A cooperative obstacle avoidance control scheme for multi-quadrotor UAV formation: a hierarchical control approach

Multi-quadrotor unmanned aerial vehicles (UAVs) are defined by their multirotor actuation features and multiple degrees of freedom, which enable flexible trajectory tracking and agile attitude adjustment^[1−3]. These capabilities make multi-quadrotor UAVs well suited for cooperative missions. Using cooperative control algorithms, multi-quadrotor UAV systems can accomplish swarm tasks, supporting applications such as load transportation^[4], target surveillance^[5], and search and strike^[6]. When obstacle-free scenarios are considered, formation control can be addressed effectively. However, in practical mission scenarios, the spatial constraints imposed by complex three-dimensional (3D) obstacle environments tightly couple formation maintenance with obstacle avoidance. This poses challenges for conventional cooperative control algorithms in achieving both objectives simultaneously.

The main formation control strategies include virtual structure methods^[7−9], behavior-based methods^[10−12], and consensus algorithms^[13−15]. Belkacem et al.^[16] developed a distributed algorithm for achieving consensus tracking in second-order multiagent systems that avoids the chattering effect typically induced by traditional sliding-mode control protocols. Zhang et al.^[17] framed a leader–follower cooperative guidance law via backstepping approach based on graph theoretic communication topology. Ollervides-Vazquez et al.^[18] developed a sectorial fuzzy consensus approach for the formation flight of multi-quadrotor UAVs based on the Newton–Euler model and a sectorial fuzzy controller. Miao et al.^[19] introduced a distributed formation control scheme that operates without requiring outer-loop linear velocity or inner-loop angular velocity measurements. In distributed formation control, individual coordination is strongly linked to collective behavior, with heavy reliance on cooperative error feedback and accurate system models. This reliance reduces flexibility and substantially complicates controller design as system complexity increases. Moreover, multifunctionality and scalability are often constrained by packaging limitations. Accordingly, Wang et al.^[20] presented a hierarchical distributed control framework that decouples the problem into a reference generation layer and a tracking control layer. Furthermore, Wang et al.^[21] investigated the consensus problem of second-order leader–follower systems with velocity constraints and developed a hierarchical constrained distributed control scheme.

Unknown obstacles in practical mission scenarios pose a critical challenge to the safety of cooperative formations. Consequently, various approaches have been proposed for obstacle avoidance, including graph search algorithms^[22], genetic algorithms^[23], and reinforcement learning methods^[24]. Compared with the aforementioned methods, the artificial potential field (APF) method guides the agent by superimposing an attractive potential toward the goal and a repulsive potential away from obstacles, thereby generating an obstacle avoidance trajectory from the start to the goal^[25]. As the APF method features structural simplicity, real-time implementability, and rapid responsiveness to environmental changes, it has been widely applied to collision avoidance^[26−28] and obstacle avoidance^[29−31]. Matoui et al.^[32] developed a centralized APF-based planner to generate trajectories for multirobot systems that operate in dynamic environments. Hu et al.^[33] reported an integrated approach that combines Voronoi partitions with a conventional APF to achieve distributed formation control and collision avoidance. To mitigate the inherent local minima and oscillatory behavior of conventional APF methods, Pan et al.^[34] developed a hybrid formation control scheme by combining a rotational potential field with a leader–follower strategy, enabling follower UAVs to maintain prescribed relative angles and distances with respect to the leader. Huang et al.^[35] introduced a parallel search strategy to mitigate the local minimum trap and goal inaccessibility problems that arise near obstacles in conventional APF methods. For dynamic obstacle avoidance, Wang et al.^[36] modified the repulsive potential function and introduced an adaptive repulsion coefficient that depends on the obstacle velocity. Furthermore, Liu et al.^[37] developed an improved repulsive force with a continuously differentiable regulation mechanism, which eliminates the influence of obstacles outside the detection range. Despite the proven feasibility of existing formation obstacle avoidance methods, the limited flexibility of traditional distributed control frameworks poses a challenge.

Inspired by the aforementioned research, this paper proposes a hierarchical distributed formation obstacle avoidance control scheme for multi-quadrotor UAVs in 3D obstacle environments. The proposed design consists of three steps. First, to cope with the increased collision risks induced by 3D obstacles during formation maneuvering, the formation is enclosed by a virtual sphere whose center is the virtual leader, and an adaptive artificial potential field (AAPF)-based planner is used to generate an obstacle avoidance trajectory for this sphere so that the entire formation can pass through cluttered spaces safely. Second, a distributed reference signal generator is designed to maintain the desired formation configuration and produce obstacle avoidance reference trajectories for the multi-quadrotor UAVs by embedding the virtual leader's planned trajectory. Finally, the generator outputs are taken as the reference trajectories for each multi-quadrotor UAV, and extended state observer (ESO)-based composite controllers are designed to achieve trajectory tracking under conditions of disturbances and uncertainties. The main contributions of this paper are twofold:

1. By incorporating an adaptive gain mechanism into the repulsive force, the proposed AAPF method alleviates oscillations near the obstacle avoidance boundary that commonly arise in traditional APF schemes. This design reduces sensitivity to gain tuning and enhances adaptability across different scenarios.

2. The proposed control scheme decouples the traditional distributed formation obstacle avoidance problem into a two layer structure, based on the virtual leader's obstacle avoidance trajectory planned by the AAPF method. This hierarchical framework improves the flexibility and robustness of the system design.

The rest of this paper is organized as follows. Section “Preliminaries and problem formulation” provides the preliminaries and formulates the problem. Section “Main Results” develops a hierarchical distributed formation obstacle avoidance control scheme for multi-quadrotor UAV systems. Section “Experiments” reports experimental validations and discusses the results. Finally, some conclusions are drawn in Section “Conclusions”.

