Collision-aware adaptive horizon model predictive control for multi-agent path planning

Abstract

Recent research in unmanned system autonomy has focused on multi-robot systems, such as vehicles or unmanned aerial vehicles (UAVs), performing missions autonomously without mutual collisions in dynamic environments. In multi-agent operational settings, conventional centralized path planning methods face limitations in system scalability, as computational complexity increases sharply with the number of agents. Therefore, this research proposes a collision-aware adaptive horizon model predictive control (MPC) algorithm based on distributed model predictive control, which is advantageous for scalability. For computational efficiency, the proposed algorithm dynamically adjusts the length of the prediction horizon based on whether a collision is predicted on the planned path, and integrates a control barrier function (CBF) as a constraint to ensure safety even when the prediction horizon is shortened. The entire optimization problem is formulated as a computationally efficient quadratic programming; however, the linearized constraints used in this formulation can lead to deadlock. To address this issue, this work applies a detour strategy to increase the success rate of path planning. The performance of the proposed algorithm was validated in a three-dimensional simulation of a path-crossing scenario with a multi-agent system of UAVs. Specifically, an ablation study analyzing the computational efficiency of the adaptive horizon and the safety enhancement from the CBF demonstrated that the proposed method enables agents to reach their target destinations efficiently and safely, reducing the average computation time by 35% and increasing the mission success rate by 13%.

Introduction

Path planning for obstacle avoidance in constrained environments is an essential element for the safe operation of unmanned systems. A variety of studies have been conducted, ranging from a single-agent avoiding static obstacles to multi-agent systems coping with dynamic situations.^1,2 Path planning for multi-agent systems can be categorized into centralized planning, where a single problem is formulated to plan all paths, and distributed planning, where each agent plans its path independently. Early research favored centralized path planning due to computational limitations and the need to ensure the safe navigation of a small number of agents.^3,4 In recent research, however, distributed approaches with enhanced scalability are being actively studied to apply a large number of agents to diverse missions. ⁵

Techniques such as a potential field method and geometric guidance have been used for path planning in unmanned systems, and more recently, learning-based methods have also been researched. First, a potential field method ⁶ defines a potential field function with a negative gradient toward the target and a positive gradient away from obstacles, and generates a path that decreases this energy function. The potential field method is easy to implement and can intuitively avoid obstacles; however, it is known to have the disadvantage of easily getting trapped in local minima when used alone. To improve upon this, Sun et al. ⁷ enhanced the conventional artificial potential field to resolve the issue of getting trapped in local minima. However, their work did not include simulations for complex scenarios with potential inter-agent collisions, and it has limitations in generating efficient paths, as agents may stop to avoid collisions. Second, geometric guidance refers to a class of techniques that reactively avoid collisions based on the agent’s current kinematic state, using a collision-predicting geometry. Geometric guidance ⁸ includes methods such as the velocity obstacle and collision cone, which enable reactive collision avoidance by forming geometries based on the obstacle’s velocity and the relative velocity between agents. Jenie et al. ⁹ devised the selective velocity obstacle method, an improvement on the conventional velocity obstacle, and successfully performed collision avoidance by following a right-of-way rule. However, reactive techniques generate avoidance paths based on the current kinematic state, without considering their own or other agents’ predicted trajectories. This approach fails to guarantee path optimality and is susceptible to local minima. Therefore, enabling safe and efficient navigation for large-scale multi-agent systems requires a more systematic avoidance strategy wherein agents exchange their planned trajectories.

With recent advancements in artificial intelligence-based technologies, research on learning-based collision avoidance is also being actively conducted. In learning-based collision avoidance methods, an agent collects data by interacting with the surrounding environment and other agents in simulation, ultimately generating a policy that optimizes a reward function. Long et al. ¹⁰ trained a policy that enables a neural network to select appropriate collision avoidance velocities, based on how optimal reciprocal collision avoidance responds to the environment. Meanwhile, inspired by how humans store limited past experiences and recall the most relevant information for the current situation, Singla et al. ¹¹ trained a unmanned aerial vehicle (UAV) using a temporal attention mechanism to emphasize data from past observations that are critical for decision-making. However, learning-based algorithms require extensive training time, and securing sufficient training data presents a challenge. Insufficient training limits the ability to handle unforeseen dynamic situations. Therefore, approaches that use an explicit system model to generate analyzable and stable trajectories are still being studied as an important alternative.

