Review of Aerial Transportation of Suspended-Cable Payloads with Quadrotors

Citation: Estevez, J.; Garate, G.; Lopez-Guede, J.M.; Larrea, M. Review of Aerial Transportation of Suspended-Cable Payloads with Quadrotors. Drones 2024,8, 35. https://doi.org/10.3390/ drones8020035 Academic Editor: Abdessattar Abdelkefi Received: 20 November 2023 Revised: 18 January 2024 Accepted: 23 January 2024 Published: 25 January 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). drones Review Review of Aerial Transportation of Suspended-Cable Payloads with Quadrotors Julian Estevez 1,* , Gorka Garate 1, Jose Manuel Lopez-Guede 2and Mikel Larrea 1 1 Group of Computational Intelligence, Faculty of Engineering of Gipuzkoa, University of the Basque Country (UPV/EHU), 20080 San Sebastian, Spain; [email protected] (G.G.); [email protected] (M.L.) 2Group of Computational Intelligence, Faculty of Engineering of Vitoria, University of the Basque Country (UPV/EHU), 01006 Vitoria, Spain; [email protected] *Correspondence: [email protected] Abstract: Payload transportation and manipulation by rotorcraft drones are receiving a lot of attention from the military, industrial and logistics research areas. The interactions between the UAV and the payload, plus the means of object attachment or manipulation (such as cables or anthropomorphic robotic arms), may be nonlinear, introducing difficulties in the overall system performance. In this paper, we focus on the current state of the art of aerial transportation systems with suspended loads by a single UAV and a team of them and present a review of different dynamic cable models and control systems. We cover the last sixteen years of the existing literature, and we add a discussion for evaluating the main trends in the referenced research works. Keywords: UAVs; suspended payload; collaborative; control engineering; cable modeling 1. Introduction When dealing with the aerial transportation of payloads, the first approach historically taken was to deal with the problem of a load suspended on a crane. In this problem, two types of models could be used: global-mass models and distributed-mass models [1]. Lumped-mass models are characterized by a massless cable, where the payload is lumped with the hook and represented by a point mass. This model is simple while capturing the complex dynamics of payload motion [2–4]. Distributed-mass models are composed of a distributed-mass cable and a lumped point mass modeling the payload. The only model published that falls into this category is the planar model developed by d’Andrea-Novel et al. and Abdel-Rahman et al. [ 1 , 5 ]. However, Choo and Casarella [ 6 ], in their review comparing several modeling methods, including some continuous and discrete cable models, arrived at the conclusion that the lumped-mass representation, despite the heavy computer workload needed for its implementation, is the most versatile of them all. This technique models the cable as a finite series of rigid links of lumped masses at the joints. Focusing on aerial applications, over the past few decades, towed-cable systems have been extensively researched for diverse applications, often promoted by military interests, such as the delivery and retrieval of payloads [ 7 , 8 ], aerostats [ 9 ], tethering systems [ 10 , 11 ] and aerial refueling systems [ 12 ]. A typical towed-cable system is composed of three components: a towing vehicle, a cable (string or tether) and a towed body (drogue) [13]. As UAV research progressed, the evolution of air transport using UAVs also began to generate interest. This resulted in the possibility of performing a wider range of transport tasks using UAVs [ 14 ]. These tasks include various activities, such as transporting larger and diverse objects, examining and maintaining different elements and surfaces and carrying out industrial and emergency-related applications [ 15 ]. Most current research is focused on the dynamic modeling and control of the system encompassing the UAVs and the payload. The coupling of the UAV and the payload introduces strong nonlinearities Drones 2024,8, 35. https://doi.org/10.3390/drones8020035 https://www.mdpi.com/journal/drones Drones 2024,8, 35 2 of 21 into established equations that depend on the specific kind of system [ 16 ]. Two major carrying strategies have been researched by the scientific community: the direct attachment of the payload to the quadcopter body and the suspension of the cargo with cables [ 17 , 18 ]. For the former, the cargo is attached to the robot body (normally below the center of gravity) through claws, robotic hands or electromagnetic grippers [ 19 ]. This method allows for a quicker attachment/release of the load, but it increases the inertia moment of the system, thus making it slower and harder for agile maneuvers and rapid attitude changes [20–22]. For the latter, the load suspended with cables adds degrees of freedom to the inherently underactuated nature of the quadrotor, altering the flight dynamics [ 23 ]. In both cases, the system controller needs special requirements added to those used for UAVs without a load [ 24 , 25 ]. However, the fulfillment of the special conditions to obtain fast, stable, rapid and robust flight has no optimal solution, and this leaves the door open for a large number of controller designs. This survey focuses on the transportation of cable-suspended loads with multirotors, namely, quadrotors. At the moment, recent reviews on the civil applications of UAVs do not cover all the design possibilities, including individual or collaborative schemes, cable modeling or fast maneuvers. Some other research reviews related to UAV payload applications have been published lately. For instance, refs. [ 26 – 28 ] present reviews of multirotors transporting a payload, but they compare different methods for that. Among these last papers, several designs are described: suspended loads, grasping or the usage of arms, and specific issues, such as interactions with objects and the required sensors, are covered. But these papers do not describe the control strategies used in the field. Another recent and highly cited review by Ruggiero et al. [ 29 ] pays much attention to quadrotors that have arms and interact with objects, which is one of the main areas of expertise in their research group. The main contribution of our review is the exclusive study of multirotors carrying suspended loads with cables. The nonlinear nature of drone behavior is further compounded by a greater constraint than when it flies with no load, making it an extremely complex problem and, at the same time, challenging for future applications. We cover the mathematical modeling of cables and control strategies for both individual robots and teams of robots. It is important to note that, in this research review article, we will not deal with hardware platforms or sensors. Instead, our investigation will be directed toward the mathematical modeling of cables, control strategies and subsequent experimental validation studies (when possible). This deliberate scope allows us to delve deeper into the specific areas of interest, providing a comprehensive analysis and valuable insights while avoiding unnecessary redundancy in the discussion of hardware and sensors, which are often well documented elsewhere