Slung Load Research Articles

Nonlinear control of a planar vertical take‐off and landing with a slung load

AbstractThis paper presents the development of the dynamical model of a planar vertical take‐off and landing (PVTOL) carrying a suspended load. The complete model is obtained using the Euler–Lagrange approach. Furthermore, the synthesis of a nonlinear control is presented that stabilizes the vehicle to a desired position, and the load is stabilized as well. The stability is obtained using LaSalle invariance theorem. The performance of the obtained controller is shown in numerical simulations.

On Robust Stabilization of Motion of a Quadrotor with Slung Load

One of the important tasks that can be performed by quadrotors is the transportation of various payloads. If the load is suspended from the quadrotor and can move relative to the quadrotors body, this motion must be taken into account in the control system, in particular, in order to suppress and prevent unwanted oscillations of the load. In the present paper, a mechanical system is considered that consists of a quadrotor and a load suspended to it with a weightless rod. It is assumed that the cross-sectional area of the load is large enough so that the aerodynamic forces acting on it cannot be neglected. It is known that for a number of shapes of payload casing, this aerodynamic force is not reduced only to the drag force, but also contains a component orthogonal to the drag force, that is, the lift force. In order to these forces, the quasi-steady approach is used. At the same time, accurate information about the aerodynamic capabilities for each particular payload is, generally speaking, not available. However, it is known that the values of aerodynamic coefficients for a fairly wide class of body shapes are lie in a specific range. Here we discuss the problem of developing the quadrotor control that would ensure robust stabilization of the ascent and descent of the system in the conditions of incomplete information about the aerodynamic load. A method is proposed for constructing the quadrotor control for robust stabilization of uniform vertical ascent and descent of the system as a whole. It is shown that this control ensures stabilization of the target mode within a fairly wide range of system parameters. Restrictions on the target speed of quadrotor motion are determined, violation of which makes the robust stabilization impossible.

Handling Qualities Assessment and Discussion for Helicopter with Slung Load Systems Utilizing Various Sling Configurations

Sling configurations significantly influence the coupled dynamics of the helicopter with slung load system (HSLS), resulting in alterations to handling qualities (HQs) that remain inadequately understood. This study introduces a computer-oriented, generalized method for constructing the HSLS model with various sling configurations. To evaluate the HQs of 1-point, 2-point, and 4-point sling configurations, both the stability and response criteria outlined in ADS-33E and a newly proposed criterion for slung loads towards the updated ADS-33F were employed. Modal analysis was conducted to elucidate the coupled mechanisms of the HSLS under different sling configurations. The findings reveal that the dynamics of the main rotor can attenuate the lateral swing motions of the load in the 4-point sling configuration. While multiple-point sling configurations can enhance the helicopter’s bandwidth, they also amplify the magnitude notch in the helicopter’s response. Nevertheless, when a larger hook distance is employed, the notch frequency is sufficiently distant from the load swing bandwidth, leading to a reduced degradation in HQs. A 4-point configuration with lateral and longitudinal hook distances equal to twice the width and length of the slung load is recommended in practice to achieve sufficient swing stability and mitigate HQ degradation.

Adaptive Multi-Surface Sliding Mode Control with Radial Basis Function Neural Networks and Reinforcement Learning for Multirotor Slung Load Systems

While using multirotor UAVs for transport of suspended payloads, there is a need for stability along the desired path, in addition to avoidance of any excessive payload oscillations, and a good level of precision in maintaining the desired path of the vehicle. However, due to the nonlinear and underactuated nature of the system, in addition to the presence of mismatched uncertainties, the development of a control system for this application poses an interesting research problem. This paper proposes a control architecture for a multirotor slung load system by integrating a Multi-Surface Sliding Mode Control, aided by a Radial Basis Function Neural Network, with a Deep Q-Network Reinforcement Learning agent. The former will be used to ensure asymptotic tracking stability, while the latter will be used to suppress payload oscillations. First, we will present the dynamics of a multirotor slung load system, represented here as a quadrotor with a single pendulum load suspended from it. We will then propose a control method in which a multi-surface sliding mode controller, based on an adaptive RBF Neural Network for trajectory tracking of the quadrotor, works in tandem with a Deep Q-Network Reinforcement Learning agent whose reward function aims to suppress the oscillations of the single pendulum slung load. Simulation results demonstrate the effectiveness and potential of the proposed approach in achieving precise and reliable control of multirotor slung load systems.