Model predictive control (MPC) is a technique that performs optimization over a finite time window, known as horizon, using system constraints and a user-defined cost function. In the past, its application was limited to systems with slow dynamics due to high-computational complexity. However, with advancements in computing power, it is now actively being applied to various unmanned systems. For instance, several studies have applied centralized MPC to collision avoidance for networked vehicles.^12,13 In a centralized MPC framework for path planning, the states of all agents must be considered simultaneously, leading to an exponential increase in computation time as the number of agents grows. In contrast, a distributed MPC approach is more advantageous for scalability. Because each agent plans its path independently, the problem is formulated using only its own state, thereby reducing the overall computational complexity. A comparative study between distributed and centralized MPC has demonstrated that the distributed approach offers enhanced scalability. ¹⁴

To address the high-computational complexity of MPC, some studies have tackled the problem by linearizing the collision avoidance constraints. ³ Additionally, to achieve faster computation, other research has attempted to approximate trajectories using various polynomials, without explicitly considering dynamics or kinematics constraints. ¹⁵ However, the linearization of constraints shrinks the feasible space for planning, and trajectories approximated by polynomials can be difficult for an agent to actually follow due to actuator limits. Furthermore, existing studies that either linearly approximate collision avoidance constraints or represent trajectories as polynomials share a common limitation: they do not directly address the length of the prediction horizon, which is the key factor determining the scale of the optimization problem.

Conventional MPC calculates an optimal control command that satisfies given constraints over a fixed horizon, irrespective of collision risk. While rapid computation is required for on-line local path planning, conventional fixed-horizon methods are computationally inefficient, as they must compute over the entire horizon even in safe regions where no collisions are anticipated. To reduce unnecessary computational costs, Ma et al. ¹⁶ proposed an event-triggered approach where the time interval for solving the optimization problem is increased based on the optimal path and current state error, thereby reducing the problem size and computational burden. Additionally, Zhang et al. ¹⁷ reduced the computational burden for an omnidirectional mobile robot tracking a reference trajectory by adaptively adjusting the prediction horizon according to its current velocity and path curvature. However, the criteria for adjusting the prediction horizon in the studies^16,17 are based on system state tracking error and single-robot kinematic metrics, respectively. Thus, they do not incorporate potential collision risks from a multi-agent environment into the horizon length adjustment. Persson and Wahlberg ¹⁸ also solved the problem of landing a helicopter on a moving deck by incorporating the horizon length into the cost function. However, the method proposed by Persson and Wahlberg ¹⁸ increases the problem’s complexity by including the horizon length as an optimization variable, which limits its on-line applicability. Although other attempts have been made to mitigate the computational burden in multi-agent collision avoidance, research focused on maximizing computational efficiency by adaptively adjusting the prediction horizon based on predicted collision information has not yet been reported. Therefore, this article proposes a collision-aware adaptive horizon MPC (CA-AH-MPC) framework to enhance both safety and computational efficiency. The proposed algorithm organically integrates two key strategies. First, the algorithm improves computational efficiency by dynamically adjusting the length of the prediction horizon in response to an anticipated collision. Second, it addresses the potential safety degradation caused by a reduced prediction horizon, a control barrier function (CBF), which guarantees safety through set invariance, is incorporated as a constraint.