Notations: $ \mathbb{R}^n $ denotes the set of $ n $-dimensional real vectors, and $ \mathbb{R}^{n\times m} $ denotes the set of $ n\times m $ real matrices. Let $ {\bf{0}}_m=[0,\ldots,0]^T\in\mathbb{R}^m $ and $ {\bf{0}}_{n\times m}\in\mathbb{R}^{n\times m} $ be the zero vector and the zero matrix, respectively. $ {I}_n \in \mathbb{R}^{n \times n} $ denotes the $ n \times n $ identity matrix. For a symmetric matrix $ A\in\mathbb{R}^{n\times n} $, $ \lambda_{\min}(A) $ and $ \lambda_{\max}(A) $ denote its smallest and largest eigenvalues, respectively. The Euclidean norm of a vector is denoted by $ \|\cdot\|_2 $. A basic property of the Rayleigh quotient is that, for any symmetric matrix $ {\boldsymbol{P}} \in \mathbb{R}^{n \times n} $ and nonzero vector $ {\boldsymbol{x}} \in \mathbb{R}^n $, $ \lambda_{\min}({\boldsymbol{P}})\|{\boldsymbol{x}}\|_2^2 \le {{\boldsymbol{x}}^T {\boldsymbol{P}} {\boldsymbol{x}}} \le \lambda_{\max}({\boldsymbol{P}})\|{\boldsymbol{x}}\|_2^2 $.

Graph theory notions

For the leader–follower case, node $ 0 $ represents the leader, whereas nodes $ 1,\ldots,N $ represent the followers. The communication topology among the followers is described by an undirected graph $ G = ({\cal{V}}, {\cal{E}}, {\cal{A}}) $, where $ {\cal{V}} = \{1, \ldots, N\} $ is the node set, $ {\cal{E}} \subseteq {\cal{V}} \times {\cal{V}} $ is the edge set, and $ {\cal{A}} = [a_{ij}] \in \mathbb{R}^{N \times N} $ is the weighted adjacency matrix with $ a_{ij} = a_{ji} \gt 0 $ if $ (j, i) \in {\cal{E}} $, whereas $ a_{ij} = 0 $ otherwise, and $ a_{ii} = 0, \forall i \in {\cal{V}} $. The neighbor set of node $ i $ is $ {\cal{N}}_i = \{j \in {\cal{V}} \mid (j,i) \in {\cal{E}}\} $. The Laplacian matrix of $ G $ is $ L = [l_{ij}] \in \mathbb{R}^{N \times N} $, where $ l_{ii} = \sum_{j \in {\cal{N}}_i} a_{ij} $ and $ l_{ij} = -a_{ij} $ for $ i \neq j $. An undirected graph is connected if there is a path between each node pair. The overall graph including the leader and followers is denoted by a directed graph $ \bar{G} $ with the node set $ \bar{{\cal{V}}} = \{0\} \cup {\cal{V}} $. The communication from the leader to follower $ i $ is unidirectional with an edge weight $ b_i $, where $ b_i \gt 0 $ if connected and $ b_i = 0 $ otherwise. Define $ B = \text{diag}\{b_1, \ldots, b_N\} $ and $ M = L + B $. A directed graph has a directed spanning tree if at least one node has paths to all other nodes.

Useful lemmas

Lemma 1. If a directed graph $ \bar{G} $ contains at least one directed spanning tree (i.e., $ B \neq 0 $), then its graph matrix $ M $ is positive definite^[38].

Lemma 2. Let $ x, y \in \mathbb{R} $, and let $ \varkappa \gt 0 $ be an arbitrary positive constant. Suppose the constants $ p \gt 1 $ and $ q \gt 1 $ satisfy the conjugacy condition $ (p - 1)(q - 1) = 1 $. Then, $ xy $ holds $ xy \leq \dfrac{\varkappa^p}{p} |x|^p + \dfrac{1}{q \varkappa^q} |y|^q $^[39].

Definition 1. Consider the system $ \dot{x}=f(t,x,u) $, where $ f:[0,+\infty)\times \mathbb{R}^n\times \mathbb{R}^m\to\mathbb{R}^n $ is piecewise continuous in $ t $, and locally Lipschitz in $ x $ and $ u $. The input $ u(t) $ is a piecewise continuous, bounded function of $ t $ for all $ t\ge 0 $. The system $ \dot{x}=f(t,x,u) $ is said to be input-to-state stable (ISS) if there exist a class $ {\cal{K}}{\cal{L}} $ function $ \beta(\cdot,\cdot) $ and a class $ {\cal{K}} $ function $ \gamma(\cdot) $ such that for any initial state $ x(t_0) $ and bounded input $ u(t) $, the solution $ x(t) $ exists $ \forall t \geq t_0 $ and satisfies $ \|x(t)\|_2 \le \beta\big(\|x(t_0)\|_2, \,t-t_0\big) + \gamma \left(\sup_{t_0\le \tau \le t}\|u(\tau)\|_2\right) $^[40].

Lemma 3. Suppose $ f $ in Definition 1 is continuously differentiable and globally Lipschitz in $ (x,u) $, uniformly in $ t $. If the unforced system $ \dot{x}=f(t,x,{\bf{0}}_m) $ is globally uniformly exponentially stable at the origin, then the system is ISS.^[40]

System modeling and problem formulation

System modeling

A team of $ N $ multi-quadrotor UAVs operating in a 3D workspace is considered. Two coordinate frames are adopted. The inertial-reference frame is denoted by $ {\cal{F_e}}=\{O_e,X_e,Y_e,Z_e\} $, the origin $ O_e $ is fixed at a designated point on the ground, the $ O_eX_e $-axis can be chosen to point along an arbitrary horizontal direction, the $ O_eZ_e $-axis is perpendicular to the ground and points upward, and the $ O_eY_e $-axis follows the right-hand rule to complete a right-handed triad. The body-reference frame attached to each UAV is denoted by $ {\cal{F_b}}=\{O_b,X_b,Y_b,Z_b\} $, the origin $ O_b $ is fixed at the UAV's center of mass, the $ O_bX_b $-axis aligns with the body-forward direction, the $ O_bZ_b $-axis is normal to the UAV body plane, and the $ O_bY_b $-axis follows the right-hand rule. Each UAV generates control forces and moments by independently regulating the rotational speeds of four rotors, thereby producing a total thrust along the $ O_bZ_b $-axis and three body torques about the $ O_bX_b $, $ O_bY_b $, and $ O_bZ_b $-axes.

The communication among the multi-quadrotor UAVs is described by an undirected graph $ G=({\cal{V}},{\cal{E}},{\cal{A}}) $, where $ {\cal{V}}=\{1,\ldots,N\} $ is the set of follower UAVs, $ {\cal{E}} \subseteq\cal{V}\times{\cal{V}} $ is the set of undirected communication links, and $ {\cal{A}}=[a_{ij}] $ is the associated weighted adjacency matrix. An undirected edge $ (j,i)\in{\cal{E}} $ indicates that UAVs $ i $ and $ j $ can exchange information with each other. Accordingly, the neighbor set of UAV $ i $ is defined as $\mathcal N_i=\{j\in\mathcal V\mid (j,i)\in\mathcal E\}$. The overall leader–follower interaction topology is represented by a directed graph $ \bar G $ with a node set $ \bar{{\cal{V}}}=\{0\}\cup{\cal{V}} $, where node $ 0 $ represents the virtual leader and each node $ i\in{\cal{V}} $ corresponds to a follower UAV. The graph $ \bar G $ is assumed to include at least one directed spanning tree.

