Antonio Franchi

Fabio Pasqualetti, Antonio Franchi, Francesco Bullo

The subject of this work is the patrolling of an environment with the aid of a team of autonomous agents. We consider both the design of open-loop trajectories with optimal properties, and of distributed control laws converging to optimal trajectories. As performance criteria, the refresh time and the latency are considered, i.e., respectively, time gap between any two visits of the same region, and the time necessary to inform every agent about an event occurred in the environment. We associate a graph with the environment, and we study separately the case of a chain, tree, and cyclic graph. For the case of chain graph, we first describe a minimum refresh time and latency team trajectory, and we propose a polynomial time algorithm for its computation. Then, we describe a distributed procedure that steers the robots toward an optimal trajectory. For the case of tree graph, a polynomial time algorithm is developed for the minimum refresh time problem, under the technical assumption of a constant number of robots involved in the patrolling task. Finally, we show that the design of a minimum refresh time trajectory for a cyclic graph is NP-hard, and we develop a constant factor approximation algorithm.

Antonio Franchi, Paolo Robuffo Giordano

The goal of this work is to propose an extension of the popular leader-follower framework for multi-agent collective tracking and formation maintenance in presence of a time- varying leader. In particular, the leader is persistently selected online so as to optimize the tracking performance of an exogenous collective velocity command while also maintaining a desired formation via a (possibly time-varying) communication-graph topology. The effects of a change in the leader identity are theoretically analyzed and exploited for defining a suitable error metric able to capture the tracking performance of the multi- agent group. Both the group performance and the metric design are found to depend upon the spectral properties of a special directed graph induced by the identity of the chosen leader. By exploiting these results, as well as distributed estimation techniques, we are then able to detail a fully-decentralized adaptive strategy able to periodically select online the best leader among the neighbors of the current leader. Numerical simulations show that the application of the proposed technique results in an improvement of the overall performance of the group behavior w.r.t. other possible strategies.

Giulia Michieletto, Angelo Cenedese, Luca Zaccarian et al.

We consider the hovering control problem for a class of multi-rotor aerial platforms with generically oriented propellers. Given the intrinsically coupled translational and rotational dynamics of such vehicles, we first discuss some assumptions for the considered systems to reject torque disturbances and to balance the gravity force, which are translated into a geometric characterization of the platforms that is usually fulfilled by both standard models and more general configurations. Hence, we propose a control strategy based on the identification of a zero-moment direction for the applied force and the dynamic state feedback linearization around this preferential direction, which allows to asymptotically stabilize the platform to a static hovering condition. Stability and convergence properties of the control law are rigorously proved through Lyapunov-based methods and reduction theorems for the stability of nested sets. Asymptotic zeroing of the error dynamics and convergence to the static hovering condition are then confirmed by simulation results on a star-shaped hexarotor model with tilted propellers.

Chiara Gabellieri, Yaolei Shen, Martina Paolucci et al.

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.

Giuseppe Silano, Amr Afifi, Martin Saska et al.

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.

Giuseppe Silano, Daniel Bonilla Licea, Davide Liuzza et al.

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.

Sofia Girardello, Giulia Michieletto, Angelo Cenedese et al.

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.

Benedetta Rota, Mirko Mizzoni, Amr Afifi et al.

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.

Antonio Franchi, Chiara Gabellieri

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.

Pieter van Goor, Chiara Gabellieri, Antonio Franchi

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.

Antonio Franchi

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.

Antonio Franchi

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.

Antonio Franchi

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.

Antonio Franchi

We prove that aerodynamic co-contraction in a redundant dual-rotor actuator can tune a passive, trim-defined aero-mechanical damping while keeping the commanded net force constant. In particular, we define an incremental damping coefficient as the local sensitivity of net thrust to air-relative velocity at a trim and prove that it increases monotonically along constant-force fibers under a mild aerodynamic hardening condition. We then validate the required damping and hardening properties from a first-principles Blade Element Theory derivation, which yields a minimal thrust model affine in inflow and explicitly reveals the speed--inflow coupling driving the effect. The resulting mechanism is formalized as a Variable Aerodynamic Damping Actuator (VADA) and shown to be dynamically isomorphic to stiffness modulation in antagonistic variable-stiffness actuation (VSA), similar to the co-contraction of tendons by muscle co-activation. The same fiber-density principle also enhances the active aerodynamic promptness measure of redundant multirotors. Finally, an impedance-form representation clarifies the roles of common-mode and differential-mode actuation in the control of passive impedance and the equilibrium velocity of the VADA system.