Barrier Lyapunov function‐based nonlinear cooperative control approach for dual‐quadrotor slung load system

AbstractDue to the limited payload capacity of single‐quadrotor unmanned aerial vehicles (UAVs) in cargo transportation, there is a pressing need for the collaborative transportation of heavy goods using multiple quadrotor UAVs. In this context, the dual‐quadrotor aerial transportation system stands out for its heightened research significance, driven by its stringent requirements for controller swing reduction performance. In practical transportation scenarios, uncertainties such as disturbances and emergency avoidance constraints elevate the risk associated with excessive variations in the relative distances between quadrotor aircraft during collaborative transportation. Building upon the established nonlinear model by D'Alembert, this paper proposes a nonlinear coordinated control strategy based on the barrier Lyapunov function. The strategy employs an innovative energy storage approach, incorporating cooperative error constraints to effectively restrict relative errors between quadrotor aircraft, thereby mitigating the risk of collisions. Furthermore, this control strategy facilitates rapid convergence of the positions of quadrotor aircraft and the swing angles of suspended loads. Theoretical analyses, grounded in LaSalle's invariance theorem, provide evidence of the stability of the closed‐loop system. Finally, comparative assessments conducted using the Matlab/Simulink visualization platform validate the superior control performance of the designed controller in collaborative transportation scenarios.

Autonomous flight performance maximization for slung load carrying rotary wing mini unmanned aerial vehicle

PurposeThis research study aims to minimize autonomous flight cost and maximize autonomous flight performance of a slung load carrying rotary wing mini unmanned aerial vehicle (i.e. UAV) by stochastically optimizing autonomous flight control system (AFCS) parameters. For minimizing autonomous flight cost and maximizing autonomous flight performance, a stochastic design approach is benefitted over certain parameters (i.e. gains of longitudinal PID controller of a hierarchical autopilot system) meanwhile lower and upper constraints exist on these design parameters.Design/methodology/approachA rotary wing mini UAV is produced in drone Laboratory of Iskenderun Technical University. This rotary wing UAV has three blades main rotor, fuselage, landing gear and tail rotor. It is also able to carry slung loads. AFCS variables (i.e. gains of longitudinal PID controller of hierarchical autopilot system) are stochastically optimized to minimize autonomous flight cost capturing rise time, settling time and overshoot during longitudinal flight and to maximize autonomous flight performance. Found outcomes are applied during composing rotary wing mini UAV autonomous flight simulations.FindingsBy using stochastic optimization of AFCS for rotary wing mini UAVs carrying slung loads over previously mentioned gains longitudinal PID controller when there are lower and upper constraints on these variables, a high autonomous performance having rotary wing mini UAV is obtained.Research limitations/implicationsApproval of Directorate General of Civil Aviation in Republic of Türkiye is essential for real-time rotary wing mini UAV autonomous flights.Practical implicationsStochastic optimization of AFCS for rotary wing mini UAVs carrying slung loads is properly valuable for recovering autonomous flight performance cost of any rotary wing mini UAV.Originality/valueEstablishing a novel procedure for improving autonomous flight performance cost of a rotary wing mini UAV carrying slung loads and introducing a new process performing stochastic optimization of AFCS for rotary wing mini UAVs carrying slung loads meanwhile there exists upper and lower bounds on design variables.