The inner–outer-loop structure is employed to facilitate controller design for the multi-quadrotor UAVs. The outer (position) loop generates the desired thrust and attitude commands for the inner loop. The inner (attitude) loop, typically implemented by an onboard proportional–integral–derivative (PID) module, ensures fast attitude stabilization and tracking. This cascaded architecture enables outer-loop trajectory tracking for formation and obstacle avoidance tasks while preserving the fast response and robustness of the inner-loop attitude dynamics. The position loop model of the $ i $th multi-quadrotor UAV is given by

where $ \ddot{\boldsymbol{q}}_i=[\ddot{x}_i,\ddot{y}_i,\ddot{z}_i]\mathrm{^T} $ denotes the translational acceleration expressed in $ {\cal{F_e}} $ and $ \boldsymbol{q}_i=[x_i,y_i,z_i]\mathrm{^T} $ represents the position vector of the $ i $-th UAV in $ {\cal{F_e}} $. The thrust vector in $ {\cal{F_b}} $ is $ \boldsymbol{F}_{bi}=[0,0,F_i]\mathrm{^T} $, where $ F_i $ is the total thrust acting along the $ O_b Z_b $-axis. Here, $ m_i $ represents the mass of UAV $ i $, $ \boldsymbol{G}=[0,0,g]\mathrm{^T} $ denotes the gravity vector, and $ {\boldsymbol{d}}_i^{p}\in\mathbb{R}^3 $ denotes the lumped disturbance accounting for external disturbances and model uncertainties. Moreover, $ {\boldsymbol{R_i}} $ denotes the rotation matrix from $ \cal{F_b} $ to $ \cal{F_e} $, which is expressed as

where $ c \triangleq \cos $, $ s \triangleq \sin $, and $ \phi_i $, $ \theta_i $, and $ \psi_i $ are the Euler angles of UAV $ i $.

To address the underactuation of the position subsystem, the virtual control input $ {\boldsymbol{u}}_i = {\boldsymbol{R}}_i\dfrac{{\boldsymbol{F}}_{bi}}{m_i} $ is defined, where $ \boldsymbol{u}_i=[u_{xi},u_{yi},u_{zi}]\mathrm{^T} $, $ i \in{\cal{V}} $. Then, the translational dynamics of the $ i $th UAV are given by

The Euler-angle kinematics satisfy $ \dot{{\boldsymbol{\Theta}}}_i={\boldsymbol{T}}({\boldsymbol{\Theta}}_i){\boldsymbol{\omega}}_i $, where $ \boldsymbol{\Theta}_i=[\phi_i,\theta_i,\psi_i]\mathrm{^T} $ collects the roll, pitch, and yaw angles, $ \dot{\boldsymbol{\Theta}}_i=[\dot{\phi}_i,\dot{\theta}_i,\dot{\psi}_i]^{\mathrm{T}} $ denotes the Euler-angle rate vector, $ \boldsymbol{\omega}_i=[\omega_{x_i},\omega_{y_i},\omega_{z_i}]\mathrm{^T} $ denotes the angular velocity expressed in $ {\cal{F_b}} $, and $ {\boldsymbol{T}}({\boldsymbol{\Theta}}_i) $ is the associated transformation matrix given by

where $ c \triangleq \cos $, $ s \triangleq \sin $, and $ t \triangleq \tan $.

The attitude dynamics of the $ i $th multi-quadrotor UAV under lumped disturbances are described by the following equation:

where $ J_i = \text{diag}\{ J_{xx_i}, J_{yy_i}, J_{zz_i} \} $ is the inertia matrix, $ \boldsymbol{\tau}_i=[\tau_{x_i},\tau_{y_i},\tau_{z_i}]\mathrm{^T} $ denotes the control moment vector in $ {\cal{F_b}} $, and $ \boldsymbol{d}_i^a=[d_i^{\phi},d_i^{\theta},d_i^{\psi}]\mathrm{^T} $ represents the lumped disturbance vector of the attitude loop.

Remark 1. The obstacle is modeled in the inertial-reference frame $ {\cal{F_e}} $ as a vertical cylinder capped by an upper hemisphere. The center of the cylinder base is denoted by $ {\boldsymbol{c}}=[x_c,y_c,z_c]^{\rm{T}}\in\mathbb{R}^3 $, where $ z_c=0 $ when the obstacle rests on the ground plane. The cylinder radius and height are $ r_o>0 $ and $ h_o>0 $, respectively. The cylinder–hemisphere model provides a compact and practical geometric representation for common 3D obstacles. The hemispherical top removes the sharp rim of a pure cylinder, yielding a smoother boundary and well-defined repulsive directions near the top region. Moreover, the repulsive-force computation for both the cylindrical and hemispherical parts can be carried out using a unified formula, which reduces computational complexity and facilitates real-time AAPF-based trajectory planning.

Problem formulation

A team of $ N $ multi-quadrotor UAVs, indexed by $ {\cal{V}}=\{1,\ldots,N\} $, is considered to operate in a cluttered 3D environment containing cylinder–hemisphere obstacles. The formation center is selected as a virtual leader, whose motion is described by the first-order kinematics

where $ {\boldsymbol{q}}_0=\big[x_0,\,y_0,\,z_0\big]^{\rm{T}}\in\mathbb{R}^3 $ and $ {\boldsymbol{v}}_0=\big[v_{x0},\,v_{y0},\,v_{z0}\big]^{\rm{T}}\in\mathbb{R}^3 $ denote the virtual leader position and velocity, respectively, with $ {\boldsymbol{v}}_0 $ generated by the AAPF-based planner to achieve 3D obstacle avoidance.