Ahmed Ali, Chiara Gabellieri, Antonio Franchi

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.

Giuseppe Silano, Quentin Sablé, Marco Tognon et al.

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.

Antonio Franchi

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.

Enrica Rossi, Marco Tognon, Ruggero Carli et al.

In this work we consider the problem of mobile robots that need to manipulate/transport an object via cables or robotic arms. We consider the scenario where the number of manipulating robots is redundant, i.e. a desired object configuration can be obtained by different configurations of the robots. The objective of this work is to show that communication can be used to implement cooperative local feedback controllers in the robots to improve disturbance rejection and reduce structural stress in the object. In particular we consider the realistic scenario where measurements are sampled and transmitted over wireless, and the sampling period is comparable with the system dynamics time constants. We first propose a kinematic model which is consistent with the overall systems dynamics under high-gain control and then we provide sufficient conditions for the exponential stability and monotonic decrease of the configuration error under different norms. Finally, we test the proposed controllers on the full dynamical systems showing the benefit of local communication.

Enrica Rossi, Marco Tognon, Luca Ballotta et al.

In this paper, we propose an inverse-kinematics controller for a class of multi-robot systems in the scenario of sampled communication. The goal is to make a group of robots perform trajectory tracking in a coordinated way when the sampling time of communications is much larger than the sampling time of low-level controllers, disrupting theoretical convergence guarantees of standard control design in continuous time. Given a desired trajectory in configuration space which is precomputed offline, the proposed controller receives configuration measurements, possibly via wireless, to re-compute velocity references for the robots, which are tracked by a low-level controller. We propose joint design of a sampled proportional feedback plus a novel continuous-time feedforward that linearizes the dynamics around the reference trajectory: this method is amenable to distributed communication implementation where only one broadcast transmission is needed per sample. Also, we provide closed-form expressions for instability and stability regions and convergence rate in terms of proportional gain $k$ and sampling period $T$. We test the proposed control strategy via numerical simulations in the scenario of cooperative aerial manipulation of a cable-suspended load using a realistic simulator (Fly-Crane). Finally, we compare our proposed controller with centralized approaches that adapt the feedback gain online through smart heuristics, and show that it achieves comparable performance.

Markus Ryll, Davide Bicego, Mattia Giurato et al.

We present FAST-Hex, a micro aerial hexarotor platform that allows to seamlessly transit from an under-actuated to a fully-actuated configuration with only one additional control input, a motor that synchronously tilts all propellers. The FAST-Hex adapts its configuration between the more efficient but under-actuated, collinear multi-rotors and the less efficient, but full-pose-tracking, which is attained by non-collinear multi-rotors. On the basis of prior work on minimal input configurable micro aerial vehicle we mainly stress three aspects: mechanical design, motion control and experimental validation. Specifically, we present the lightweight mechanical structure of the FAST-Hex that allows it to only use one additional input to achieve configurability and full actuation in a vast state space. The motion controller receives as input any reference pose in $\mathbb{R}^3\times \mathrm{SO}(3)$ (3D position + 3D orientation). Full pose tracking is achieved if the reference pose is feasible with respect to actuator constraints. In case of unfeasibility a new feasible desired trajectory is generated online giving priority to the position tracking over the orientation tracking. Finally we present a large set of experimental results shading light on all aspects of the control and pose tracking of FAST-Hex.

Davide Bicego, Jacopo Mazzetto, Ruggero Carli et al.

