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In this work, we present a model-based optimal boundary control design for an aerial robotic system composed of a quadrotor carrying a flexible cable. The whole system is modeled by partial differential equations (PDEs) combined with boundary conditions described by ordinary differential equations (ODEs). The proper orthogonal decomposition (POD) method is adopted to project the original infinite-dimensional system on a subspace spanned by orthogonal basis functions. Based on the reduced order model, nonlinear model predictive control (NMPC) is implemented online to realize shape trajectory tracking of the flexible cable in an optimal predictive fashion. The proposed reduced modeling and optimal control paradigms are numerically verified against an accurate high-dimensional FDM-based model in different scenarios and the controller's superior performance is shown compared to an optimally tuned PID controller.

In this letter, we address the problem of re-targeting a commercial under-actuated robotic system to a higher dimensional output task. Commercial platforms are equipped with an on-board low-level internal controller that provides the user some virtual references inputs and cannot be replaced. Such controller may control in practice only a subset of the total degrees-of-freedom of the system. Our primary objective is to augment these systems by introducing supplementary inputs, attaining increased output capability. Integrating such additional inputs into the control framework introduces a layer of complexity, raising questions about the compatibility and cohesiveness of the overall system. We derive necessary and sufficient conditions under which it is possible to extend the controlled outputs by adding extra inputs when one is forced to keep the internal controller unmodified. We underscore the efficacy and universality of our proposed methodology through the presentation of two relevant examples.

This work answers positively the question whether non-stop flights are possible for maintaining constant the pose of cable-suspended objects. Such a counterintuitive answer paves the way for a paradigm shift where energetically efficient fixed-wing flying carriers can replace the inefficient multirotor carriers that have been used so far in precise cooperative cable-suspended aerial manipulation. First, we show that one or two flying carriers alone cannot perform non-stop flights while maintaining a constant pose of the suspended object. Instead, we prove that three flying carriers can achieve this task provided that the orientation of the load at the equilibrium is such that the components of the cable forces that balance the external force (typically gravity) do not belong to the plane of the cable anchoring points on the load. Numerical tests are presented in support of the analytical results.

Large-scale infrastructures are prone to deterioration due to age, environmental influences, and heavy usage. Ensuring their safety through regular inspections and maintenance is crucial to prevent incidents that can significantly affect public safety and the environment. This is especially pertinent in the context of electrical power networks, which, while essential for energy provision, can also be sources of forest fires. Intelligent drones have the potential to revolutionize inspection and maintenance, eliminating the risks for human operators, increasing productivity, reducing inspection time, and improving data collection quality. However, most of the current methods and technologies in aerial robotics have been trialed primarily in indoor testbeds or outdoor settings under strictly controlled conditions, always within the line of sight of human operators. Additionally, these methods and technologies have typically been evaluated in isolation, lacking comprehensive integration. This paper introduces the first autonomous system that combines various innovative aerial robots. This system is designed for extended-range inspections beyond the visual line of sight, features aerial manipulators for maintenance tasks, and includes support mechanisms for human operators working at elevated heights. The paper further discusses the successful validation of this system on numerous electrical power lines, with aerial robots executing flights over 10 kilometers away from their ground control stations.

This paper proposes a method for designing human-robot collaboration tasks and generating corresponding trajectories. The method uses high-level specifications, expressed as a Signal Temporal Logic (STL) formula, to automatically synthesize task assignments and trajectories. To illustrate the approach, we focus on a specific task: a multi-rotor aerial vehicle performing object handovers in a power line setting. The motion planner considers limitations, such as payload capacity and recharging constraints, while ensuring that the trajectories are feasible. Additionally, the method enables users to specify robot behaviors that take into account human comfort (e.g., ergonomics, preferences) while using high-level goals and constraints. The approach is validated through numerical analyzes in MATLAB and realistic Gazebo simulations using a mock-up scenario., Comment: 8 pages, 7 figures, accepted for presentation to the 2023 International Conference on Unmanned Aircraft Systems (ICUAS) at Lazarski University, Warsaw, Poland

This paper presents a method for designing energy-aware collaboration tasks between humans and robots, and generating corresponding trajectories to carry out those tasks. The method involves using high-level specifications expressed as Signal Temporal Logic (STL) specifications to automatically synthesize task assignments and trajectories. The focus is on a specific task where a Multi-Rotor Aerial Vehicle (MRAV) performs object handovers in a power line setting. The motion planner takes into account constraints such as payload capacity and refilling, while ensuring that the generated trajectories are feasible. The approach also allows users to specify robot behaviors that prioritize human comfort, including ergonomics and user preferences. The method is validated through numerical analyses in MATLAB and realistic Gazebo simulations in a mock-up scenario., Comment: 2 pages, 2 figures, Accepted for presentation to the "Energy Efficient Aerial Robotic Systems" Workshop at ICRA'23, ExCeL, London, UK

This paper introduces for the first time the design, modelling, and control of a novel morphing multi-rotor Unmanned Aerial Vehicle (UAV) that we call the OmniMorph. The morphing ability allows the selection of the configuration that optimizes energy consumption while ensuring the needed maneuverability for the required task. The most energy-efficient uni-directional thrust (UDT) configuration can be used, e.g., during standard point-to-point displacements. Fully-actuated (FA) and omnidirectional (OD) configurations can be instead used for full pose tracking, such as, e.g., constant attitude horizontal motions and full rotations on the spot, and for full wrench 6D interaction control and 6D disturbance rejection. Morphing is obtained using a single servomotor, allowing possible minimization of weight, costs, and maintenance complexity. The actuation properties are studied, and an optimal controller that compromises between performance and control effort is proposed and validated in realistic simulations. Preliminary tests on the prototype are presented to assess the propellers' mutual aerodynamic interference., Comment: This version of the article has been accepted for publication, after peer review. But is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record of this article is published in Journal of Intelligent & Robotic Systems and is available online at https://doi.org/10.1007/s10846-024-02054-x