Conventional schemes enforce formation coordination directly on the states of the multi-quadrotor UAVs, thereby coupling coordination with tracking transients and uncertainties. A distributed reference signal generator is developed over a network of second-order virtual agents to decouple reference generation from tracking. The virtual agent network inherits the communication topology of the multi-quadrotor UAV system. Through local information exchanges, it propagates the leader reference and generates reference signals for all multi-quadrotor UAVs. The dynamics of the virtual agent are formulated as

where $ {\boldsymbol{u}}_i^*=[u_{xi}^*,\,u_{yi}^*,\,u_{zi}^*]^{\rm{T}}\in\mathbb{R}^3 $ is the control input, $ \boldsymbol{q}_i^*=[x_i^*,\, y_i^*,\, z_i^*]\mathrm{^T} $ and $ \boldsymbol{v}_i^*=[v_{xi}^*,\, v_{yi}^*,\, v_{zi}^*]\mathrm{^T} $ represent the position and velocity of the $ i $-th virtual agent, respectively.

The objective is to guide the multi-quadrotor UAV formation from a given initial position to a desired goal in a 3D obstacle environment while maintaining the prescribed formation configuration and ensuring obstacle avoidance. A hierarchical distributed formation obstacle avoidance control scheme is proposed, as depicted in Fig. 1. At the reference signal generation layer, an AAPF-based planner generates a 3D obstacle avoidance trajectory for the virtual leader $ {\boldsymbol{q}}_0 $ such that the formation enclosing sphere remains collision-free, i.e., the clearance distance between the surfaces of the formation enclosing sphere and the obstacle satisfies $ d_{{\rm{obs}}}({\boldsymbol{q}}_0)=\|{\boldsymbol{q}}_0- $ $ {\boldsymbol{q}}_{{\rm{obs}}}({\boldsymbol{q}}_0)\|_2- r_{{o}}-r_{ f}>0 $. Here, the formation is enclosed by $ {\cal{B}}({\boldsymbol{q}}_0,r_{ f}) $ centered at $ {\boldsymbol{q}}_0 $, where the formation radius satisfies $ \|{\boldsymbol{q}}_i-{\boldsymbol{q}}_0\|_2 \le r_{ f} $, equivalently $ r_{ f}=\max_{i\in{\cal{V}}}\|{\boldsymbol{q}}_i-{\boldsymbol{q}}_0\|_2 $. Meanwhile, a distributed reference signal generator propagates $ ({\boldsymbol{q}}_0,{\boldsymbol{v}}_0) $ to a network of second-order virtual agents through local communication and incorporates the prescribed offsets $ {\boldsymbol{h}}_i=\big[h_{xi},h_{yi},h_{zi}\big]^{\rm{T}} $, i.e., the desired relative displacement of UAV $ i $ with respect to the virtual leader, thereby yielding formation-consistent references that satisfy $ \lim_{t\to+\infty}\|{\boldsymbol{q}}_i^*(t)-{\boldsymbol{q}}_0(t)-{\boldsymbol{h}}_i\|_2=0 $ and $ \lim_{t\to+\infty}\|{\boldsymbol{v}}_i^*(t)-{\boldsymbol{v}}_0(t)\|_2= 0 $. At the multi-quadrotor UAV trajectory tracking layer, each UAV employs a local composite controller to track its reference trajectory, thereby ensuring formation maintenance and safe obstacle avoidance in the 3D obstacle environment.

Figure 1. 

Block diagram of the hierarchical distributed formation obstacle avoidance control scheme.

The AAPF method is utilized for 3D motion planning. The goal generates an attractive potential, whereas obstacles generate repulsive potentials. Formation-level safety is enforced by enclosing the formation within a safety sphere and activating the repulsive action when the sphere-obstacle clearance falls below a prescribed obstacle avoidance threshold. The virtual leader advances in the direction of the resultant force, guiding the formation toward the target while avoiding obstacles.

Attractive field and force design

The attractive potential is expressed as^[25]

where $ {\boldsymbol{q}}_0 $ represents the virtual leader's position and $ \boldsymbol{q}_{\rm{goal}}= [x_g,\, y_g,\, z_g]^{\mathrm{T}} $denotes its desired goal position. The Euclidean distance from the virtual leader to the goal is defined as $ d_{{\rm{goal}}}({\boldsymbol{q}}_0,{\boldsymbol{q}}_{{\rm{goal}}})=\|{\boldsymbol{q}}_0-{\boldsymbol{q}}_{{\rm{goal}}}\|_2 $, and $ K_{{\rm{att}}}>0 $ is the attractive gain.

The attractive force is given by

Repulsive field and force design

The equivalent obstacle center $ {\boldsymbol{q}}_{{\rm{obs}}}({\boldsymbol{q}}_0) $ is introduced to unify the repulsive action for the cylinder and hemisphere, and it is determined by the virtual leader position $ {\boldsymbol{q}}_0 $:

where $ z_0 $ is the virtual leader's altitude, $ h_o $ is the cylinder height, and $ {\boldsymbol{c}}=[x_c,y_c,z_c]^{\rm{T}}\in\mathbb{R}^3 $ represents the center of the cylinder base.

The repulsive term is activated when the formation-enclosing sphere enters the obstacle-avoidance region. Therefore, the repulsive potential is defined as

where $ d_0>0 $ denotes the obstacle avoidance threshold, i.e., the distance between the obstacle surface and the boundary of the avoidance region. The condition $ d_{{\rm{obs}}}({\boldsymbol{q}}_0)\le d_0 $ indicates that the formation-enclosing sphere has entered the avoidance region, and thus the repulsive potential is activated to generate an avoidance action.

Remark 2. The 3D obstacle avoidance is implemented at the formation level by enclosing the multi-quadrotor UAV formation within $ {\cal{B}}({\boldsymbol{q}}_0,r_f) $. For a cylinder-hemisphere obstacle standing on the ground plane, where $ z_c=0 $, the equivalent obstacle center in Eq. (10) is chosen as $ [x_c,\, y_c,\, z_0]\mathrm{^T} $ for $ z_0 \le h_o $ and as $ [x_c,\, y_c,\, h_o]\mathrm{^T} $ for $ z_0 \gt h_o $, so that the repulsive action is consistently applied to both the cylindrical part and the hemispherical cap.

The repulsive gain is adaptively adjusted as a distance-dependent function:

where $ \Delta K_{{\rm{rep}}}=K_{{\rm{rep}}}^{\max}-K_{{\rm{rep}}}^{\min} $, with $ K_{{\rm{rep}}}^{\min} $ and $ K_{{\rm{rep}}}^{\max} $ are the minimum and maximum repulsive gains, respectively.