in the literature. By narrowing our focus, we aim to provide readers with a more targeted and informative examination of the key facets within the purview of our study. This article is divided into the following parts: In Section 2, we present the methodology and article selection criteria that we followed in order to complete this review article. Section 3describes different approaches to cable modeling for the transportation of objects using suspended-load transportation with quadrotors. Section 3is divided into individual and collaborative transport. Next, Section 4discusses control strategies for payload transportation by aerial systems, including different optimization strategies. Once again, the section is divided into single and collaborative groups of rotorcraft. The actual knowledge in this field today, future trends in research and technical challenges that still need to be dealt with are discussed in Section 5. Finally, Section 6gives some remarks about the presented concepts. Drones 2024,8, 35 3 of 21 2. Methodology The works cited in this article were chosen according to their relevance and interest in the field of modeling and control of the transportation of objects by single or teams of UAVs, more specifically, individual and teams of quadrotors using cable-suspended payloads. These systems are complex and nonlinear and require elaborate mathematical models to describe their dynamics, as well as to design adequate controllers. Because of the complexity of these systems, the requirement for carrying out practical experiments in addition to simulations was mandatory for the selection made in this survey. Another filter used was the non-inclusion of theses and unpublished dissertations. In order to evaluate their relevance and interest, the aspects considered were the technical quality of models of both dynamics and control and the innovation of the presented proposal. Finally, in seeking relevant works in the field, the selected articles were manually perused and are presented in a reference list. Table 1summarizes the criteria used in this survey. Table 1. Article selection search criteria. Criteria Data Scientific Database IEEEXplore, Google Scholar, ISI Web of Knowledge, ScienceDirect Publication Period From 2007 to November 2023 Keywords (“quadrotor” OR “rotorcraft” OR “quadcopter” “UAV” OR “multi-rotor” OR “multiple quadrotor” OR “swarm robot” OR “collaborative robots” OR “team of quadrotors”) AND (“delivery” OR “transportation” OR “transport” OR “retrieval” OR “cargo” OR “cable” OR “payload” OR “suspended load”) 3. Cable Modeling for Payload Transportation with UAVs In the following paragraphs, different cable models used for suspended-load transportation, both with individual robots and with a team of robots, are presented. 3.1. Individual Transport Early researchworks about UAVstransporting payloads appearedinthe late 1990s[ 30 , 31 ]. For payload transportation by UAVs, the cable treatment is a key factor for modeling the system and the exerted forces experienced by the quadrotor when the lifting, transport and delivery stages have distinct characteristics [ 32 ]. During the transport phase, the payload transmits tension through the cable, while in the very beginning of the lifting stage, there is no force transferred through the cable [ 33 ]. For simplicity, researchers tend to reduce such force transfer to whether the cable is taut or not [34]. This dynamic model represents the payload as a mass particle and the cable as a massless rigid bar that permanently maintains a constant distance between the payload and the quadrotor and can only transmit axial forces through it. Under these conditions, in 3D scenarios, the payload system is defined by two angles in space, while in planar cases, one angle is enough, similar to a pendulum [35], as can be seen in Figure 1. Normally, extra restrictions are considered in the dynamic modeling of these systems [33,36,37]: 1. The quadrotor is modeled as a symmetric rigid body. 2. The cable is modeled as inextensible, massless and attached to the center of the quadrotor, and the payload is modeled as a point mass attached to the cable. 3. The mass of the payload is small compared to the mass of the quadrotor, which implies that its motion has little impact on the motion of the quadrotor. 4. The effects of the payload and the cable are treated as an external force applied to the UAV. Drones 2024,8, 35 4 of 21 Figure 1. Payload with taut-cable modeling in 3D (left) and 2D (right) scenarios. Taut-cable approaches became successful because they permitted an easier stabilization of the UAV positioning. Lupashin and D’Andrea [ 38 ] proposed a tethered quadrotor and modeled the cable as taut, and they used this cable as a user interaction medium for a low-cost, small hovering UAV in order to stabilize the orientation and the position. With the taut cable, researchers proved that simple inertial measurement sensors are enough for the quadrotor to recover its position and attitude after external perturbations. Following this approach, Sreenath et al. [ 39 ] modeled the cable of a suspended load as taut for both the tense-cable and zero-tension cases. In a 3D scenario and a model with nonzero cable tension, the equation dynamics of the system turn out to have 8 degrees of freedom, with 4 degrees underactuated. On the contrary, when the cable transmits no tension, they considered that the UAV and cable form separate systems, and the load is in free fall. In both cases, they validated the models using simulations and real experimentation using taut cables, which permits a high realistic performance for trajectories with curves. Despite the simplicity of payload modeling, it is a widely accepted technical solution among scientists, as different works from the last two years reveal [ 40 – 43 ], where the mathematical formulation and constraints of the model have remained unchanged. The limitations of the model of a taut cable are revealed when the quadrotor performs certain critical tasks [ 17 , 44 , 45 ]. Klausen et al. [ 46 ] tested a taut-cable model for aggressive maneuvers and highlighted that there is a substantial load deflection during sudden accelerations and that the payload keeps oscillating when the UAV reaches the hovering state, despite being low-amplitude swings. These limitations are the reason for other cable model proposals. One of those critical tasks is the lifting of the load from the ground, where the quadrotor and payload system experience different dynamics and a taut cable no longer makes sense. Cruz et al. [ 47 , 48 ] proposed a hybrid model of the cable and UAV, consisting of dividing the process, from lifting the payload to completely separating it from the ground, into three phases (Setup,Pull and Raise), and for each of them, they developed different switching dynamics. These switching dynamics, known as cable collision [ 49 ], arise when the cable state passes instantaneously from slack to taut; moreover, the UAV undergoes another tension jump when the load is completely in the air. These three steps can be seen in Figure 2. The Setup phase is defined solely by the dynamics of the UAV, while the payload has no effect. At the precise moment the UAV makes the cable vertical, it changes the tension from slack to taut, and it