In this paper, we propose, discuss, and validate an online Nonlinear Model Predictive Control (NMPC) method for multi-rotor aerial systems with arbitrarily positioned and oriented rotors which simultaneously addresses the local reference trajectory planning and tracking problems. This work brings into question some common modeling and control design choices that are typically adopted to guarantee robustness and reliability but which may severely limit the attainable performance. Unlike most of state of the art works, the proposed method takes advantages of a unified nonlinear model which aims to describe the whole robot dynamics by explicitly including a realistic physical description of the actuator dynamics and limitations. As a matter of fact, our solution does not resort to common simplifications such as: 1) linear model approximation, 2) cascaded control paradigm used to decouple the translational and the rotational dynamics of the rigid body, 3) use of low-level reactive trackers for the stabilization of the internal loop, and 4) unconstrained optimization resolution or use of fictitious constraints. More in detail, we consider as control inputs the derivatives of the propeller forces and propose a novel method to suitably identify the actuator limitations by leveraging experimental data. Differently from previous approaches, the constraints of the optimization problem are defined only by the real physics of the actuators, avoiding conservative -- and often not physical -- input/state saturations which are present, e.g., in cascaded approaches. The control algorithm is implemented using a state-of-the-art Real Time Iteration (RTI) scheme with partial sensitivity update method. CONTINUES...

Yuri S. Sarkisov, Min Jun Kim, Davide Bicego et al.

High risk of a collision between rotor blades and the obstacles in a complex environment imposes restrictions on the aerial manipulators. To solve this issue, a novel system cable-Suspended Aerial Manipulator (SAM) is presented in this paper. Instead of attaching a robotic manipulator directly to an aerial carrier, it is mounted on an active platform which is suspended on the carrier by means of a cable. As a result, higher safety can be achieved because the aerial carrier can keep a distance from the obstacles. For self-stabilization, the SAM is equipped with two actuation systems: winches and propulsion units. This paper presents an overview of the SAM including the concept behind, hardware realization, control strategy, and the first experimental results.

Matthias Faessler, Antonio Franchi, Davide Scaramuzza

In this paper, we prove that the dynamical model of a quadrotor subject to linear rotor drag effects is differentially flat in its position and heading. We use this property to compute feed-forward control terms directly from a reference trajectory to be tracked. The obtained feed-forward terms are then used in a cascaded, nonlinear feedback control law that enables accurate agile flight with quadrotors. Compared to state-of-the-art control methods, which treat the rotor drag as an unknown disturbance, our method reduces the trajectory tracking error significantly. Finally, we present a method based on a gradient-free optimization to identify the rotor drag coefficients, which are required to compute the feed-forward control terms. The new theoretical results are thoroughly validated trough extensive comparative experiments.

Sara Spedicato, Antonio Franchi, Giuseppe Notarstefano

In this paper we present a maneuver regulation scheme for Vertical Take-Off and Landing (VTOL) micro aerial vehicles (MAV). Differently from standard trajectory tracking, maneuver regulation has an intrinsic robustness due to the fact that the vehicle is not required to chase a virtual target, but just to stay on a (properly designed) desired path with a given velocity profile. In this paper we show how a robust maneuver regulation controller can be easily designed by converting an existing tracking scheme. The resulting maneuvering controller has three main appealing features, namely it: (i) inherits the robustness properties of the tracking controller, (ii) gains the appealing features of maneuver regulation, and (iii) does not need any additional tuning with respect to the tracking controller. We prove the correctness of the proposed scheme and show its effectiveness in experiments on a nano-quadrotor. In particular, we show on a nontrivial maneuver how external disturbances acting on the quadrotor cause instabilities in the standard tracking, while marginally affect the maneuver regulation scheme.

Antonio Franchi, Ruggero Carli, Davide Bicego et al.

In this paper, we define a general class of abstract aerial robotic systems named Laterally Bounded Force (LBF) vehicles, in which most of the control authority is expressed along a principal thrust direction, while in the lateral directions a (smaller and possibly null) force may be exploited to achieve full-pose tracking. This class approximates well platforms endowed with non-coplanar/non-collinear rotors that can use the tilted propellers to slightly change the orientation of the total thrust w.r.t. the body frame. For this broad class of systems, we introduce a new geometric control strategy in SE(3) to achieve, whenever made possible by the force constraints, the independent tracking of position-plus-orientation trajectories. The exponential tracking of a feasible full-pose reference trajectory is proven using a Lyapunov technique in SE(3). The method can deal seamlessly with both under- and fully-actuated LBF platforms. The controller guarantees the tracking of at least the positional part in the case that an unfeasible full-pose reference trajectory is provided. The paper provides several experimental tests clearly showing the practicability of the approach and the sharp improvement with respect to state of-the-art approaches.