The repulsive force is given by

Remark 3. The repulsive gain is adjusted linearly between $ K_{\text{rep}}^{\text{min}} $ and $ K_{\text{rep}}^{\text{max}} $ according to the proximity to the obstacle. Specifically, as $ d_{{\rm{obs}}}({\boldsymbol{q}}_0) $ decreases from $ d_0 $ to $ 0 $, $ K_{\text{rep}}^{*} $ increases linearly from $ K_{\text{rep}}^{\text{min}} $ to $ K_{\text{rep}}^{\text{max}} $, yielding stronger repulsion near obstacles while preserving smooth transitions in the control action.

Accordingly, the resultant force is computed as

Remark 4. In the traditional APF method, a fixed repulsive gain is typically selected. When the repulsive gain is chosen inappropriately, it may cause overly aggressive avoidance maneuvers near the safety boundary or result in an insufficient avoidance response, thereby increasing the risk of collision. Therefore, an adaptive repulsive gain mechanism is introduced, which reduces sensitivity to parameter tuning and mitigates chattering in the repulsive force.

Distributed reference signal generator design

The virtual leader's control input is obtained from the resultant force generated by the AAPF method:

where $ {\boldsymbol{q}}_0=[x_0,y_0,z_0]^T\in\mathbb{R}^3 $ and $ {\boldsymbol{v}}_0=[v_{x0},v_{y0},v_{z0}]^T\in\mathbb{R}^3 $ represent the virtual leader's position and velocity, respectively.

Remark 5. The obstacle avoidance trajectory is generated by planning the motion of the virtual leader $ {\boldsymbol{q}}_0 $. In the AAPF method, the virtual leader is treated as a kinematic agent driven by the resultant force $ {\boldsymbol{\Gamma}}^*_{{\rm{total}}}({\boldsymbol{q}}_0) $ in Eq. (15), which is composed of an attractive term pulling the virtual leader toward the goal and a repulsive term preventing collisions with obstacles. For the cylinder–hemisphere obstacles, the repulsive direction is determined by the equivalent obstacle center in Eq. (10). The repulsive term is activated only when the surface-to-surface clearance $ d_{{\rm{obs}}}({\boldsymbol{q}}_0) $ between the formation-enclosing sphere and the obstacle is less than or equal to the obstacle avoidance threshold distance $ d_0 $. Therefore, Eq. (15) provides a 3D obstacle avoidance reference trajectory for the virtual leader, which is subsequently embedded into the distributed reference signal generator to generate multi-quadrotor UAV reference trajectories.

Assumption 1. The virtual leader reference trajectory generated by the AAPF method is admissible (i.e., feasible for implementation). For analytical tractability, the virtual leader velocity is idealized as a constant vector in the subsequent stability analysis, i.e., $ \dot{{\boldsymbol{v}}}_0(t)={\bf{0}}_3 $.

The distributed reference signal generator produces the formation obstacle avoidance reference trajectories for the multi-quadrotor UAVs as

where $ {\boldsymbol{q}}_i^*=[x_i^*,y_i^*,z_i^*]^T\in\mathbb{R}^3 $ and $ {\boldsymbol{v}}_i^*=[v_{xi}^*,v_{yi}^*,v_{zi}^*]^T\in\mathbb{R}^3 $ represent the position and velocity generated by the generator, respectively, and $ \mu_1,\mu_2>0 $ are design gains. Moreover, $ {\boldsymbol{h}}_i\in\mathbb{R}^3 $ and $ {\boldsymbol{h}}_j\in\mathbb{R}^3 $ are the formation configuration vectors of the $ i $-th and $ j $-th virtual agents with respect to the virtual leader, respectively.

The formation tracking errors of the generator are defined as

Based on Eqs. (16)–(18), the formation tracking error system is

As the $ x $, $ y $, and $ z $ components of the generator formation tracking error are decoupled, the one-dimensional analysis can be directly extended to the 3D case. The one-dimensional error dynamics are given by

where $ \tilde{{\boldsymbol{q}}} = [\tilde{{q}}_1, \dots, \tilde{{q}}_N]^T \in \mathbb{R}^{N} $ and $ \tilde{{\boldsymbol{v}}} = [\tilde{{v}}_1, \dots, \tilde{{v}}_N]^T \in \mathbb{R}^{N} $.

Proposition 1. If Assumption 1 is satisfied, the origin of the error dynamics associated with the distributed reference signal generator given by Eqs (16) and (17) is exponentially stable. The formation position and velocity tracking errors satisfy $ \lim_{t\to+\infty}\tilde{{\boldsymbol{q}}}(t)={\bf{0}}_N $ and $ \lim_{t\to+\infty}\tilde{{\boldsymbol{v}}}(t)={\bf{0}}_N $. Equivalently, for each virtual agent $ i\in{\cal{V}} $, one has $ \lim_{t\to+\infty}\big\|{\boldsymbol{q}}_i^{*}(t)-{\boldsymbol{q}}_0(t)-{\boldsymbol{h}}_i\big\|_2=0 $ and $ \lim_{t\to+\infty}\left\|{\boldsymbol{v}}_i^{*}(t)-{\boldsymbol{v}}_0(t)\right\|_2=0 $. Consequently, the generator achieves the desired formation obstacle avoidance configuration as $ t\to+\infty $.

Proof. The formation tracking error dynamics in Eq. (20) can be expressed in the following compact form:

The augmented error state is defined as $ {\boldsymbol{\delta}}=\left[\begin{array}{*{20}{c}}\tilde{{\boldsymbol{q}}}^{\rm{T}}, \tilde{{\boldsymbol{v}}}^{\rm{T}}\end{array}\right]^{\rm{T}}\in \mathbb{R}^{2N} $ so that Eq. (21) can be rewritten as $ \dot{{\boldsymbol{\delta}}}=D{\boldsymbol{\delta}} $, where $ D\in\mathbb{R}^{2N\times 2N} $. Based on Lemma 1 and the conditions $ \mu_1>0 $ and $ \mu_2>0 $, the matrix $ D $ is Hurwitz. Therefore, for any given symmetric positive definite matrix $ Q_f\in\mathbb{R}^{2N\times 2N} $, there exists a unique symmetric positive definite matrix $ P_f\in\mathbb{R}^{2N\times 2N} $ such that