is calculated by the collision effect presented in [ 49 ]. Next, in the Pull phase, the payload is still in contact with the ground, and thus, researchers take into account the normal force that the ground is exerting on the particle mass; although the cable is still not fully tense, it is already considered taut. Finally, in the Raise phase, the cable is tense, and the particle loses contact with the ground. However, Alothman et al. [ 50 ] presented work in which they researched the transition from lifting to transporting the payload, and they split the dynamic equations into two. In the first stage, the quadrotor has no tension at all, and the dynamic equations do not take the cargo into account. In the following phase, when the aerial robot exceeds the height of Drones 2024,8, 35 5 of 21 the cable length, the system is transformed into a UAV and a slung-load system, modeling the cable as taut. The transition from one phase to the other is more abrupt than in the case of [ 47 ], and they validated the model only with simulations. Similarly, Estevez et al. [ 51 ] developed a taut cable modeled as a pendulum for the lifting phase, considering no friction with the ground. They did not get rid of any switching dynamics between the phases and validated it through experiments. Moreover, according to the trends in recent years, this payload-lifting procedure remains the simplest possible, and the cable keeps switching from a slack to a taut phase when exceeding a height threshold [52–56]. Figure 2. The lift maneuver: (a)Setup, (b)Pull, and (c)Raise. While works seen until now modeled the cable as a massless rigid link, Kotaru et al. [ 17 ] considered the cable to be elastic, and they validated their model by focusing on robotic application studies, where cable elasticity cannot be ignored and thus, the rigid-rod model is no longer valid. For that, they included a damping and a spring in their cable model (see Figure 3) and tested the system stability under perturbations and with different damping and stiffness values; however, their study was validated only through simulations. The procedure for modeling this cable as a damper combined with a spring has been applied to the study of other UAV-navigation-related tasks [ 57 ], which suggests that the model is still considered valid for capturing the mentioned specific payload effects, particularly large payload swings. Figure 3. Cable model with damping and linear spring. C and k are damping and stiffness coefficients, lrefers to the cable length, and xQand xLrefer to quadrotor and load positions. Later, Goodarzi et al. [ 24 ] introduced another flexible-cable model, formed by a series of weighted segments of different sizes connected with spherical joints (see Figure 4). The links between joints can elongate, and the researchers aimed to obtain a more precise dynamic model for the aggressive maneuvers of UAVs, with payloads modeled as a serial chain of n connected links, which aimed to prove the stability of a coupled system composed Drones 2024,8, 35 6 of 21 of a tethered cable and a UAV performing flight maneuvers in 3D. The authors considered the vibrations of the cable through vibrations of the n connected links. Nevertheless, to the knowledge of the authors of the current article, this schema has not been widely followed in the literature. Figure 4. Cable model developed by [24]. In terms of landing, the research community has covered the process for UAVs not carrying payloads [ 58 , 59 ]. However, the challenge of landing with a payload has not been studied in depth [ 32 ], and the literature reflects just some attempts. One of them was developed by Goodarzi [ 60 ], who used a variable-length cable to lower the payload to the ground, and he validated the research through simulations. Next, Qian et al. [ 32 ] proved, through real experimentation, that with a precise control design, the assumption of a taut cable is valid for the delivery of a slung payload on the ground. 3.2. Collaborative Transport Collaborative systems are useful for the transportation and orientation of the payload. Actually, the use of multiple UAVs can manage to perform more complex tasks and overcome the limitations of an individual load, such as the enhancement of the load capacity and better control of oscillations [ 61 ]. However, these pros come at the cost of increasing the system complexity and aerial vehicle coordination, which must avoid collisions with one another [ 62 ]. Their dynamics and additional control requirements are extensively discussed in [29,63,64]. Therefore, the optimization of these variables is not solved yet. The literature has introduced solutions involving the rigid attachment of multiple quadrotors to objects, as detailed in [ 65 , 66 ]. However, these cases have demonstrated that manipulation is considerably more challenging to achieve than transportation. This difficulty arises from the underactuation property of multirotors [ 67 ]. To address these limitations, a reliable alternative has emerged in the form of rigid links connected through spherical joints to the payload, as evidenced in [ 68 – 71 ]. This approach ensures the full actuation of the platform by robots. Furthermore, substituting rigid links with cables enables the design of flexible floating transportation structures. Notably, these cables facilitate the partial decoupling of the vehicle’s rotational dynamics from that of the carried payload. Additionally, employing spherical joints enhances the flexibility of robot formation shapes, while the lightweight nature of the cables significantly increases the robots’ payload capacity. Many papers consider the usage of massless rigid links due to their lower complexity [ 34 , 64 , 72 ]. Michael et al. [ 73 ] presented a model to transport a disc-type payload via towed cables with quadrotors. The problem is analogous to that of cable-actuated parallel manipulators operating in three dimensions, as both types of manipulators are designed to control the pose of the payload with varying robot positions and in aerial systems, and the payload orientation is modified with aerial cable towing performed by quadrotors (see Figure 5). They used three different approaches to solve the problem: inverse kinematics of the payload and UAVs, the direct problem and an optimization of that last direct problem. Moreover, the same research group modeled the transportation of a suspended DLO (deformable linear object) [ 74 ] and designed a deep mathematical background for the Drones 2024,8, 35 7 of 21 formulation of the system’s stability and control, but with severe dynamic limitations and quasistatic conditions. Figure 5. A team of three point-model robots manipulates a payload in three dimensions [73]. Another cable alternative was proposed by Pizetta et al. [ 62 ], who used a model of elastic cables, and they relied on their traction force to reject the disturbances created by the payload on the UAV. Moreover, they proved that their proposal is valid for lifting the payload from the ground, using a single system of dynamics and a series of assumptions: (1) the cable is massless; (2) when the load is on the ground and the cable is slack, there is no effect on the vehicles; (3) the aerodynamic effects on the load and vehicle are negligible. They simulated their