Marco Tognon, Antonio Franchi

We consider the problem of controlling an aerial robot connected to the ground by a passive cable or a passive rigid link. We provide a thorough characterization of this nonlinear dynamical robotic system in terms of fundamental properties such as differential flatness, controllability, and observability. We prove that the robotic system is differentially flat with respect to two output pairs: elevation of the link and attitude of the vehicle; elevation of the link and longitudinal link force (e.g., cable tension, or bar compression). We show the design of an almost globally convergent nonlinear observer of the full state that resorts only to an onboard accelerometer and a gyroscope. We also design two almost globally convergent nonlinear controllers to track any sufficiently smooth time-varying trajectory of the two output pairs. Finally we numerically test the robustness of the proposed method in several far-from-nominal conditions: nonlinear cross-coupling effects, parameter deviations, measurements noise and non ideal actuators.

Antonio Franchi, Antonio Petitti, Alessandro Rizzo

We present two distributed methods for the estimation of the kinematic parameters, the dynamic parameters, and the kinematic state of an unknown planar body manipulated by a decentralized multi-agent system. The proposed approaches rely on the rigid body kinematics and dynamics, on nonlinear observation theory, and on consensus algorithms. The only three requirements are that each agent can exert a 2D wrench on the load, it can measure the velocity of its contact point, and that the communication graph is connected. Both theoretical nonlinear observability analysis and convergence proofs are provided. The first method assumes constant parameters while the second one can deal with time-varying parameters and can be applied in parallel to any task-oriented control law. For the cases in which a control law is not provided, we propose a distributed and safe control strategy satisfying the observability condition. The effectiveness and robustness of the estimation strategy is showcased by means of realistic MonteCarlo simulations.

Thomas Nestmeyer, Paolo Robuffo Giordano, Heinrich H. Bülthoff et al.

This paper presents a novel decentralized control strategy for a multi-robot system that enables parallel multi-target exploration while ensuring a time-varying connected topology in cluttered 3D environments. Flexible continuous connectivity is guaranteed by building upon a recent connectivity maintenance method, in which limited range, line-of-sight visibility, and collision avoidance are taken into account at the same time. Completeness of the decentralized multi-target exploration algorithm is guaranteed by dynamically assigning the robots with different motion behaviors during the exploration task. One major group is subject to a suitable downscaling of the main traveling force based on the traveling efficiency of the current leader and the direction alignment between traveling and connectivity force. This supports the leader in always reaching its current target and, on a larger time horizon, that the whole team realizes the overall task in finite time. Extensive Monte~Carlo simulations with a group of several quadrotor UAVs show the scalability and effectiveness of the proposed method and experiments validate its practicability.

Daniel Zelazo, Antonio Franchi, Heinrich H. Bülthoff et al.

This work proposes a fully decentralized strategy for maintaining the formation rigidity of a multi-robot system using only range measurements, while still allowing the graph topology to change freely over time. In this direction, a first contribution of this work is an extension of rigidity theory to weighted frameworks and the rigidity eigenvalue, which when positive ensures the infinitesimal rigidity of the framework. We then propose a distributed algorithm for estimating a common relative position reference frame amongst a team of robots with only range measurements in addition to one agent endowed with the capability of measuring the bearing to two other agents. This first estimation step is embedded into a subsequent distributed algorithm for estimating the rigidity eigenvalue associated with the weighted framework. The estimate of the rigidity eigenvalue is finally used to generate a local control action for each agent that both maintains the rigidity property and enforces additional con- straints such as collision avoidance and sensing/communication range limits and occlusions. As an additional feature of our approach, the communication and sensing links among the robots are also left free to change over time while preserving rigidity of the whole framework. The proposed scheme is then experimentally validated with a robotic testbed consisting of 6 quadrotor UAVs operating in a cluttered environment.

Antonio Franchi, Paolo Stegagno, Giuseppe Oriolo

We present a control framework for achieving encirclement of a target moving in 3D using a multi-robot system. Three variations of a basic control strategy are proposed for different versions of the encirclement problem, and their effectiveness is formally established. An extension ensuring maintenance of a safe inter-robot distance is also discussed. The proposed framework is fully decentralized and only requires local communication among robots; in particular, each robot locally estimates all the relevant global quantities. We validate the proposed strategy through simulations on kinematic point robots and quadrotor UAVs, as well as experiments on differential-drive wheeled mobile robots.