Finite-Time Convergence Control for a Quadrotor Unmanned Aerial Vehicle With a Slung Load

This work investigates the control technique for a quadrotor unmanned aerial vehicle with a slung load. By taking the advantage of the cascade property, a new hierarchical control scheme is designed that divides the control problem into three parts. For the attitude motion control of the quadrotor, the non-singularity terminal sliding mode based control law is proposed. For the translation motion control of the quadrotor, the super-twisting based control law is designed. Additional, for the swing attenuation of the slung load, a nonlinear anti-swing control design is provided. A Lyapunov stability analysis is presented to show the stability of the closed loop system, together with the fast convergence of the quadrotor's translational and attitude tracking, and exponential convergence of the slung load's swing motion. The real time experiments verifies the well performance of the proposed controller.

Anti-Saturation Backstepping Control for Quadrotor Slung Load System with Fixed-Time Prescribed Performance

Anti-Saturation Backstepping Control for Quadrotor Slung Load System with Fixed-Time Prescribed Performance

Trajectory Tracking Control for Quadrotor Slung Load System With Unknown Load's Linear Velocity and Cable Length

This paper addresses the trajectory tracking control problem for a quadrotor suspended load system without load's linear velocity measurement and cable length information. Firstly, the cable length is estimated by designing an immersion and invariance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf{I\&amp;I}$</tex-math></inline-formula> )-based adaptive law. Secondly, a virtual thrust force vector is designed for the load position subsystem with the denoted auxiliary variables in the lack of load's linear velocity measurement. Then, through the cable direction subsystem and quadrotor attitude subsystem, the angular velocity input is presented to drive the real thrust input to virtual thrust input via the backstepping method. Thereafter, the uniformly boundedness of the whole closed-loop system is obtained by means of building suitable Lyapunov functions. Ultimately, numerical simulations attest to the performance of the proposed trajectory tracking control law.

Path-following control for an unmanned aerial vehicle slung load system

A multirotor unmanned aerial vehicle (UAV) slung load system (SLS) is a nonlinear dynamics with eight degrees of freedom and four inputs that can be used for load transportation. The suspended payload can be modelled as a two degree-of-freedom pendulum attached to the UAV. This paper presents a path-following control (PFC) for an SLS. The PFC renders motions along any smooth Jordan curve in R 3 for payload position controlled-invariant. This property has practical benefits over traditional time-based trajectory tracking. Furthermore, the PFC prescribes UAV yaw and a desired payload speed profiles along the path. The PFC adopts dynamic extension and input-output state feedback linearisation. The closed-loop has a 1-dimensional zero-dynamics which is shown to be bounded. Hence, the PFC error dynamics is exponentially stable. Simulations are provided to validate the design.

An Improved Method for Swing State Estimation in Multirotor Slung Load Applications

A method is proposed to estimate the swing state of a suspended payload in multirotor drone delivery scenarios. Starting from the equations of motion of the coupled slung load system, defined by two point masses interconnected by a rigid link, a recursive algorithm is developed to estimate cable swing angle and rate from acceleration measurements available from an onboard Inertial Measurement Unit, without the need for extra sensors. The estimation problem is addressed according to the Extended Kalman Filter structure. With respect to the classical linear formulation, the proposed approach allows for improved estimation accuracy in both stationary and maneuvering flight. As an additional contribution, filter performance is enhanced by accounting for aerodynamic disturbance force, which largely affects the estimation accuracy in windy flight conditions. The validity of the proposed methodology is demonstrated as follows. First, it is applied to an octarotor platform where propellers are modeled according to blade element theory and the load is suspended by an elastic cable. Numerical simulations show that estimated swing angle and rate represent suitable feedback variables for payload stabilization, with benefits on flying qualities and energy demand. The algorithm is finally implemented on a small-scale quadrotor and is investigated through an outdoor experimental campaign, thus proving the effectiveness of the approach in a real application scenario.