system with two UAVs considering only the longitudinal plane for payload swings. The group transportation and orientation of a rigid two-dimensional payload is achieved by using a cable system that is modeled as a series of connected links [ 75 ] (see Figure 6), as demonstrated in the works presented in the previous sections, [ 24 , 76 ], which demonstrate the robustness of this approach to payload transportation with UAVs. Figure 6. Quadrotor UAVs with a rigid-body payload. Cables are modeled as a serial connection of an arbitrary number of links. However, taut cables are not the only mechanical elements that have been researched in order to achieve a better representation of reality, and [ 77 ] developed what they call tensegrity muscles. This element consists of a finite number of tensegrity prism cells, where each prism cell is made of tethers and rigid bars, and they can apply tension and compression efforts. The key to their approach is to consider these elements as a continuum deformable element, which permits them to scale the number of UAVs in the aerial transport task, thus gaining some advantages, such as an increase in robustness, reconfiguration Drones 2024,8, 35 8 of 21 capabilities and the ability of the system to navigate in constrained environments, such as narrow channels. Catenaries are widely accepted by the scientific community as a dynamic cable model representation and have been used in submarine mooring cable simulations [ 78 – 80 ]. However, models based on catenaries have not been fully exploited for aerial towing, despite the promising results presented in previous works [ 78 , 81 , 82 ]. Works using this cable formulation defend the advantages of catenaries for their quasistatic configuration, ease of computation and well-established rigid–solid mechanics equation. Catenaries can be used to formulate discrete or continuous models. Estevez et al. [ 83 ] presented a collaborative quadrotor system for DLO transportation using catenaries, as shown in Figure 7. They created an equiload quadrotor height configuration for the transportation of a cable with the same vertical load for each robot under the following assumptions: • The cable diameter is negligible compared to its length. Thus, the cable can be modeled as a 1D object. • The mass per unit length of the cable is constant. • The cable cannot elastically lengthen (Young’s modulus is large). • There is no torsion in the cable. Figure 7. Transportation of DLO with a team of quadrotors. The same research group evolved their work and turned their proposal into a hybrid parabola and catenary switching model, so the team of UAVs does not collapse the catenaries when they get too close in aggressive maneuvers or sharp trajectories [ 84 ]. The approach to modeling cables with catenaries has been adopted by other research groups, such as [ 85 , 86 ], who experimentally tested the validity of the solution. However, both of them just use two rotorcraft in the formation. However, very few of the multi-robot transport proposals in this section take into account lift-off or landing procedures. Although Goodarzi and Lee [ 87 ] and Michael et al. [ 73 ] performed experiments showing that their systems are able to lift and land, they do not describe the mathematical modeling of the cable for a transient regime. Including the dynamic properties of the cable during these phases increases the cost of computation. The scientific literature in this field is very scarce and relies on some simplifications to ease the calculus and computational cost [ 88 ]. For instance, Bacelar et al. [ 89 ] presented two AR Drone 2.0 quadrotors for transporting a suspended load and specified that they are always assumed to be taut. Next, Pizetta et al. [ 90 , 91 ] proposed a system of two quadrotors transporting a point-mass load with two cables formed by point-like masses joined by springs and dampers (Kelvin–Voigt models). This cable model is able to absorb the contact with the ground and linearly reduce the tension of the cables. Geng et al. [ 92 ] and Goodman et al. [ 93 ] used the same cable dynamic model. Lately, some other researchers have reproduced this schema for loading baror rod-shaped payloads, as can be seen in Figure 8. While elastic cables offer the advantage of mitigating impulsive forces on the bar, excessive oscillations can induce unwanted forceful movements, potentially jeopardizing the safety of the collaborative task. Therefore, the implementation of elastic cables with enhanced stiffness and damping is crucial to safeguard the bar during the transportation Drones 2024,8, 35 9 of 21 process. For instance, Goodman et al. again validated their results with simulations in [ 94 ], while Gabellieri et al. [95] validated their proposal with real experiments. Figure 8. Quadrotors transporting a cable-suspended bar ( left ) and cable section represented by mass–spring–damper systems (right). Finally, Shirani et al. [ 88 ] presented a mathematically simple cable collapse-andcollision model for lift-off and landing based on the geometric coordinates and distance between the UAVs and the payload. Surprisingly, the trend in recent years has been to extend the cable model that switches the state of the cable from slack to taut when a height threshold is achieved with a team of rotorcraft [ 69 , 91 , 96 , 97 ], which is apparently the simplest formulation, mathematically speaking. This slung-load option prevails as one of the most used alternatives, both for experiments including payload lifting and for those without it. However, for the former, these studies are limited to smooth maneuvers. 4. Control Strategies Dynamic models of multirotor-type UAVs usually consider that the geometry and mass distribution are symmetrical, which allows for some simplifications of the dynamic equations. The mass distribution of an aerial robot with a payload is no longer symmetrical, as it varies widely with the movement of the manipulator or cable mass. In the following paragraphs, we discuss the state of the art in control design for several of the above configurations. 4.1. Individual Transport During flight, the payload adds passive dynamic effects, which could come from either the cable or the payload, and generates swinging that modifies the dynamics of the UAV and alters its dynamic performance. The most common way to deal with the perturbations caused by the payload is to stabilize the system, minimizing the load swings [36,98] . Alternatively, some works used feedback control to track the desired load trajectories or trajectory-planning algorithms for the quadrotor-with-load multi-body system [ 99 ]. Some other researchers divided the cable model into different subsystems. In these hybrid dynamic models, each subsystem has its specific and specialized controller, and the switching among the simple controllers is performed by a supervisory system [ 39 , 47 ]. In contrast, other groups worked on the search for a general solution to the problem of suspended-cable transport, no matter what stage the mission is in [23,50,100]. The dynamic system of a quadrotor with a hanging payload in 3D has eight degrees of freedom and only four control inputs. Thus, the same four model simplifications mentioned in Section 3.1 referring to the UAV and payload are assumed, but still, the four degrees of underactuation make the controller design challenging [ 101 ]. This subsection is divided into three different control-oriented approaches for the UAV and the payload system. They include swing attenuation of the payload, optimal trajectory tracking and control for aggressive maneuvers. Drones 2024,8, 35 16 of 21 References 1. Abdel-Rahman, E.M.; Nayfeh, A.H.; Masoud, Z.N. Dynamics and control of cranes: A review. Modal Anal. 2003 ,9, 863–908. [CrossRef] 2. Kaya, U.C.; Subbarao, K. Momentum Preserving Simulation of Cooperative Multirotors with Flexible-Cable Suspended Payload. J. Dyn. Syst. Meas. Control 2022,144, 041007. [CrossRef] 3. Yurchenko, D.; Alevras, P.; Zhou, S.; Wang, J.; Litak, G.; Gaidai, O.; Ye, R. Nonlinear vibration mitigation of a crane’s payload using pendulum absorber. Mech. Syst. Signal Process. 