The Lyapunov function is given by

Taking the time derivative of Eq. (23) yields

From Eq. (24) and $ \lambda_{\min}(P_f)\|{\boldsymbol{\delta}}\|_2^2\leq V_f \le \lambda_{\max}(P_f)\|{\boldsymbol{\delta}}\|_2^2 $, it holds that

where $ \kappa=\dfrac{\lambda_{\min}(Q_f)}{\lambda_{\max}(P_f)}>0 $. It follows that $ V_f(t) $ decays exponentially, i.e., $ V_f(t)\le V_f(0)e^{-\kappa t} $, $ \forall t\ge 0 $. Hence, the origin of the formation tracking error system (21) is exponentially stable. Consequently, the formation position tracking error $ \tilde{{\boldsymbol{q}}}(t) $ converges exponentially to $ {\bf{0}}_N $, that is, $ \lim_{t\to+\infty}\tilde{{\boldsymbol{q}}}(t)={\bf{0}}_N $. Accordingly, $ \lim_{t\to+\infty}\left\|{\boldsymbol{q}}_i^{*}(t)-{\boldsymbol{q}}_0(t)-{\boldsymbol{h}}_i\right\|_2=0 $, $ i\in{\cal{V}} $. Moreover, the formation velocity tracking error $ \tilde{{\boldsymbol{v}}}(t) $ converges exponentially to $ {\bf{0}}_N $, namely, $ \lim_{t\to+\infty}\tilde{{\boldsymbol{v}}}(t)={\bf{0}}_N $. Accordingly, $ \lim_{t\to+\infty}\left\|{\boldsymbol{v}}_i^{*}(t)-{\boldsymbol{v}}_0(t)\right\|_2=0 $, $ i\in{\cal{V}} $. This completes the proof. □

Multi-quadrotor UAVs trajectory tracking control design

The position subsystem is extended by treating the lumped disturbance as an additional state variable:

where $ {\boldsymbol{\xi}}_i \in \mathbb{R}^3 $ denotes the time derivative of the lumped disturbance and is unknown but bounded, i.e., $ \|{\boldsymbol{\xi}}_i(t)\|_2 \le H_i $ for all $ t \ge 0 $, where $ H_i>0 $ is a constant.

An ESO is designed to estimate the states and the lumped disturbance of the position subsystem:

where $ \beta_1,\ \beta_2,\ \beta_3 \gt 0 $ are observer design gains.

The composite controller with disturbance estimation of the position loop is designed as follows:

where $ {\boldsymbol{u}}_i = [u_{xi}, u_{yi}, u_{zi}]^T $ denotes the control input vector and $ {\boldsymbol{K}}_{pi}={\rm{diag}} \{k_{pi,1},k_{pi,2},k_{pi,3}\} $ and $ {\boldsymbol{K}}_{di}={\rm{diag}} \{k_{di,1},k_{di,2},k_{di,3}\} $ denote the design gain matrices, respectively.

The inner loop adopts the PID controller for tracking the attitude angle. Based on the virtual acceleration control inputs and the desired yaw angle $ \psi_{di} $ (specified by the user), the desired total thrust, roll angle, and pitch angle are computed, respectively, as $ F_i = m_i \sqrt{u_{xi}^2 + u_{yi}^2 + u_{zi}^2} $, $ \phi_{di} = \arcsin \left[\dfrac{m_i}{F_i}\big(u_{xi}\sin\psi_{di}-u_{yi}\cos\psi_{di}\big)\right] $, and $ \theta_{di} = \arctan \left(\dfrac{u_{xi}\cos\psi_{di}+u_{yi}\sin\psi_{di}}{u_{zi}} \right) $, $ i\in{\cal{V}} $.

Theorem 1. For the position loop dynamics of the multi-quadrotor UAVs described by Eq. (3) in the presence of lumped disturbances, under Assumption 1, by designing the tracking controller represented by Eq. (28) together with the ESO (Eq. 27), the positions and velocities of the multi-quadrotor UAVs achieve bounded tracking of the reference signals generated by the distributed reference signal generator given in Eqs (16) and (17). Then, the formation obstacle avoidance control goal is achieved.

Proof. The ESO estimation errors are defined as

Computing the time derivative of the estimation errors in Eq. (29) and substituting Eqs (26) and (27) yields

The augmented estimation error vector is denoted by $\boldsymbol{\varepsilon}_i= [\tilde{\boldsymbol q}_{oi}^T,\tilde{\boldsymbol v}_{oi}^T,(\tilde{\boldsymbol d}_i^p)^T]^T\in\mathbb R^9$. To facilitate the stability analysis, the error dynamics can be compactly written as $ \dot{{\boldsymbol{\varepsilon}}}_i = A_e {\boldsymbol{\varepsilon}}_i + E {\boldsymbol{\xi}}_i,\ i\in{\cal{V}}, $ where the system matrices are defined as

With $\omega_o \gt 0$ and the observer design gains chosen as $ \beta_1 = 3\omega_o $, $ \beta_2 = 3\omega_o^2 $, and $ \beta_3 = \omega_o^3 $, the matrix $ A_e $ is Hurwitz and has all its eigenvalues equal to $ -\omega_o $. Therefore, for any given symmetric positive definite matrix $ Q_e \in \mathbb{R}^{9\times 9} $, there exists a unique symmetric positive definite matrix $ P_e\in \mathbb{R}^{9\times 9} $ that satisfies the Lyapunov equation:

The following Lyapunov function is selected:

Taking the time derivative of Eq. (34) and invoking Lemma 2 give

By utilizing the bound $ V_{oi} \le \lambda_{\max}(P_e) \|{\boldsymbol{\varepsilon}}_i\|_2^2 $, one has

where $ \alpha = \dfrac{\lambda_{\min}(Q_e)}{2\lambda_{\max}(P_e)} $ and $ \vartheta_i = \dfrac{2 \|P_e E\|_2^2 H_i^2}{\lambda_{\min}(Q_e)} $.

The solution of Eq. (36) satisfies

From Eq. (37), $ V_{oi}(t) $ is uniformly ultimately bounded (UUB), and thus the ESO estimation error $ {\boldsymbol{\varepsilon}}_i $ is UUB.

