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.

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.

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.

Global Geometry of Orthogonal Foliations in the Control Allocation 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. Through this geometric framework, classical pseudo-linear static allocation strategies are shown to inevitably intersect singular boundary hyperplanes, triggering infinite-derivative kinetic singularities and fragmenting the task space into an exponential number of singularity-separated sectors. In contrast, allocators derived from the orthogonal manifolds yield continuously differentiable global sections with only a linear number of sectors for transversal layers, or can even form a single global diffeomorphism to the task space in the case of the two extremal layers, thus completely avoiding geometric rank-loss and boundary-crossing singularities. These theoretical results directly apply to the control allocation of propeller-driven architectures, including multirotor UAVs, marine, and underwater vehicles.

Communications-Aware NMPC for Multi-Rotor Aerial Relay Networks Under Jamming Interference

Multi-Rotor Aerial Vehicles (MRAVs) are increasingly used in communication-dependent missions where connectivity loss directly compromises task execution. Existing anti-jamming strategies often decouple motion from communication, overlooking that link quality depends on vehicle attitude and antenna orientation. In coplanar platforms, "tilt-to-translate" maneuvers can inadvertently align antenna nulls with communication partners, causing severe degradation under interference. This paper presents a modular communications-aware control framework that combines a high-level max-min trajectory generator with an actuator-level Nonlinear Model Predictive Controller (NMPC). The trajectory layer optimizes the weakest link under jamming, while the NMPC enforces vehicle dynamics, actuator limits, and antenna-alignment constraints. Antenna directionality is handled geometrically, avoiding explicit radiation-pattern parametrization. The method is evaluated in a relay scenario with an active jammer and compared across coplanar and tilted-propeller architectures. Results show a near two-order-of-magnitude increase in minimum end-to-end capacity, markedly reducing outage events, with moderate average-capacity gains. Tilted platforms preserve feasibility and link quality, whereas coplanar vehicles show recurrent degradation. These findings indicate that full actuation is a key enabler of reliable communications-aware operation under adversarial directional constraints.

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.

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.

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.

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.