2021,156, 107558. [CrossRef] 4. Strip, D. Swing-free transport of suspended objects: A general treatment. IEEE Trans. Robot. Autom. 1989 ,5, 234–236. [CrossRef] 5. D’Andrea-Novel, B.; Boustany, F.; Conrad, F. Control of an overhead crane: Stabilization of flexibilities. In Boundary Control and Boundary Variation; Springer: Berlin/Heidelberg, Germany, 1992; pp. 1–26. 6. Choo, Y.I.; Casarella, M.J. A Survey of Analytical Methods for Dynamic Simulation of Cable-Body Systems. J. Hydronautics 1973 , 7, 137–144. [CrossRef] 7. Skop, R.A.; Choo, Y.I. The configuration of a cable towed in a circular path. J. Aircr. 1971,8, 856–862. [CrossRef] 8. Anderson, V. Method and Apparatus for Pickup and Delivery by Aircraft in Flight. U.S. Patent 2295537, 15 September 1942. 9. De Laurier, J.D. A stability analysis for tethered aerodynamically shaped balloons. J. Aircr. 1972,9, 646–651. [CrossRef] 10. Kamman, J.W.; Huston, R.L. Modeling of variable length towed and tethered cable systems. J. Guid. Control. Dyn. 1999 , 22, 602–608. [CrossRef] 11. Etkin, B. Stability of a towed body. J. Aircr. 1998,35, 197–205. [CrossRef] 12. Ro, K.; Kamman, J.W. Modeling and simulation of hose-paradrogue aerial refueling systems. J. Guid. Control. Dyn. 2010 ,33, 53–63. [CrossRef] 13. Sun, L. Dynamic Modeling, Trajectory Generation and Tracking for Towed Cable Systems. Ph.D. Thesis, Brigham Young University, Provo, UT, USA, 2012. 14. Yi, J.; Zhang, H.; Wang, F.; Ning, C.; Liu, H.; Zhong, G. An Operational Capacity Assessment Method for an Urban Low-Altitude Unmanned Aerial Vehicle Logistics Route Network. Drones 2023,7, 582. [CrossRef] 15. Hoffmann, G.M.; Huang, H.; Waslander, S.L.; Tomlin, C.J. Precision flight control for a multi-vehicle quadrotor helicopter testbed. Control Eng. Pract. 2011,19, 1023–1036. [CrossRef] 16. Pizetta, I.H.B.; Brandao, A.S.; Sarcinelli-Filho, M. Modelling and control of a PVTOL quadrotor carrying a suspended load. In Proceedings of the 2015 International Conference on Unmanned Aircraft Systems (ICUAS), Denver, CO, USA, 9–12 June 2015; pp. 444–450. 17. Kotaru, P.; Wu, G.; Sreenath, K. Dynamics and control of a quadrotor with a payload suspended through an elastic cable. In Proceedings of the 2017 American Control Conference (ACC), Seattle, WA, USA, 24–26 May 2017; pp. 3906–3913. 18. Chen, T.; Shan, J.; Liu, H.H. Cooperative transportation of a flexible payload using two quadrotors. J. Guid. Control. Dyn. 2021 , 44, 2099–2107. [CrossRef] 19. Theobald, K.; Zhu, W.; Waters, T.; Cherrett, T.; Oakey, A.; Royall, P.G. Stability of Medicines Transported by Cargo Drones: Investigating the Effects of Vibration from Multi-Stage Flight. Drones 2023,7, 658. [CrossRef] 20. Godbole, A.R.; Subbarao, K. Nonlinear control of unmanned aerial vehicles with cable suspended payloads. Aerosp. Sci. Technol. 2019,93, 105299. [CrossRef] 21. Chen, T.; Shan, J. A novel cable-suspended quadrotor transportation system: From theory to experiment. Aerosp. Sci. Technol. 2020,104, 105974. [CrossRef] 22. Thomas, J.; Loianno, G.; Polin, J.; Sreenath, K.; Kumar, V. Toward autonomous avian-inspired grasping for micro aerial vehicles. Bioinspir. Biomimetics 2014,9, 025010. [CrossRef] 23. Guo, K.; Jia, J.; Yu, X.; Guo, L.; Xie, L. Multiple observers based anti-disturbance control for a quadrotor UAV against payload and wind disturbances. Control Eng. Pract. 2020,102, 104560. [CrossRef] 24. Goodarzi, F.A.; Lee, D.; Lee, T. Geometric control of a quadrotor UAV transporting a payload connected via flexible cable. Int. J. Control. Autom. Syst. 2015,13, 1486–1498. [CrossRef] 25. Guerrero, M.; Mercado, D.; Lozano, R.; García, C. Passivity based control for a quadrotor UAV transporting a cable-suspended payload with minimum swing. In Proceedings of the 2015 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, 15–18 December 2015; pp. 6718–6723. 26. Villa, D.K.D.; Brandão, A.S.; Sarcinelli-Filho, M. A Survey on Load Transportation Using Multirotor UAVs. J. Intell. Robot. Syst. 2020,98, 267–296. [CrossRef] 27. Ding, X.; Guo, P.; Xu, K.; Yu, Y. A review of aerial manipulation of small-scale rotorcraft unmanned robotic systems. Chin. J. Aeronaut. 2019,32, 200–214. [CrossRef] 28. Bonyan Khamseh, H.; Janabi-Sharifi, F.; Abdessameud, A. Aerial manipulation—A literature survey. Robot. Auton. Syst. 2018 , 107, 221–235. [CrossRef] 29. Ruggiero, F.; Lippiello, V.; Ollero, A. Aerial Manipulation: A Literature Review. IEEE Robot. Autom. Lett. 2018 ,3, 1957–1964. [CrossRef] 30. Oshman, Y.; Isakow, M. Mini-UAV altitude estimation using an inertially stabilized payload. IEEE Trans. Aerosp. Electron. Syst. 1999,35, 1191–1203. [CrossRef] Drones 2024,8, 35 17 of 21 31. Borky, J.M. Payload technologies and applications for uninhabited air vehicles (UAVs). In Proceedings of the 1997 IEEE Aerospace Conference, Snowmass, CO, USA, 13 February 1997; Volume 3, pp. 267–283. 32. Qian, L.; Graham, S.; Liu, H.H.T. Guidance and control law design for a slung payload in autonomous landing: A drone delivery case study. IEEE/ASME Trans. Mechatron. 2020,25, 1773–1782. [CrossRef] 33. Guo, M.; Gu, D.; Zha, W.; Zhu, X.; Su, Y. Controlling a quadrotor carrying a cable-suspended load to pass through a window. J. Intell. Robot. Syst. 2020,98, 387–401. [CrossRef] 34. Tang, S.; Wüest, V.; Kumar, V. Aggressive flight with suspended payloads using vision-based control. IEEE Robot. Autom. Lett. 2018,3, 1152–1159. [CrossRef] 35. Sun, L.; Wang, K.; Mishamandani, A.H.A.; Zhao, G.; Huang, H.; Zhao, X.; Zhang, B. A novel tension-based controller design for the quadrotor–load system. Control Eng. Pract. 2021,112, 104818. [CrossRef] 36. Lv, Z.; Zhao, Q.; Li, S.; Wu, Y. Finite-time control design for a quadrotor transporting a slung load. Control Eng. Pract. 2022 , 122, 105082. [CrossRef] 37. Zameroski, D.; Starr, G.; Wood, J.; Lumia, R. Rapid swing-free transport of nonlinear payloads using dynamic programming. J. Dyn. Syst. Meas. Control 2008,130, 041001. [CrossRef] 38. Lupashin, S.; D’Andrea, R. Stabilization of a flying vehicle on a taut tether using inertial sensing. In Proceedings of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan, 3–7 November 2013; pp. 2432–2438. 39. Sreenath, K.; Michael, N.; Kumar, V. Trajectory generation and control of a quadrotor with a cable-suspended load—A differentially-flat hybrid system. In Proceedings of the 2013 IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, 6–10 May 2013; pp. 4888–4895. 