Combining Eq. (37) with $ \lambda_{\min}(P_e)\| {\varepsilon_i}\|_2^2 \le V_{oi} $ yields

Therefore, for any $ \zeta_{oi} \gt \sqrt{\dfrac{\vartheta_i}{\alpha \lambda_{\min}(P_e)}} $, there exists a constant $ T_{oi} \gt 0 $ such that for all $ t \gt T_{oi} $, $ \|{\boldsymbol{\varepsilon}}_i\|_2 \leq \zeta_{oi} $. That is, the estimation error $ {\boldsymbol{\varepsilon}}_i $ converges to the compact set $\Omega_{oi} = \{\boldsymbol{\varepsilon}_i \in \mathbb{R}^{9} \mid \|\boldsymbol{\varepsilon}_i\|_2 \leq \zeta_{oi}\} $, where $ \zeta_{oi} $ can be rendered arbitrarily small by appropriately adjusting the observer bandwidth $ \omega_o $ and satisfying the stability condition. This indicates that the estimation errors $ \tilde{\boldsymbol{q}}_{oi} $, $ \tilde{\boldsymbol{v}}_{oi} $, and $ \tilde{{\boldsymbol{d}}}^p_i $ converge to a prescribed neighborhood of the origin.

The closed-loop tracking errors under the composite controller given by Eq. (28) are defined as

Substituting Eq. (28) into Eq. (26) yields

Noting that $ \dot{{\boldsymbol{e}}}_{vi}=\dot{{\boldsymbol{v}}}_i^{*}-\dot{{\boldsymbol{v}}}_i $, one has

The closed-loop tracking error dynamics are given by

The reduced system without $ \tilde{{\boldsymbol{d}}}_i^p $ is considered

The error dynamics (Eq. 43) is a linear system. If the gain matrices $ {\boldsymbol{K}}_{pi}={\rm{diag}} \{k_{pi,1},k_{pi,2},k_{pi,3}\} $ and $ {\boldsymbol{K}}_{di}={\rm{diag}} \{k_{di,1},k_{di,2},k_{di,3}\} $ with $ k_{pi,j}>0 $ and $ k_{di,j}>0 $ for $ j=1,2,3 $, then the associated system matrix is Hurwitz, and the origin of Eq. (43) is globally exponentially stable. Furthermore, Eq. (38) implies that there exists a constant $ \bar d_i>0 $ such that $ \sup_{t\ge 0}\|\tilde{{\boldsymbol{d}}}_i^{p}(t)\|_2\le \bar d_i $. According to Lemma 3, the system (Eq. 42) is ISS. Hence, the tracking errors $ {\boldsymbol{e}}_{qi} $ and $ {\boldsymbol{e}}_{vi} $ are bounded. This completes the proof.

Remark 6. In the absence of measurement noise, if the lumped disturbance $ {\boldsymbol{d}}_i^{p}(t) $ satisfies $ \lim_{t\to+\infty}\dot{{\boldsymbol{d}}}_i^{p}(t)={\bf{0}}_3 $, then the corresponding estimation error satisfies $ \lim_{t\to+\infty}\tilde{{\boldsymbol{d}}}_i^{p}(t)={\bf{0}}_3 $. Hence, the closed-loop position and velocity tracking errors asymptotically converge to the origin, i.e., $ \lim_{t\to+\infty}{\boldsymbol{e}}_{qi}(t)={\bf{0}}_3 $ and $ \lim_{t\to+\infty}{\boldsymbol{e}}_{vi}(t)={\bf{0}}_3 $.

Two experiments are presented to validate the effectiveness of the proposed hierarchical distributed control scheme for cooperative formation and obstacle avoidance. Based on the position-loop model in Eq. (3), the outer-loop translational dynamics of the multi-quadrotor UAVs are modeled as second-order integrator dynamics. The obstacle avoidance trajectory for the virtual leader is then generated using the AAPF method, as described in Eq. (15). Then, the distributed reference signal generator given in Eqs (16) and (17) produces the desired formation obstacle avoidance trajectories for all multi-quadrotor UAVs. The composite controller in Eq. (28) drives each multi-quadrotor UAV to track its desired trajectory. The corresponding attitude commands are then obtained by a small-angle-based inversion, which yields the required thrust and the desired roll and pitch angles, while the desired yaw angle is set to zero. These commands are applied to the inner-loop attitude dynamics, where the onboard PID module performs attitude tracking.

A. Experimental setup: In the experiments, a comprehensive platform is built around the Crazyflie 2.1 multi-quadrotor UAV^[41] and a vision-based motion capture system. The markers attached to each multi-quadrotor UAV are utilized by the motion capture system to reliably identify individual UAVs and precisely reconstruct their real-time 3D positions. The overall data flow of the experimental platform and the communication topology of the three multi-quadrotor UAVs are depicted in Fig. 2. Crazyflie 2.1 uses an STM32F405 as the main MCU and communicates with the ground-station PC over a 2.4 GHz link through a Crazyradio dongle connected to the PC. A motion capture system consisting of eight MC1300 cameras from CHINGMU Company provides localization for the multi-quadrotor UAVs. The ground-station PC reconstructs the 3D position, encapsulates the position data into a predefined Robot Operating System (ROS) message, and publishes it to a dedicated ROS topic. The proposed hierarchical distributed formation obstacle avoidance control scheme then subscribes to this topic and executes the control algorithm.

Figure 2. 

The experimental platform.