Analogous to how control Lyapunov function theory ensures stability via asymptotic stability, CBF theory guarantees safety by ensuring the set invariance of a predefined safe set. A CBF guarantees the set invariance of a safe set $\mathcal{C}=\{\mathbf{x}\in {\mathbb{R}}^n|h(\mathbf{x})\ge 0\}$ by using a continuously differentiable function $h:{\mathbb{R}}^n\to \mathbb{R}$ . This ensures that if the initial state ${\mathbf{x}}_0$ is in the interior of the safe set, ${\mathbf{x}}_0\in \mathrm{Int}(\mathcal{C})$ , then the state will remain in the interior for all time $t$ , $\mathbf{x}(t,{\mathbf{x}}_0)\in \mathrm{Int}(\mathcal{C})$ . For instance, as demonstrated by Zeng et al., ¹⁹ a minimum safety distance $d_{min}$ can be ensured by defining $h(\mathbf{x})=\Vert {\mathbf{p}}_i-{\mathbf{p}}_{\text{obs}}{\Vert }^2-d_{min}^2$ with respect to the agent’s position ${\mathbf{p}}_i$ and the obstacle’s position ${\mathbf{p}}_{\text{obs}}$ . Ames et al. ²⁰ solidified the theory by classifying CBFs into reciprocal CBFs and zeroing CBFs based on Nagumo’s theorem, and applied this framework to adaptive cruise control and lane-keeping problems. Mali et al. ²¹ defined a CBF based on the relative position and velocity between UAVs to maintain a safe distance, applying it as a constraint in an MPC framework to generate safe paths. Furthermore, studies combining MPC and CBF have pointed out a limitation of conventional MPC: its distance-based constraints are only activated when an obstacle is in close proximity.^19,22 By imposing a CBF as a constraint, these studies effectively achieved obstacle avoidance. Within the proposed CA-AH-MPC framework, the CBF enforces safety constraints even when the prediction horizon is shortened. This complementary design mitigates the potential safety degradation caused by a reduced prediction horizon and generates locally safer paths.

This study proposes the CA-AH-MPC algorithm to achieve efficient on-line path planning and safe collision avoidance in multi-agent operations. The proposed algorithm addresses the limitations of conventional approaches by integrating several key features. First, the length of the prediction horizon is dynamically adjusted based on collision detection on the predicted path. This enhances computational efficiency by reducing the horizon when no collision is detected while extending it to ensure safe maneuvers when a collision is predicted. To mitigate the potential safety degradation from a shortened horizon, a CBF-based safety constraint is incorporated. This guarantees a safe path margin at all times, regardless of the horizon’s length. Finally, the algorithm employs a detour strategy, which modifies the initial path guess to resolve deadlocks that can occur when formulating the quadratic programming (QP) problem with linearized constraints.

The remainder of this article is organized as follows. Section “Problem statement” defines the basic MPC problem for path planning. Section “CA-AH-MPC algorithm” explains the process of formulating the MPC problem defined in Section “Problem statement” into a QP form suitable for on-line optimization, and describes how the CBF constraint is integrated. It then details the mechanism for adjusting the prediction horizon and the detour strategy for deadlock prevention. Finally, Section “Numerical simulation” discusses the impact of the CA-AH-MPC algorithm on computational efficiency and path safety based on simulation results. Section “Conclusions and future works” concludes the article.

Problem statement

This section presents the problem definition for distributed multi-agent system path planning and outlines the assumptions made in this work. The mission is for a team of $N$ agents to transition from their initial states (position, velocity, and acceleration) to their final states within a three-dimensional (3D) space. Each agent is assumed to have a dynamic model capable of hovering in the air or remaining stationary on the ground. Each agent $i\in \{1,\dots N\}$ determines a sequence of optimal acceleration commands to generate a feasible trajectory that satisfies the constraints on position( ${\mathbf{p}}_i$ ), velocity( ${\mathbf{v}}_i$ ), acceleration( ${\mathbf{a}}_i$ ), and jerk ( ${\mathbf{j}}_i$ ), which reflect its actuator limits. To ensure a safe mission, each agent defines its own cost function and formulates constraints for mutual collision avoidance within its prediction horizon. Each agent constructs collision avoidance constraints by sharing its planned position trajectory at synchronized intervals. The trajectory-sharing delay is modeled as the sum of the communication delay and the time required for each agent to solve its optimization problem. If this delay exceeds the planning interval, each agent uses the trajectories of the other agents from the previous step. A more detailed description is provided in the Section “CA-AH-MPC algorithm.”