40. Akhtar, A.; Saleem, S.; Shan, J. Path following of a quadrotor with a cable-suspended payload. IEEE Trans. Ind. Electron. 2022 , 70, 1646–1654. [CrossRef] 41. Reis, J.; Yu, G.; Cabecinhas, D.; Silvestre, C. High-performance quadrotor slung load transportation with damped oscillations. Int. J. Robust Nonlinear Control 2022,33, 10227–10256. [CrossRef] 42. Belguith, M.; Samaali, S.; Bennaceur, S. Modeling and Control of Quadrotor Transporting Cable-Suspended Load in the Longitudinal & Lateral Planes. In Proceedings of the 2023 European Control Conference (ECC), Bucharest, Romania, 13–16 June 2023; pp. 1–6. 43. de Angelis, E.L.; Giulietti, F. Stability and control issues of multirotor suspended load transportation: An analytical closed–form approach. Aerosp. Sci. Technol. 2023,135, 108201. [CrossRef] 44. Estevez, J.; Lopez-Guede, J.M.; Garate, G.; Graña, M. A hybrid control approach for the swing free transportation of a double pendulum with a quadrotor. Appl. Sci. 2021,11, 5487. [CrossRef] 45. Castillo, A.; Sanz, R.; Garcia, P.; Qiu, W.; Wang, H.; Xu, C. Disturbance observer-based quadrotor attitude tracking control for aggressive maneuvers. Control Eng. Pract. 2019,82, 14–23. [CrossRef] 46. Klausen, K.; Fossen, T.I.; Johansen, T.A. Nonlinear Control with Swing Damping of a Multirotor UAV with Suspended Load. J. Intell. Robot. Syst. 2017,88, 379–394. [CrossRef] 47. Cruz, P.J.; Oishi, M.; Fierro, R. Lift of a cable-suspended load by a quadrotor: A hybrid system approach. In Proceedings of the 2015 American Control Conference (ACC), Chicago, IL, USA, 1–3 July 2015; pp. 1887–1892. 48. Cruz, P.J.; Fierro, R. Cable-suspended load lifting by a quadrotor UAV: Hybrid model, trajectory generation, and control. Auton. Robot. 2017,41, 1629–1643. [CrossRef] 49. Bisgaard, M.; Bendtsen, J.D.; la Cour-Harbo, A. Modeling of generic slung load system. J. Guid. Control. Dyn. 2009,32, 573–585. [CrossRef] 50. Alothman, Y.; Jasim, W.; Gu, D. Quad-rotor lifting-transporting cable-suspended payloads control. In Proceedings of the 2015 21st International Conference on Automation and Computing (ICAC), Glasgow, UK, 11–12 September 2015; pp. 1–6. 51. Estévez, J.; Lopez-Guede, J.M. Control of transitory take-off regime in the transportation of a pendulum by a quadrotor. In From Bioinspired Systems and Biomedical Applications to Machine Learning, Proceedings of the 8th International Work-Conference on the Interplay between Natural and Artificial Computation, IWINAC 2019, Almería, Spain, 3–7 June 2019; Proceedings, Part II 8; Springer: Cham, Switzerland, 2019; pp. 117–126. 52. Li, G.; Liu, X.; Loianno, G. RotorTM: A Flexible Simulator for Aerial Transportation and Manipulation. arXiv 2022 , arXiv:2205.05140. 53. Brandão, A.S.; Smrcka, D.; Pairet, É.; Nascimento, T.; Saska, M. Side-pull maneuver: A novel control strategy for dragging a cable-tethered load of unknown weight using a UAV. IEEE Robot. Autom. Lett. 2022,7, 9159–9166. [CrossRef] 54. Yi, K.; Han, J.; Liang, X.; He, Y. Contact transition control with acceleration feedback enhancement for a quadrotor. ISA Trans. 2021,109, 288–294. [CrossRef] [PubMed] 55. Romero, J.G.; Rodríguez-Cortés, H. Asymptotic stability for a transformed nonlinear UAV model with a suspended load via energy shaping. Eur. J. Control 2020,52, 87–96. [CrossRef] 56. Bingöl, Ö.; Güzey, H.M. Fixed-time neuro-sliding mode controller design for quadrotor UAV transporting a suspended payload. Eur. J. Control 2023,73, 100879. [CrossRef] 57. Chang, P.; Yang, S.; Tong, J.; Zhang, F. A new adaptive control design for a quadrotor system with suspended load by an elastic rope. Nonlinear Dyn. 2023,111, 19073–19092. [CrossRef] 58. Luo, C.; Zhao, W.; Du, Z.; Yu, L. A neural network based landing method for an unmanned aerial vehicle with soft landing gears. Appl. Sci. 2019,9, 2976. [CrossRef] Drones 2024,8, 35 18 of 21 59. Gautam, A.; Sujit, P.; Saripalli, S. Application of guidance laws to quadrotor landing. In Proceedings of the 2015 International Conference on Unmanned Aircraft Systems (ICUAS), Denver, CO, USA, 9–12 June 2015; pp. 372–379. 60. Goodarzi, F.A. Autonomous aerial payload delivery with quadrotor using varying length cable. In Proceedings of the 2016 International Conference on Advanced Mechatronic Systems (ICAMechS), Melbourne, VIC, Australia, 30 November–3 December 2016; pp. 394–399. 61. Tan, Y.H.; Lai, S.; Wang, K.; Chen, B.M. Cooperative control of multiple unmanned aerial systems for heavy duty carrying. Annu. Rev. Control 2018,46, 44–57. [CrossRef] 62. Pizetta, I.H.B.; Brandão, A.S.; Sarcinelli-Filho, M. Avoiding obstacles in cooperative load transportation. ISA Trans. 2019 , 91, 253–261. [CrossRef] [PubMed] 63. Parra-Vega, V.; Sanchez, A.; Izaguirre, C.; Garcia, O.; Ruiz-Sanchez, F. Toward aerial grasping and manipulation with multiple UAVs. J. Intell. Robot. Syst. 2013,70, 575–593. [CrossRef] 64. Wu, P.X.; Yang, C.C.; Cheng, T.H. Cooperative Transportation of UAVs Without Inter-UAV Communication. IEEE/ASME Trans. Mechatron. 2023,28, 2340–2351. [CrossRef] 65. Loianno, G.; Kumar, V. Cooperative transportation using small quadrotors using monocular vision and inertial sensing. IEEE Robot. Autom. Lett. 2017,3, 680–687. [CrossRef] 66. Mellinger, D.; Shomin, M.; Michael, N.; Kumar, V. Cooperative grasping and transport using multiple quadrotors. In Distributed Autonomous Robotic Systems; Springer: Berlin/Heidelberg, Germany, 2013; pp. 545–558. 67. Sanalitro, D.; Savino, H.J.; Tognon, M.; Cortés, J.; Franchi, A. Full-pose manipulation control of a cable-suspended load with multiple UAVs under uncertainties. IEEE Robot. Autom. Lett. 2020,5, 2185–2191. [CrossRef] 68. Nguyen, H.N.; Park, S.; Lee, D. Aerial tool operation system using quadrotors as rotating thrust generators. In Proceedings of the 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany, 28 September–2 October 2015; pp. 1285–1291. 69. Mohammadi, K.; Sirouspour, S.; Grivani, A. Passivity-Based Control of Multiple Quadrotors Carrying a Cable-Suspended Payload. IEEE/ASME Trans. Mechatron. 2021,27, 2390–2400. [CrossRef] 70. Tagliabue, A.; Kamel, M.; Siegwart, R.; Nieto, J. Robust collaborative object transportation using multiple MAVs. Int. J. Robot. Res. 2019,38, 1020–1044. [CrossRef] 71. Six, D.; Briot, S.; Chriette, A.; Martinet, P. Dynamic modelling and control of flying parallel robots. Control Eng. Pract. 2021 , 117, 104953. [CrossRef] 72. Arab, F.; Shirazi, F.A.; Yazdi, M.R.H. Planning and distributed control for cooperative transportation of a non-uniform slung-load by multiple quadrotors. Aerosp. Sci. Technol. 2021,117, 106917. [CrossRef] 73. Michael, N.; Fink, J.; Kumar, V. Cooperative manipulation and transportation with aerial robots. Auton. Robot. 2010 ,30, 73–86. [CrossRef] 74. Jiang, Q.; Kumar, V. Determination and Stability Analysis of Equilibrium Configurations of Objects Suspended From Multiple Aerial Robots. J. Mech. Robot. 2012,4, 021005. [CrossRef] 75. Goodarzi, F.A.; Lee, T. Stabilization of a rigid body payload with multiple cooperative quadrotors. J. Dyn. Syst. Meas. Control 2016,138, 121001. [CrossRef] 76. Lee, T. Geometric controls for a tethered quadrotor UAV. In Proceedings of the 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, 15–18 December 2015; pp. 2749–2754. 77. Rastgoftar, H.; Atkins, E.M. Cooperative aerial lift and manipulation (CALM). Aerosp. Sci. Technol. 