Cooperative Transportation of a Flexible Payload Using Two Quadrotors

I N RECENT years, unmanned aerial vehicles (UAVs), especially quadrotors, and their applications have received significant attention. Applications have included mapping [1], aerial transportation [2], construction [3], and so on. A popular approach for aerial transportation is to connect the cargo to the quadrotor with a cable. A lot of work has been done to solve the dynamics, control, and navigation problem of such a slung load system [4–7]. The key challenge of such a system is that the cable-suspended payload increases the degrees of freedom to be controlled; i.e., the payload oscillation has to be controlled with limited sensors and actuators. Usually, the payload capacity of a quadrotor is limited. Hence, to manipulate a heavy payload or ensure the agility of the transportation system, one possible solution is to use multiple quadrotors cooperatively. In general, similar to the payload transportation using a quadrotor, there are mainly two ways to mount the cargo to the quadrotor body, i.e., the cable-suspended or grasping approach. Many works on cooperative aerial transportation using these two approaches have been reported in the literature [8–10]. For the cooperative transportation of a cable-suspended payload, the swinging payload changes the dynamic behaviors of the quadrotor systems significantly, and it is quite challenging to build the accurate model considering that the cables may be flexible or even slack. The differential flatness property of such a cooperative transportation system of a cable-suspended payload is discussed in [9] to define dynamically feasible trajectories. The cables can, in a sense, be considered as the actuators for the payloadmovement; i.e., to drive the payload to track the desired trajectory, one can derive the necessary cable tensions, based on which the control commands for quadrotors are obtained. For example, Geng and Langelaan proposed a load-leading control method for the cooperative manipulation of a cable-suspended payload using multiple quadrotors to drive the payload to track the desired trajectory [2]. Masone et al. considered the cooperative transportation system of a cable-suspended payload as a reconfigurable cable-driven parallel robot and designed a controller based on the internal motion between payload and quadrotors [11]. Another method is to realize the transportation of cable-suspended payload based on the formation flying of a group of quadrotors. For instance, Qian and Liu designed a hierarchical controller based on a velocity stabilization control to stabilize the payload and drive the quadrotors along a given trajectory [12]. Tagliabue et al. presented an admittance control method under a master–slave architecture for quadrotors carrying a heavy payload via spherical joints or short cables, which implies that the quadrotor attitude motions are decoupled from the payloadmotion [10]. Furthermore, some researchers have considered cable flexibility. For example, Goodarzi andLee built coordinate-free dynamics equations for the cooperative transportation of a cablesuspended payload by modeling the cables as a serial connection of links and designed a controller based on the linearized equations of motion [13]. Ariyibi and Tekinalp developed a simulation model for the systemof two quadrotors carrying a load using flexible cables and designed a formation controller to realize the quadrotor control [14]. To avoid the difficulties caused by the cables and enable a direct control of the payload’s state, some scholars have studied themanipulation of a payload using aerial graspers ormanipulators [15–21]. For instance, Kim et al. equipped the quadrotor with a robotic arm and studied the transportation of a slender payload using two quadrotors based on a motion planner and a robust controller [17]. The same research group has also considered problems such as efficientmotion planning [18] and collision avoidance [19] for such a group of aerial manipulators. Mellinger et al. modeled multiple quadrotors grasping a payload as a large multirotor and presented a control method to drive the system to track a 3D trajectory [20]. Loianno and Kumar focused on the state estimation, path planning, and coordinated control of the aerial transportation of a heavy payload using permanent electromagnets to connect the payload to quadrotors’ bodies [21]. Overall, unlike quadrotors transporting a cable-suspended payload, quadrotors in payload transportation via rigid connectors are strongly coupled; i.e., the movement of any quadrotor will definitely affect the behaviors of other quadrotors and payload. To reduce the complexity of the entire system, this paper focuses on the transportation of a flexible payload connected to two quadrotors using permanent magnets. Therefore, there is no relative movement between the quadrotor body and the connection point on the payload. For such a system, Refs. [20,21] modeled the entire system as a large multirotor and allocated control commands for all quadrotors based on the relative position and orientation between quadrotors in the team. However, in some cases, the payload to be transported may not be rigid, such as the flexible ring [22] or flexible hose [23]. For a flexible payload, aerial manipulation probably causes the payload vibrating [22,24], which will change the relative pose between quadrotors. Consequently, the possible payload deformation will introduce significant challenges in dynamics modeling and controller design. In [22], Ritz and D’Andrea considered the transportation of a thin and flexible ring using six quadrotors. Essentially, they modeled the ring individually by treating thevehicles as some special actuators based on the assumption that each quadrotor can generate two scalar inputs. Motivated by active firefighting using hoses to carry water, Kotaru and Sreenath built the system model using small links to approximate the continuous hose, analyzed its differential flatness, and designed a state feedback controller based on linear–quadratic regulator (LQR) [23]. Essentially, they used the idea similar to the dynamic modeling of the flexible cable in [13] todescribe the behavior of such a flexiblehose.To the best of the authors’ knowledge, there are not many works on the Received 11 January 2021; revision received 19 May 2021; accepted for publication 22May 2021; published online 7 July 2021. Copyright © 2021 by Ti Chen, Jinjun Shan, and Hugh Liu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC atwww.copyright. com; employ the eISSN 1533-3884 to initiate your request. See also AIAA Rights and Permissions www.aiaa. org/randp. *Professor, State Key Laboratory ofMechanics and Control ofMechanical Structures, 29 Yudao Street, Jiangsu; chenti@nuaa.edu. cn. Member AIAA. Professor, Department of Earth and Space Science and Engineering, 4700 Keele Street; jjshan@yorku.ca. Associate Fellow AIAA (Corresponding Author). Professor, The Institute for Aerospace Studies, 4925 Dufferin Street, liu@utias.utoronto. ca. Associate Fellow AIAA.