Each agent generates a trajectory that satisfies the following dynamics:

$${\displaystyle \frac{d}{dt}\left[\begin{array}{c}\mathbf{p}(t)\\ \mathbf{v}(t)\end{array}\right]=\left[\begin{array}{c}\dot{\mathbf{p}}(t)\\ \dot{\mathbf{v}}(t)\end{array}\right]=\left[\begin{array}{cc}{\mathbf{0}}_3& {\mathbf{I}}_3\\ {\mathbf{0}}_3& {\mathbf{0}}_3\end{array}\right]\left[\begin{array}{c}\mathbf{p}(t)\\ \mathbf{v}(t)\end{array}\right]+\left[\begin{array}{c}{\mathbf{0}}_3\\ {\mathbf{I}}_3\end{array}\right]\mathbf{a}(t)}$$

(1)

Here, $\mathbf{p}(t),\mathbf{v}(t),\text{and }\mathbf{a}(t)$ denote position, velocity, and acceleration in ${\mathbb{R}}^3$ , respectively; ${\mathbf{0}}_3$ denotes the $3\times 3$ zero matrix, and ${\mathbf{I}}_3$ denotes the $3\times 3$ identity matrix. These dynamics, along with kinematic constraints to be introduced later, can be used to limit parameters such as turning radius and speed.

To formulate the optimal path planning problem as an optimization problem, the continuous-time dynamics of the agent $i$ is discretized with a time step $\mathrm{\Delta }t$ . Assuming that the acceleration ${\mathbf{a}}_i[k]$ remains constant during each time step, the discrete-time state equations are derived by integrating the continuous-time model as follows:

$${\mathbf{p}}_i[k+1]={\mathbf{p}}_i[k]+\mathrm{\Delta }t{\mathbf{v}}_i[k]+\frac{\mathrm{\Delta }{t}^2}{2}{\mathbf{a}}_i[k]$$

(2)

$${\mathbf{v}}_i[k+1]={\mathbf{v}}_i[k]+\mathrm{\Delta }t{\mathbf{a}}_i[k]$$

(3)

Here, the index $k=0$ denotes the current time step, and $k\in \{1,\dots ,K\}$ represents the future time steps within the prediction horizon. Furthermore, since only acceleration is used as the decision variable for the optimization problem, the position and velocity at any future time step can be expressed as a sequence of accelerations based on the initial position and velocity:

$${\mathbf{p}}_i[k]={\mathbf{p}}_i[0]+k\mathrm{\Delta }t{\mathbf{v}}_i[0]+\frac{\mathrm{\Delta }{t}^2}{2}\sum _{j=0}^{k-1}(2k-(2j+1)){\mathbf{a}}_i[j]$$

(4)

$${\mathbf{v}}_i[k]={\mathbf{v}}_i[0]+\mathrm{\Delta }t\sum _{j=0}^{k-1}{\mathbf{a}}_i[j]$$

(5)

Using these linear equations for position and velocity with respect to acceleration, all states within the prediction horizon can be expressed in a matrix form equation, where acceleration is the variable. To this end, the decision variable (acceleration sequence) ${\mathbf{U}}_i\in {\mathbb{R}}^{3K}$ , the predicted position vector ${\mathbf{P}}_i\in {\mathbb{R}}^{3K}$ , and the predicted velocity vector ${\mathbf{V}}_i\in {\mathbb{R}}^{3K}$ are defined as follows:

$${\mathbf{U}}_i={\left[\begin{array}{c}{\mathbf{a}}_i[0{]}^T{\mathbf{a}}_i[1{]}^T\cdots {\mathbf{a}}_i[K-1{]}^T\end{array}\right]}^T$$

(6)

$${\mathbf{P}}_i={\left[\begin{array}{c}{\mathbf{p}}_i[1{]}^T{\mathbf{p}}_i[2{]}^T\cdots {\mathbf{p}}_i[K{]}^T\end{array}\right]}^T$$

(7)

$${\mathbf{V}}_i={\left[\begin{array}{c}{\mathbf{v}}_i[1{]}^T{\mathbf{v}}_i[2{]}^T\cdots {\mathbf{v}}_i[K{]}^T\end{array}\right]}^T$$

(8)