2018 ,82, 105–118. [CrossRef] 78. Chatjigeorgiou, I.K. A finite differences formulation for the linear and nonlinear dynamics of 2D catenary risers. Ocean Eng. 2008 , 35, 616–636. [CrossRef] 79. Gobat, J.I.; Grosenbaugh, M.A. Dynamics in the touchdown region of catenary moorings. Int. J. Offshore Polar Eng. 2001 ,11, ISOPE-01-11-4-273. 80. Suzuki, M.; Yokota, S.; Matsumoto, A.; Hashimoto, H.; Chugo, D. Position Estimation of the Drone Based on the Tensile Force of Cooperatively Towed Tube. In Proceedings of the IECON 2018—44th Annual Conference of the IEEE Industrial Electronics Society, Washington, DC, USA, 21–23 October 2018; pp. 4294–4299. 81. Doroudgar, S. Static and Dynamic Modeling and Simulation of the Umbilical Cable in a Tethered Unmanned Aerial System. Ph.D. Thesis, Simon Fraser University, Burnaby, BC, Canada, 2016. 82. Clifton, J.M.; Schmidt, L.V.; Stuart, T.D. Dynamic modeling of a trailing wire towed by an orbiting aircraft. J. Guid. Control. Dyn. 1995,18, 875–881. [CrossRef] 83. Estevez, J.; Graña, M.; Lopez-Guede, J.M. Online fuzzy modulated adaptive PD control for cooperative aerial transportation of deformable linear objects. Integr. Comput.-Aided Eng. 2017,24, 41–55. [CrossRef] 84. Estevez, J.; Lopez-Guede, J.M.; Garate, G.; Graña, M. Hybrid Modeling of Deformable Linear Objects for Their Cooperative Transportation by Teams of Quadrotors. Appl. Sci. 2022,12, 5253. [CrossRef] 85. D’antonio, D.S.; Cardona, G.A.; Saldana, D. The Catenary Robot: Design and Control of a Cable Propelled by Two Quadrotors. IEEE Robot. Autom. Lett. 2021,6, 3857–3863. [CrossRef] 86. Abhishek, V.; Srivastava, V.; Mukherjee, R. Towards a heterogeneous cable-connected team of UAVs for aerial manipulation. In Proceedings of the 2021 American Control Conference (ACC), New Orleans, LA, USA, 25–28 May 2021; pp. 54–59. Drones 2024,8, 35 19 of 21 87. Goodarzi, F.A.; Lee, T. Dynamics and control of quadrotor UAVs transporting a rigid body connected via flexible cables. In Proceedings of the American Control Conference (ACC), Chicago, IL, USA, 1–3 July 2015; pp. 4677–4682. 88. Shirani, B.; Najafi, M.; Izadi, I. Cooperative load transportation using multiple UAVs. Aerosp. Sci. Technol. 2019 ,84, 158–169. [CrossRef] 89. Bacelar, T.; Madeiras, J.; Melicio, R.; Cardeira, C.; Oliveira, P. On-board implementation and experimental validation of collaborative transportation of loads with multiple UAVs. Aerosp. Sci. Technol. 2020,107, 106284. [CrossRef] 90. Doakhan, M.; Kabganian, M.; Azimi, A. Cooperative payload transportation with real-time formation control of multi-quadrotors in the presence of uncertainty. J. Frankl. Inst. 2023,360, 1284–1307. [CrossRef] 91. Doakhan, M.; Kabganian, M.; Azimi, A. Robust adaptive control for formation-based cooperative transportation of a payload by multi quadrotors. Eur. J. Control 2023,69, 100763. [CrossRef] 92. Geng, J.; Langelaan, J.W. Cooperative transport of a slung load using load-leading control. J. Guid. Control. Dyn. 2020 , 43, 1313–1331. [CrossRef] 93. Goodman, J.R.; Beckers, T.; Colombo, L.J. Geometric control for load transportation with quadrotor UAVs by elastic cables. IEEE Trans. Control. Syst. Technol. 2023,31, 2848–2862. [CrossRef] 94. Goodman, J.; Colombo, L. Geometric control of two quadrotors carrying a rigid rod with elastic cables. J. Nonlinear Sci. 2022 , 32, 65. [CrossRef] 95. Gabellieri, C.; Tognon, M.; Sanalitro, D.; Franchi, A. Equilibria, Stability, and Sensitivity for the Aerial Suspended Beam Robotic System Subject to Parameter Uncertainty. IEEE Trans. Robot. 2023,39, 3977–3993. [CrossRef] 96. Arab, F.; Shirazi, F.A.; Yazdi, M.R.H. Cooperative parameter estimation of a nonuniform payload by multiple quadrotors. Robotica 2022,40, 1587–1606. [CrossRef] 97. Rao, N.; Sundaram, S. Integrated decision control approach for cooperative safety-critical payload transport in a cluttered environment. IEEE Trans. Aerosp. Electron. Syst. 2023,59, 8800–8811. [CrossRef] 98. Xian, B.; Wang, S.; Yang, S. An online trajectory planning approach for a quadrotor UAV with a slung payload. IEEE Trans. Ind. Electron. 2019,67, 6669–6678. [CrossRef] 99. Foehn, P.; Falanga, D.; Kuppuswamy, N.; Tedrake, R.; Scaramuzza, D. Fast Trajectory Optimization for Agile Quadrotor Maneuvers with a Cable-Suspended Payload. 2017. Available online: https://dspace.mit.edu/bitstream/handle/1721.1/12452 8/RSS17_Foehn.pdf?sequence=2&isAllowed=y (accessed on 24 January 2024). 100. Villa, D.K.D.; Brandão, A.S.; Carelli, R.; Sarcinelli-Filho, M. Cooperative load transportation with two quadrotors using adaptive control. IEEE Access 2021,9, 129148–129160. [CrossRef] 101. Chen, T.; Shan, J. Distributed tracking of a class of underactuated Lagrangian systems with uncertain parameters and actuator faults. IEEE Trans. Ind. Electron. 2019,67, 4244–4253. [CrossRef] 102. Palunko, I.; Fierro, R.; Cruz, P. Trajectory generation for swing-free maneuvers of a quadrotor with suspended payload: A dynamic programming approach. In Proceedings of the 2012 IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN, USA, 14–18 May 2012; pp. 2691–2697. 103. de Angelis, E.L.; Giulietti, F.; Pipeleers, G. Two-time-scale control of a multirotor aircraft for suspended load transportation. Aerosp. Sci. Technol. 2019,84, 193–203. [CrossRef] 104. Nicotra, M.M.; Garone, E.; Naldi, R.; Marconi, L. Nested saturation control of an UAV carrying a suspended load. In Proceedings of the 2014 American Control Conference, Portland, OR, USA, 4–6 June 2014; pp. 3585–3590. 105. Zhou, X.; Liu, R.; Zhang, J.; Zhang, X. Stabilization of a quadrotor with uncertain suspended load using sliding mode control. In Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Charlotte, NC, USA, 21–24 August 2016; American Society of Mechanical Engineers: New York, NY, USA, 2016; Volume 50152. 106. Yi, K.; Liang, X.; He, Y.; Yang, L.; Han, J. Active-model-based control for the quadrotor carrying a changed slung load. Electronics 2019,8, 461. [CrossRef] 107. Yu, G.; Xie, W.; Cabecinhas, D.; Cunha, R.; Silvestre, C. Adaptive control with unknown mass estimation for a quadrotor-slungload system. ISA Trans. 2023,133, 412–423. [CrossRef] [PubMed] 108. Koksal, N.; An, H.; Fidan, B. Backstepping-based adaptive control of a quadrotor UAV with guaranteed tracking performance. ISA Trans. 2020,105, 98–110. [CrossRef] [PubMed] 109. Liang, X.; Fang, Y.; Sun, N.; Lin, H. Dynamics analysis and time-optimal motion planning for unmanned quadrotor transportation systems. Mechatronics 2018,50, 16–29. [CrossRef] 110. Blackburn, D.; Singhose, W.; Kitchen, J.; Patrangenaru, V.; Lawrence, J.; Kamoi, T.; Taura, A. Command shaping for nonlinear crane dynamics. J. Vib. Control 2010,16, 477–501. [CrossRef] 111. Alkomy, H.; Shan, J. Vibration reduction of a quadrotor with a cable-suspended payload using polynomial trajectories. Nonlinear Dyn. 2021,104, 3713–3735. [CrossRef] 112. Huo, X.; Chen, J.; Liu, Q.; He, X. Vibration elimination for quadrotor slung system based on input shaping and double closed-loop control. In Proceedings of the 2019 12th Asian Control Conference (ASCC), Kitakyushu, Japan, 9–12 June 2019; pp. 492–497. 