time and Compatibility Guarantees

We study switching among multiple square selections of output functions (melds) drawn from a deck of candidate outputs for nonlinear systems that are static feedback linearizable via outputs. Fixing an operating point, each meld induces a distinct feedback-linearizing coordinate chart defined on a common neighborhood. Switching between melds therefore produces state-dependent coordinate mismatches that are not captured by classical switched-system analyses. We quantify this effect through Lipschitz bounds on the cross-chart maps over a compact safe set and introduce a reference-compatibility constant that measures mismatch among reference families across melds. We derive an explicit dwell-time condition depending on controller decay rates and the compatibility constant, that guarantees exponential decay of the active-output tracking errors between switches, seamless tracking of outputs shared by consecutive melds, and uniform boundedness of the state error within the safe set. A planar 3R manipulator illustrates the results.

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arXiv2026

Impact-Robust Posture Optimization for Aerial Manipulation

We present a novel method for optimizing the posture of kinematically redundant torque-controlled robots to improve robustness during impacts. A rigid impact model is used as the basis for a configuration-dependent metric that quantifies the variation between pre- and post-impact velocities. By finding configurations (postures) that minimize the aforementioned metric, spikes in the robot's state and input commands can be significantly reduced during impacts, improving safety and robustness. The problem of identifying impact-robust postures is posed as a min-max optimization of the aforementioned metric. To overcome the real-time intractability of the problem, we reformulate it as a gradient-based motion task that iteratively guides the robot towards configurations that minimize the proposed metric. This task is embedded within a task-space inverse dynamics (TSID) whole-body controller, enabling seamless integration with other control objectives. The method is applied to a kinematically redundant aerial manipulator performing repeated point contact tasks. We test our method inside a realistic physics simulator and compare it with the nominal TSID. Our method leads to a reduction (up to 51% w.r.t. standard TSID) of post-impact spikes in the robot's configuration and successfully avoids actuator saturation. Moreover, we demonstrate the importance of kinematic redundancy for impact robustness using additional numerical simulations on a quadruped and a humanoid robot, resulting in up to 45% reduction of post-impact spikes in the robot's state w.r.t. nominal TSID.

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arXiv2026

Stability Analysis of Geometric Control for a Canonical Class of Underactuated Aerial Vehicles with Spurious Forces

Standard geometric control relies on force-moment decoupling, an assumption that breaks down in many aerial platforms due to spurious forces naturally induced by control moments. While strategies for such coupled systems have been validated experimentally, a rigorous theoretical certification of their stability is currently missing. This work fills this gap by providing the first formal stability analysis for a generic class of floating rigid bodies subject to spurious forces. We introduce a canonical model and construct a Lyapunov-based proof establishing local exponential stability of the hovering equilibrium. Crucially, the analysis explicitly addresses the structural challenges - specifically the induced non-minimum-phase behavior - that prevent the application of standard cascade arguments.

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arXiv2026

Nonlinear Predictive Control of the Continuum and Hybrid Dynamics of a Suspended Deformable Cable for Aerial Pick and Place

This paper presents a framework for aerial manipulation of an extensible cable that combines a high-fidelity model based on partial differential equations (PDEs) with a reduced-order representation suitable for real-time control. The PDEs are discretised using a finite-difference method, and proper orthogonal decomposition is employed to extract a reduced-order model (ROM) that retains the dominant deformation modes while significantly reducing computational complexity. Based on this ROM, a nonlinear model predictive control scheme is formulated, capable of stabilizing cable oscillations and handling hybrid transitions such as payload attachment and detachment. Simulation results confirm the stability, efficiency, and robustness of the ROM, as well as the effectiveness of the controller in regulating cable dynamics under a range of operating conditions. Additional simulations illustrate the application of the ROM for trajectory planning in constrained environments, demonstrating the versatility of the proposed approach. Overall, the framework enables real-time, dynamics-aware control of unmanned aerial vehicles (UAVs) carrying suspended flexible cables.

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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.

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arXiv2025

Synchronous Observer Design for Landmark-Inertial SLAM with Almost-Global Convergence

Landmark Inertial Simultaneous Localisation and Mapping (LI-SLAM) is the problem of estimating the locations of landmarks in the environment and the robot's pose relative to those landmarks using landmark position measurements and measurements from Inertial Measurement Unit (IMU). This paper proposes a nonlinear observer for LI-SLAM posed in continuous time and analyses the observer in a base space that encodes all the observable states of LI-SLAM. The local exponential stability and almost-global asymptotic stability of the error dynamics in base space is established in the proof section and validated using simulations.

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