## 1 Introduction  
The cooperative control of multi-quadrotor systems has progressively attracted attention of researchers in both civil and military areas [1]. Especially, in the application of object transportation, the formation of multiple quadrotors has potential application significance [2; 3; 4; 5; 6]. The formation control problem can be categorized into two types. Namely, the formation producing problem and the formation tracking problem [7]. The former problem refers to the algorithm design for a group of vehicles to reach a predefined geometric pattern without a group reference [8; 9; 10], while the latter problem refers to the same task and meanwhile following a predefined trajectory [11; 12; 13]. The object transformation is a typical formation tracking problem, which is considered in this paper. An external reference formation trajectory (RFT) is given to the leading quadrotor(s) to guide the formation. We note that in the case of multiple leaders, they share the same RFT. According to [14; 15], the formation tracking problem can be attributed as a consensus problem. In most aggressive maneuver cases, the quadrotor is controlled in tracking a desired aggressive moving trajectory that is prescribed a prior, for instance, by polynomials w.r.t time. A widely used method is the control of geometry on Lie group (\(SE(3)\) for example). The aggressive formation problem of multiple quadrotors is investigated in [16], where the quadrotors are permitted to move quickly in 3-D environment with a tight formation. The formation of quadrotors is based on proper trajectory generation process, thereby, the full information of the trajectory (including each order derivatives) are known. However, in a multi-agent system with neighbor-based decentralized control, it is impossible to enforce the motion of quadrotor by generating polynomials-based trajectories. The flatness-based control is frequently used in the trajectory planning for high-order dynamical system. For instance, the time-optimal trajectory generation problem is in vestigated for helicopter landing in [17] and for multi-rotor in [18]. Especially, in [18], the trajectory is planned in real-time. The agile maneuvers for a quadrotor with a cable-suspended load are investigated in [19]. In this work, by means of flatness-based planning, the air vehicle is able to behave in aggressive maneuver, real-time collision avoidance, and time optimal flight. However, the planned trajectory's high-order derivatives are required for the quadrotor. In the decentralized formation tracking control of quadrotors, each quadrotor (including the leader) has to behave according to the state of neighbors, which are in general not able or difficult to get the full information of these states. In multi-agent systems, the consensus speed of agents with linear dynamics depends on the minimum non-singular eigenvalue of the interaction matrix (or Laplacian) [20] and the absolute value of the maximum pole in left half plane of agent dynamics [21]. For the formation of quadrotors, the idea in this paper is to propose a nonlinear formation controller, in order to use these existing results. One of the difficulties in the control of multi-quadrotor systems is that the quadrotor has under-actuated, nonlinear, and coupling dynamics. The existing consensus algorithms in the literature, which are mostly developed for single-integrator or double-integrator agent dynamics, have not satisfactory formation performance for the formation control of quadrotors in practice, especially in aggressive formation tracking where the small angle assumption should be removed. Furthermore, lacking velocities and its higher derivatives of the neighbors' states and the RFT makes aggressive formation non-trivial. Nevertheless, in very recent years, the researchers start to consider the nonlinearities/disturbances in formation control [1,22]. In this paper, we aimed at proposing an aggressive control framework for a class of systems with high-order dynamics (in special, quadrotor).