113. Kusznir, T.; Smoczek, J. Sliding mode-based control of a UAV quadrotor for suppressing the cable-suspended payload vibration. J. Control Sci. Eng. 2020,2020, 5058039. [CrossRef] Drones 2024,8, 35 20 of 21 114. Slabber, J.; Jordaan, H.W. Vision-Based Control of an Unknown Suspended Payload with a Multirotor. In Proceedings of the 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Prague, Czech Republic, 27 September–1 October 2021; pp. 4875–4880. 115. Lee, T. Collision avoidance for quadrotor UAVs transporting a payload via Voronoi tessellation. In Proceedings of the 2015 American Control Conference (ACC), Chicago, IL, USA, 1–3 July 2015; pp. 1842–1848. 116. Lee, T. Geometric control of quadrotor UAVs transporting a cable-suspended rigid body. IEEE Trans. Control Syst. Technol. 2017 , 26, 255–264. [CrossRef] 117. Fliess, M.; Lévine, J.; Martin, P.; Rouchon, P. Flatness and defect of non-linear systems: Introductory theory and examples. Int. J. Control 1995,61, 1327–1361. [CrossRef] 118. Qian, L.; Liu, H.H.T. Path-Following Control of A Quadrotor UAV With A Cable-Suspended Payload Under Wind Disturbances. IEEE Trans. Ind. Electron. 2020,67, 2021–2029. [CrossRef] 119. Cabecinhas, D.; Cunha, R.; Silvestre, C. A trajectory tracking control law for a quadrotor with slung load. Automatica 2019 , 106, 384–389. [CrossRef] 120. Faust, A.; Palunko, I.; Cruz, P.; Fierro, R.; Tapia, L. Automated aerial suspended cargo delivery through reinforcement learning. Artif. Intell. 2017,247, 381–398. [CrossRef] 121. Li, R.; Yang, F.; Xu, Y.; Yuan, W.; Lu, Q. Deep Reinforcement Learning-based Swing-Free Trajectories Planning Algorithm for UAV with a Suspended Load. In Proceedings of the 2022 China Automation Congress (CAC), Xiamen, China, 25–27 November 2022; pp. 6149–6154. 122. Urbina-Brito, N.; Guerrero-Sánchez, M.E.; Valencia-Palomo, G.; Hernández-González, O.; López-Estrada, F.R.; Hoyo-Montaño, J.A. A predictive control strategy for aerial payload transportation with an unmanned aerial vehicle. Mathematics 2021 ,9, 1822. [CrossRef] 123. Lee, B.Y.; Lee, H.I.; Yoo, D.W.; Moon, G.H.; Lee, D.Y.; young Kim, Y.; Tahk, M.J. Study on payload stabilization method with the slung-load transportation system using a quad-rotor. In Proceedings of the 2015 European Control Conference (ECC), Linz, Austria, 15–17 July 2015; pp. 2097–2102. 124. Son, C.Y.; Seo, H.; Kim, T.; Kim, H.J. Model predictive control of a multi-rotor with a suspended load for avoiding obstacles. In Proceedings of the 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, QLD, Australia, 21–25 May 2018; pp. 5233–5238. 125. Hanover, D.; Foehn, P.; Sun, S.; Kaufmann, E.; Scaramuzza, D. Performance, precision, and payloads: Adaptive nonlinear MPC for quadrotors. IEEE Robot. Autom. Lett. 2021,7, 690–697. [CrossRef] 126. Faessler, M.; Fontana, F.; Forster, C.; Mueggler, E.; Pizzoli, M.; Scaramuzza, D. Autonomous, vision-based flight and live dense 3D mapping with a quadrotor micro aerial vehicle. J. Field Robot. 2016,33, 431–450. [CrossRef] 127. Tal, E.; Karaman, S. Accurate tracking of aggressive quadrotor trajectories using incremental nonlinear dynamic inversion and differential flatness. IEEE Trans. Control Syst. Technol. 2020,29, 1203–1218. [CrossRef] 128. Sreenath, K.; Lee, T.; Kumar, V. Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load. In Proceedings of the 52nd IEEE Conference on Decision and Control, Philadelphia, PA, USA, 10–12 July 2013; pp. 2269–2274. 129. Torrente, G.; Kaufmann, E.; Föhn, P.; Scaramuzza, D. Data-driven MPC for quadrotors. IEEE Robot. Autom. Lett. 2021 ,6, 3769–3776. [CrossRef] 130. Sun, S.; Romero, A.; Foehn, P.; Kaufmann, E.; Scaramuzza, D. A comparative study of nonlinear MPC and differential-flatnessbased control for quadrotor agile flight. IEEE Trans. Robot. 2022,38, 3357–3373. [CrossRef] 131. Norouzi, A.; Shahpouri, S.; Gordon, D.; Winkler, A.; Nuss, E.; Abel, D.; Andert, J.; Shahbakhti, M.; Koch, C.R. Deep learning based model predictive control for compression ignition engines. Control Eng. Pract. 2022,127, 105299. [CrossRef] 132. Bangura, M.; Mahony, R. Real-time model predictive control for quadrotors. IFAC Proc. Vol. 2014,47, 11773–11780. [CrossRef] 133. Alexis, K.; Nikolakopoulos, G.; Tzes, A. On trajectory tracking model predictive control of an unmanned quadrotor helicopter subject to aerodynamic disturbances. Asian J. Control 2014,16, 209–224. [CrossRef] 134. Nguyen, H.; Kamel, M.; Alexis, K.; Siegwart, R. Model predictive control for micro aerial vehicles: A survey. In Proceedings of the 2021 European Control Conference (ECC), Rotterdam, The Netherlands, 29 June–2 July 2021; pp. 1556–1563. 135. Maza, I.; Kondak, K.; Bernard, M.; Ollero, A. Multi-UAV Cooperation and Control for Load Transportation and Deployment. J. Intell. Robot. Syst. 2009,57, 417–449. [CrossRef] 136. Ariyibi, S.O.; Tekinalp, O. Quaternion-based nonlinear attitude control of quadrotor formations carrying a slung load. Aerosp. Sci. Technol. 2020,105, 105995. [CrossRef] 137. Klausen, K.; Meissen, C.; Fossen, T.I.; Arcak, M.; Johansen, T.A. Cooperative control for multirotors transporting an unknown suspended load under environmental disturbances. IEEE Trans. Control Syst. Technol. 2020,28, 653–660. [CrossRef] 138. Tognon, M.; Gabellieri, C.; Pallottino, L.; Franchi, A. Aerial co-manipulation with cables: The role of internal force for equilibria, stability, and passivity. IEEE Robot. Autom. Lett. 2018,3, 2577–2583. [CrossRef] 139. Wehbeh, J.; Rahman, S.; Sharf, I. Distributed model predictive control for UAVs collaborative payload transport. In Proceedings of the 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Las Vegas, NV, USA, 24 October 2020–24 January 2021; pp. 11666–11672. 140. Gimenez, J.; Gandolfo, D.C.; Salinas, L.R.; Rosales, C.; Carelli, R. Multi-objective control for cooperative payload transport with rotorcraft UAVs. ISA Trans. 2018,80, 491–502. [CrossRef] [PubMed] Drones 2024,8, 35 21 of 21 141. Gimenez, J.; Salinas, L.R.; Gandolfo, D.C.; Rosales, C.D.; Carelli, R. Control for cooperative transport of a bar-shaped payload with rotorcraft UAVs including a landing stage on mobile robots. Int. J. Syst. Sci. 2020,51, 3378–3392. [CrossRef] 142. Lee, T.; Sreenath, K.; Kumar, V. Geometric control of cooperating multiple quadrotor UAVs with a suspended payload. In Proceedings of the 52nd IEEE Conference on Decision and Control, Firenze, Italy, 10–13 December 2013; pp. 5510–5515. 143. Sharma, M.; Sundaram, S. A geometric control approach for multi-UAV cooperative payload transfer. Nonlinear Dyn. 2023 ,111, 10077–10096. [CrossRef] 144. Outeiro, P.; Cardeira, C.; Oliveira, P. Control Architecture for a Quadrotor Transporting a Cable-Suspended Load of Uncertain Mass. Drones 2023,7, 201. [CrossRef] 145. Gabellieri, C.; Tognon, M.; Sanalitro, D.; Franchi, A. Force-based Pose Regulation of a Cable-Suspended Load Using UAVs with Force Bias. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2023, Detroit, MI, USA, 1–5 October 2023. 146. Estevez, J.; Lopez-Guede, J.M.; Graña, M. Quasi-stationary state transportation of a hose with quadrotors. Robot. Auton. Syst. 2015,63 Pt 2, 187–194. [CrossRef] 147. Tagliabue, A.; Kamel, M.; Verling, S.; Siegwart, R.; Nieto, J. Collaborative transportation using mavs via passive force control. In Proceedings of the 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore, 29 May–3 June 2017; pp. 5766–5773. Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.