The three multi-quadrotor UAVs are initially positioned at $ {\boldsymbol{q}}_1(0)=\bigl[0,\,0,\,0.4\bigr]^{T}\,{\rm{m}} $, $ {\boldsymbol{q}}_2(0)=\bigl[0,\,0.2,\,0.4\bigr]^{T}\,{\rm{m}} $, and $ {\boldsymbol{q}}_3(0)=\bigl[0,\,-0.2, \,0.4\bigr]^{T}\,{\rm{m}} $. The start and goal positions of the virtual leader are set to $ \bigl[0,\,0,\,0.4\bigr]^T\,{\rm{m}} $ and $ \bigl[2.4,\,1.4,\,0.6\bigr]^T\,{\rm{m}} $, respectively. Let the obstacles be indexed by $ n\in\{1,2\} $ and modeled as capped cylinders. In experimental example 1, the cylinder-base centers are located at $ (x_{c,n},y_{c,n})\in\{(1.00,\,0.45),\ (1.75,\,1.70)\}\,{\rm{m}} $, with corresponding radii $ r_{o,n}\in\{0.14,\,0.225\}\,{\rm{m}} $. The heights of the cylinders are $ h_{o,n}\in\{0.4,\,1\}\,{\rm{m}} $. In experimental example 2, $ (x_{c,n},y_{c,n})\in\{(1.00,\,0.45), \ (1.55,\,1.70)\}\,{\rm{m}} $, whereas the radii and heights of the cylinders remain $ r_{o,n}\in\{0.14,\,0.225\}\,{\rm{m}} $ and $ h_{o,n}\in\{0.4,\,1\}\,{\rm{m}} $, respectively. The formation offsets of the multi-quadrotor UAVs relative to the virtual leader are $ {\boldsymbol{h}}_1=\bigl[0.10,\,0.00,\,0.00\bigr]^{T}\,{\rm{m}} $, $ {\boldsymbol{h}}_2=\bigl[-0.12,\,0.25,\,0.00\bigr]^{T}\,{\rm{m}} $, and $ {\boldsymbol{h}}_3=\bigl[-0.12,\,-0.25,\,0.00\bigr]^{T}\,{\rm{m}} $, respectively. The AAPF parameters are set to $ K_{\text{att}}=0.1 $, $ K_{\text{rep}}^{\text{min}}=0.05 $, and $ K_{\text{rep}}^{\text{max}}=0.3 $. The obstacle avoidance threshold distance is set to $ d_0=0.12\,{\rm{m}} $ in experimental example 1 and $ d_0=0.15\,{\rm{m}} $ in experimental example 2. The distributed reference signal generator parameters are set to $ \mu_1=0.1 $ and $ \mu_2=2 $. The ESO gains are chosen as $ \beta_1=15 $, $ \beta_2=75 $, and $ \beta_3=125 $. The controller gains are $ {\boldsymbol{K}}_{pi}={\rm{diag}} \bigl\{4.5,\,4.5,\,5.4\bigr\} $ and $ {\boldsymbol{K}}_{di}={\rm{diag}} \bigl\{5,\,5,\,3\bigr\}, i\in{\cal{V}} $.

B. Experimental example 1: Results and analysis of cooperative formation obstacle avoidance in sparse obstacle environments.

The experimental results of example 1 are presented in Figs 3a, 4a, 5, and 6. As shown in Figs 3a and 4a, the proposed hierarchical distributed formation obstacle avoidance control scheme enables the three multi-quadrotor UAVs to maintain the desired triangular formation configuration while executing 3D obstacle avoidance maneuvers (overflight and detouring). The responses of the distributed reference signal generator in Eqs (16) and (17) are plotted in Fig. 5, where the second-order virtual followers maintain the desired relative positions with respect to the virtual leader and achieve velocity consensus. Figure 6 depicts the trajectory tracking errors under the composite controller given in Eq. (28). The results show that both the position and velocity tracking errors remain bounded and converge to small residual neighborhoods around the origin, confirming effective tracking of the formation obstacle avoidance references produced by Eqs (16) and (17). Overall, these results validate the effectiveness and feasibility of the proposed scheme in sparse obstacle environments.

Figure 3. 

Experimental images and multi-quadrotor UAV positions at different time instants. (a) Real-time positions of the multi-quadrotor UAVs in example 1. (b) Real-time positions of the multi-quadrotor UAVs in example 2.

Figure 4. 

Trajectories of the multi-quadrotor UAVs in 3D space. (a) 3D trajectories of the formation obstacle avoidance maneuver in example 1. (b) 3D trajectories of the formation obstacle avoidance maneuver in example 2.

Figure 5. 

Response curves of the formation tracking errors under the distributed reference signal generator given by Eqs. (16) and (17) in example 1. (a) Response curves of the formation position errors. (b) Response curves of the formation velocity errors.

Figure 6. 

Response curves of the multi-quadrotor UAVs' trajectory tracking errors under the composite controller given by Eq. (28) in example 1. (a) Response curves of the position tracking errors. (b) Response curves of the velocity tracking errors.

C. Experimental example 2: Results and analysis of cooperative formation obstacle avoidance in dense obstacle environments.

The two obstacles in experimental example 2 are closer than those in experimental example 1. Therefore, a stronger spatial constraint is imposed on the multi-quadrotor UAVs' formation obstacle avoidance trajectory. The experimental results of example 2 are presented in Figs 3b, 4b, 7, and 8. In dense obstacle environments, the proposed hierarchical distributed formation obstacle avoidance control scheme enables the three multi-quadrotor UAVs to perform 3D obstacle avoidance maneuvers (overflight and detouring) while maintaining the desired triangular formation, as illustrated in Figs 3b and 4b. Consequently, the formation configuration is maintained throughout the maneuver, and smooth trajectories are achieved even when obstacles are closely spaced, demonstrating the effectiveness and robustness of the proposed scheme under strong 3D environmental constraints. The response curves of the distributed reference signal generator in Eqs (16) and (17) are presented in Fig. 7, indicating that the second-order virtual followers preserve the desired relative positions with respect to the virtual leader and achieve velocity consensus. The trajectory tracking error responses of the multi-quadrotor UAVs under the composite controller in Eq. (28) are presented in Fig. 8. It is observed that both the position and velocity tracking errors are bounded and converge to small neighborhoods around the origin. Hence, it is verified that the designed composite controller in Eq. (28) achieves robust trajectory tracking in dense obstacle environments. In summary, these experimental results demonstrate the effectiveness and feasibility of the proposed hierarchical distributed formation obstacle avoidance control scheme in both sparse and dense obstacle environments.

Figure 7. 

Response curves of the formation tracking errors under the distributed reference signal generator given by Eqs (16) and (17) in example 2. (a) Response curves of the formation position errors. (b) Response curves of the formation velocity errors.

Figure 8. 

Response curves of the multi-quadrotor UAVs' trajectory tracking errors under the composite controller given by Eq. (28) in example 2. (a) Response curves of the position tracking errors. (b) Response curves of the velocity tracking errors.

In this study, a hierarchical distributed control scheme is developed for multi-quadrotor UAVs that achieves cooperative formation while ensuring 3D obstacle avoidance. An adaptive repulsive gain mechanism is developed within the APF method, mitigating repulsive force jitter near boundaries and reducing the parameter sensitivity inherent in fixed gain designs. The proposed control scheme is composed of two layers, i.e., an upper-layer distributed reference signal generator for formation obstacle avoidance and a lower-layer composite controller for trajectory tracking of the multi-quadrotor UAVs. The two-layer structure improves design flexibility, and the stability analysis demonstrates exponential convergence of the upper-layer formation tracking errors and boundedness of the lower-layer trajectory tracking errors. Experimental results validate the proposed hierarchical distributed formation obstacle avoidance control scheme. Future work will be focused on hierarchical distributed formation obstacle avoidance control for multi-quadrotor systems subject to velocity constraints.