Nonlinear Rigid-Elastic Coupled Modeling and Oscillation Mechanism Analysis of Rotor-Body-Slung-Load System

In order to reveal the mechanism of Category II rotor-body-slung-load coupled oscillation (RBSLCO) with the frequency range of 2.5~8 Hz, a novel nonlinear rigid-elastic coupled model is presented for the helicopter and slung load system (HSLS) with explicit formulation. The slung load system model is coupled with the current rigid-elastic coupled helicopter model, considering fuselage hook point rigid-elastic coupled movements, cable stretching, and hook point force from the slung load system. The results show that carrying the heaviest load is the vital state for Category II RBSLCO. As slung load mass ratio increases, rotor-fuselage coupling becomes stronger and the oscillation frequency shifts slightly, causing a maximum of 15% reduction in stability margin. In addition, even when the load is lightweight, another form of Category II RBSLCO may appear involving fuselage bending and cable stretching. This Category II RBSLCO behaves like the vertical bouncing but is divided into a high-frequency anti-phase oscillation and a relatively low-frequency in-phase oscillation.

Control structure design with constraints for a slung load quadrotor system

We propose a control structure for a quadrotor carrying a slung load with swing-angle constraints. This quadrotor is supposed to pass through the waypoints at specified speeds. First, a cascaded PID autopilot is designed, which adaptively gives attention to position and speed requirements as a function of their errors. Its parameters are found from an optimization problem solved using the PSO algorithm. Second, this controller’s performance is improved by adding the Complementary Controller employing an ANN. 5. Training data for the ANN is created by solving optimal control problems. The ANN is activated when the swing angle constraint is about to be violated. It is trained using optimal control values corresponding to the cases where the swing angle falls in a particular band about the upper swing angle constraint. Simulations are performed in a MATLAB environment. Finally, some of the simulation results are validated on a physical system.

Quadrotor Robust Fractional-Order Sliding Mode Control in Unmanned Aerial Vehicles for Eliminating External Disturbances

Quadrotors, commonly known as drones or unmanned aerial vehicles (UAVs), play an important role in load transportation. The complex vehicles used for transporting loads and surveillance purposes can be replaced through the ease of use and mechanical simplicity of the quadrotors. This study aims to introduce a new way of controlling the slung load system of the quadrotor after applying the fractional-order sliding mode control (FOSMC) method for performance enhancement. This method in the presence of external disturbances is likely to help stabilize and track the quadrotor with minimized swinging of the attached load. The results of this study prove the robustness of FOSMC through analysis, outcomes, and graphical representations that show the effect with various angles for a clear and conceptual understanding. The present study contributes to the literature by designing a robust FOSMC for a quadrotor with the help of external disturbances. The results of this study could be applied to the development of the design of upcoming drones which can increase the efficiency as well as the accuracy of load transportation. Further applications in the fields of rescue, agriculture, construction, research, and advancement of the fraction calculus-based control method are recommended using the FOSMC method.

Unified Motion Control for Multilift Unmanned Rotorcraft Systems in Forward Flight

Interest in multilift rotorcraft systems has reemerged in recent years to overcome some of the problems in single unmanned aerial vehicle handling and delivery systems. Using multiple unmanned rotorcrafts (URs), the load weight can be evenly distributed among the vehicles, extending the flight time and therefore increasing the working distance of such systems. Moreover, with a slung-load configuration, bigger size packages with complex shape and equipment that may interfere with the onboard electronics can be carried. In this context, this article presents a payload-based unified motion control that allows any number of URs to cooperatively transport a slung load in forward flight. The motion control comprises path-following and trajectory-tracking algorithms, considers obstacle avoidance, implements a specific strategy for load weight distribution (load equalization) by regulating the relative altitude of each UR, and is robust to disturbances such as wind. In addition, this work shows that load equalization is essential for slung-load cooperative transport, especially in forward flight. The controller’s stability is analytically studied and the good performance of the system is demonstrated through exhaustive simulations using validated dynamic models for mini-helicopters, cables, and payload. Finally, the relation between load weight and number of URs is analyzed by considering several scenarios.