This paper proposes a Nonlinear Model-Predictive Control (NMPC) method capable of finding and converging to energy-efficient regular oscillations, which require no control action to be sustained. The approach builds up on the recently developed Eigenmanifold theory, which defines the sets of line-shaped oscillations of a robot as an invariant two-dimensional submanifold of its state space. By defining the control problem as a nonlinear program (NLP), the controller is able to deal with constraints in the state and control variables and be energy-efficient not only in its final trajectory but also during the convergence phase. An initial implementation of this approach is proposed, analyzed, and tested in simulation.

This work studies how parametric uncertainties affect the cooperative manipulation of a cable-suspended beam-shaped load by means of two aerial robots not explicitly communicating with each other. In particular, the work sheds light on the impact of the uncertain knowledge of the model parameters available to an established communication-less force-based controller. First, we find the closed-loop equilibrium configurations in the presence of the aforementioned uncertainties, and then we study their stability. Hence, we show the fundamental role played in the robustness of the load attitude control by the internal force induced in the manipulated object by non-vertical cables. Furthermore, we formally study the sensitivity of the attitude error to such parametric variations, and we provide a method to act on the load position error in the presence of the uncertainties. Eventually, we validate the results through an extensive set of numerical tests in a realistic simulation environment including underactuated aerial vehicles and sagging-prone cables, and through hardware experiments.

In this work, we propose a centralized control method based on nonlinear model predictive control to let multiple UAVs manipulate the full pose of an object via cables. At the best of the authors knowledge this is the first method that takes into account the full nonlinear model of the load-UAV system, and ensures all the feasibility constraints concerning the UAV maximumum and minimum thrusts, the collision avoidance between the UAVs, cables and load, and the tautness and maximum tension of the cables. By taking into account the above factors, the proposed control algorithm can fully exploit the performance of UAVs and facilitate the speed of operation. Simulations are conducted to validate the algorithm to achieve fast and safe manipulation of the pose of a rigid-body payload using multiple UAVs. We demonstrate that the computational time of the proposed method is sufficiently small (<100 ms) for UAV teams composed by up to 10 units, which makes it suitable for a huge variety of future industrial applications, such as autonomous building construction and heavy-load transportation., Comment: 7 pages, 10 figures

Offline optimal planning of trajectories for redundant robots along prescribed task space paths is usually broken down into two consecutive processes: first, the task space path is inverted to obtain a joint space path, then, the latter is parametrized with a time law. If the two processes are separated, they cannot optimize the same objective function, ultimately providing sub-optimal results. In this paper, a unified approach is presented where dynamic programming is the underlying optimization technique. Its flexibility allows accommodating arbitrary constraints and objective functions, thus providing a generic framework for optimal planning of real systems. To demonstrate its applicability to a real world scenario, the framework is instantiated for time-optimality on Franka Emika's Panda robot. The well-known issues associated with the execution of non-smooth trajectories on a real controller are partially addressed at planning level, through the enforcement of constraints, and partially through post-processing of the optimal solution. The experiments show that the proposed framework is able to effectively exploit kinematic redundancy to optimize the performance index defined at planning level and generate feasible trajectories that can be executed on real hardware with satisfactory results.

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., Comment: 8 pages, 6 figures

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., Comment: 23 pages (main article: 14 pages; appendix: 9 pages), 18 figures; accepted for publication on Automatica; final accepted version

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.

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..., Comment: cs.RO cs.SY math.OC math.DS

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., Comment: Accepted to International Conference on Robotics and Automation (ICRA) 2019, IEEE copyright, 7 pages, 14 figures

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.

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.

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.

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.

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.

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., Comment: Accepted for publication to the IEEE Transactions on Control of Network Systems

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.

This work considers the problem of estimating the unscaled relative positions of a multi-robot team in a common reference frame from bearing-only measurements. Each robot has access to a relative bearing measurement taken from the local body frame of the robot, and the robots have no knowledge of a common or inertial reference frame. A corresponding extension of rigidity theory is made for frameworks embedded in the \emph{special Euclidean group} $SE(2) = \mathbb{R}^2 \times \mathcal{S}^1$. We introduce definitions describing rigidity for $SE(2)$ frameworks and provide necessary and sufficient conditions for when such a framework is \emph{infinitesimally rigid} in $SE(2)$. Analogous to the rigidity matrix for point formations, we introduce the \emph{directed bearing rigidity matrix} and show that an $SE(2)$ framework is infinitesimally rigid if and only if the rank of this matrix is equal to $2|\mathcal{V}|-4$, where $|\mathcal{V}|$ is the number of agents in the ensemble. The directed bearing rigidity matrix and its properties are then used in the implementation and convergence proof of a distributed estimator to determine the {unscaled}{} relative positions in a common frame. Some simulation results are also given to support the analysis., Comment: submitted to 2014 European Control Conference

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., Comment: Preprint submitted to The International Journal of Robotics Research

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., Comment: Accepted for Autonomous Robots - Springer

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.

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., Comment: Preprint submitted to IEEE Transaction on Robotics