Aero-Promptness: Drag-Aware Aerodynamic Manipulability for Propeller-driven Vehicles

This work introduces the Drag-Aware Aerodynamic Manipulability (DAAM), a geometric framework for control allocation in redundant multirotors. By equipping the propeller spin-rate space with a Riemannian metric based on the remaining symmetric acceleration capacity of each motor, the formulation explicitly accounts for motor torque limits and aerodynamic drag. Mapping this metric through the nonlinear thrust law to the generalized force space yields a state-dependent manipulability volume. The log-determinant of this volume acts as a natural barrier function, strictly penalizing drag-induced saturation and low-spin thrust loss. Optimizing this volume along the allocation fibers provides a redundancy resolution strategy inherently invariant to arbitrary coordinate scaling in the generalized-force space. Analytically, we prove that the resulting optimal allocations locally form smooth embedded manifolds, and we geometrically characterize the global jump discontinuities that inevitably arise from physical actuator limits and spin-rate sign transitions.

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.

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.

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.

Muscle Coactivation in the Sky: Geometry and Pareto Optimality of Energy vs. Promptness in Multirotors

In robotics and human biomechanics, the tension between energy economy and kinematic readiness is well recognized; this work brings that fundamental principle to aerial multirotors. We show that the limited torque of the motors and the nonlinear aerodynamic map from rotor speed to thrust naturally give rise to the novel concept of promptness-a metric akin to dynamic aerodynamic manipulability. By treating energy consumption as a competing objective and introducing a geometric fiber-bundle formulation, we turn redundancy resolution into a principled multi-objective program on affine fibers. The use of the diffeomorphic transformation linearizing the signed-quadratic propulsion model allows us to lay the foundations for a rigorous study of the interplay between these costs. Through an illustrative case study on 4-DoF allocation on the hexarotor, we reveal that this interplay is fiber-dependent and physically shaped by hardware inequalities. For unidirectional thrusters, the feasible fibers are compact, yielding interior allocations and a short Pareto arc, while torque demands break symmetry and separate the optima. Conversely, with reversible propellers, the null space enables antagonistic rotor co-contraction that drives promptness to hardware limits, making optimal endurance and agility fundamentally incompatible in those regimes. Ultimately, rather than relying on heuristic tuning or black box algorithms to empirically improve task execution, this framework provides a foundational understanding of why and how to achieve agility through geometry-aware control allocation, offering possible guidance for vehicle design, certification metrics, and threat-aware flight operation.

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.

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.

The N-5 Scaling Law: Topological Dimensionality Reduction in the Optimal Design of Fully-actuated Multirotors

The geometric design of fully-actuated and omnidirectional N-rotor aerial vehicles is conventionally formulated as a parametric optimization problem, seeking a single optimal set of N orientations within a fixed architectural family. This work departs from that paradigm to investigate the intrinsic topological structure of the optimization landscape itself. We formulate the design problem on the product manifold of Projective Lines \RP^2^N, fixing the rotor positions to the vertices of polyhedral chassis while varying their lines of action. By minimizing a coordinate-invariant Log-Volume isotropy metric, we reveal that the topology of the global optima is governed strictly by the symmetry of the chassis. For generic (irregular) vertex arrangements, the solutions appear as a discrete set of isolated points. However, as the chassis geometry approaches regularity, the solution space undergoes a critical phase transition, collapsing onto an N-dimensional Torus of the lines tangent at the vertexes to the circumscribing sphere of the chassis, and subsequently reducing to continuous 1-dimensional curves driven by Affine Phase Locking. We synthesize these observations into the N-5 Scaling Law: an empirical relationship holding for all examined regular planar polygons and Platonic solids (N <= 10), where the space of optimal configurations consists of K=N-5 disconnected 1D topological branches. We demonstrate that these locking patterns correspond to a sequence of admissible Star Polygons {N/q}, allowing for the exact prediction of optimal phases for arbitrary N. Crucially, this topology reveals a design redundancy that enables optimality-preserving morphing: the vehicle can continuously reconfigure along these branches while preserving optimal isotropic control authority.

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.

Manipulation of Elasto-Flexible Cables with Single or Multiple UAVs

This work considers a large class of systems composed of multiple quadrotors manipulating deformable and extensible cables. The cable is described via a discretized representation, which decomposes it into linear springs interconnected through lumped-mass passive spherical joints. Sets of flat outputs are found for the systems. Numerical simulations support the findings by showing cable manipulation relying on flatness-based trajectories. Eventually, we present an experimental validation of the effectiveness of the proposed discretized cable model for a two-robot example. Moreover, a closed-loop controller based on the identified model and using cable-output feedback is experimentally tested.