Robust FOSMC of quadrotor in the presence of slung load

This study aims to develop a robust control for the quadrotor slung-load system that efficiently follows a reference trajectory. A fractional-order robust sliding mode control has been chosen to control the quadrotor’s altitude, position, and attitude. An anti-swing controller was also installed to limit the swing angle of the suspended load. It was created via delayed feedback, in which the quadrotor’s position reference trajectory is changed by the difference of the load angles within a specific delayed value. Designing an adaptive FOSMC would control the system when the system uncertainties do not know the bounds. Moreover, the control parameters and the anti-swing controller for the FOSMC can be obtained using some optimization techniques to increase the controllers’ accuracy.

An innovative integrated path planning and trajectory tracking framework for a quadrotor slung load system in an urban environment

In this paper, a hybrid path planning and trajectory tracking controller for a quadrotor slung load system is presented. This controller has benefited from the fuzzy inference system in its tracking and swing stabilization tasks. This system also plays an important role in creating a grid-based obstacle avoidance method that works based on the concept of generating Non-stationary Artificial Potential Field (NAPF) in the proximity of the objects tracking a virtual target on the path computed by A* algorithm. The weakness of the conventional artificial potential field method, that is to stuck in local minima, is now resolved by this so-called hybrid A*-NAPF method in which the potential field is non-stationary. The A* algorithm as a fast optimal path determination method computes the discrete initial path using a network of grids already generated through transferring the environment to a binary occupancy map. The performance of the whole integrated system is investigated through various simulation scenarios including those with moving obstacles. The results indicate a very good performance with high adaptability characteristic.

Dual-UAV Payload Transportation Using Optimized Velocity Profiles via Real-Time Dynamic Programming

In this paper, a real-time dynamic programming (RTDP) approach was developed for the first time to jointly carry a slung load using two unmanned aerial vehicles (UAVs) with a trajectory optimized for time and energy consumption. The novel strategy applies RTDP algorithm, where the journey was discretized into horizons consisting of distance intervals, and for every distance interval, an optimal policy was obtained using a dynamic programming sweep. The RTDP-based strategy is applied for dual-UAV collaborative payload transportation using coordinated motion where UAVs act as actuators on the payload. The RTDP algorithm provides the optimal velocity decisions for the slung load transportation to either minimize the journey time or the energy consumption. The RTDP approach involves minimizing a cost function which is derived after simplifying the combined model of the dual-UAV-payload system. The cost function derivation was also accommodated to dynamically distribute the load/energy between two multi-rotor platforms during a transportation mission. The cost function is used to calculate transition costs for all stages and velocity decisions. A terminal cost is used at the last distance interval during the first phase of the journey when the velocity at the end of the current horizon is not known. In the second phase, the last stage or edge of the horizon includes the destination, hence final velocity is known which is used to calculate the transition cost of the final stage. Once all transition costs are calculated, the minimum cost is traced back from the final stage to the current stage to find the optimal velocity decision. The developed approach was validated in MATLAB simulation, software in the loop Gazebo simulation, and real experiments. The numerical and Gazebo simulations showed the successful optimization of journey time or energy consumption based on the selection of the factor λ. Both simulation and real experiments results show the effectiveness and the applicability of the proposed approach.

Stability and control issues of multirotor suspended load transportation: An analytical closed–form approach

In the present paper a fully–analytical framework is outlined to analyze the effects of cable–suspended loads on multirotor platforms. In particular, the dynamics of an isolated vehicle is first investigated by including the complete model of the electric propulsion system. Then, system description is extended to the load, which introduces non–actuated degrees of freedom and is suspended through a linear–elastic cable. In order to provide the complete slung–load system with a closed–loop desired behavior, an auxiliary controller is proposed to recover or improve the initial multirotor dynamic properties, while stabilizing load oscillations. To this end, closed–form equations are derived to design the auxiliary controller gains, based on the knowledge of a limited set of parameters. A test case is proposed relative to a commercial–off–the–shelf hexarotor whose electrical propulsion system has been characterized by an experimental campaign performed at University of Bologna premises.

Adaptive optimal controller design for an unbalanced UAV with slung load

Adaptive optimal controller design for an unbalanced UAV with slung load