The indices for ${\mathbf{U}}_i$ , ${\mathbf{P}}_i$ , and ${\mathbf{V}}_i$ are defined as above to represent the causality of a discrete-time system, where the input at step $k$ yields the state at step $k+1$ . These vectors are related by the following equations:

$${\mathbf{P}}_i=({\mathbf{M}}_{\mathrm{pos}}\otimes {\mathbf{I}}_3){\mathbf{U}}_i+({\mathbf{1}}_K\otimes {\mathbf{p}}_i[0]+\mathbf{T}\otimes {\mathbf{v}}_i[0])$$

(9)

$${\mathbf{V}}_i=({\mathbf{M}}_{\mathrm{vel}}\otimes {\mathbf{I}}_3){\mathbf{U}}_i+({\mathbf{1}}_K\otimes {\mathbf{v}}_i[0])$$

(10)

Here, the matrices ${\mathbf{M}}_{\mathrm{pos}}$ and ${\mathbf{M}}_{\mathrm{vel}}$ are given by:

$${\mathbf{M}}_{\mathrm{pos}}=\frac{\mathrm{\Delta }{t}^2}{2}\left[\begin{array}{cccc}1& 0& \cdots & 0\\ 3& 1& \cdots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 2K-1& 2K-3& \cdots & 1\end{array}\right]$$

(11)

$${\mathbf{M}}_{\mathrm{vel}}=\mathrm{\Delta }t\left[\begin{array}{cccc}1& 0& \cdots & 0\\ 1& 1& \cdots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 1& 1& \cdots & 1\end{array}\right]$$

(12)

${\mathbf{1}}_K=[1,\dots ,1{]}^T\in {\mathbb{R}}^K$ , and $\mathbf{T}=\mathrm{\Delta }t[1,2,\dots ,K{]}^T\in {\mathbb{R}}^K$ are defined, where $\otimes$ denotes the Kronecker product.

The objective function $J$ for the path optimization of each agent $i$ consists of two terms, as shown in the below equation:

$$J=w_g\sum _{k=K-\kappa }^K\Vert {\mathbf{p}}_i[k]-{\mathbf{p}}_{i,g}^{\mathrm{proj}}{\Vert }_2^2+w_s\sum _{k=1}^K\Vert {\mathbf{a}}_i[k]{\Vert }_2^2$$

(13)

Here, $\Vert \cdot {\Vert }_2$ denotes $L_2$ norm, representing the distance in a 3D space. The first term is a goal-tracking term, as depicted in Figure 1, ${\mathbf{p}}_{i,g}^{\mathrm{proj}}$ is the projection of the actual goal point, ${\mathbf{p}}_{i,g}$ , onto a sphere with a radius $r_{\mathrm{feas}}$ . This radius represents the maximum distance reachable while satisfying physical constraints. This term minimizes the distance to ${\mathbf{p}}_{i,g}^{\mathrm{proj}}$ over the final $\kappa +1$ steps of the prediction horizon, and a larger value of $\kappa$ imposes a greater penalty on the error with respect to ${\mathbf{p}}_{i,g}^{\mathrm{proj}}$ . Here, $r_{\mathrm{feas}}$ signifies the reachable distance when moving with maximum or minimum jerk in a double integrator model, and the procedure is as follows. First, a unit vector ${\mathbf{p}}_{\mathrm{dir}}$ is defined pointing from the current position ${\mathbf{p}}_i[0]$ to the destination ${\mathbf{p}}_{i,g}$ . The current velocity vector ${\mathbf{v}}_i[0]$ and the previous step’s acceleration vector ${\mathbf{a}}_i[-1]$ are projected onto ${\mathbf{p}}_{\mathrm{dir}}$ to obtain ${\mathbf{v}}_{i,\parallel }$ and ${\mathbf{a}}_{i,\parallel }$ . Based on these projected initial states, $r_{\mathrm{feas}}$ is found through a maneuver using the maximum jerk, $j_{max}$ . In this process, the maximum travel distance is analytically calculated while satisfying the maximum acceleration and velocity constraints (16) and (15). The second term is a path-smoothing term that encourages a smoother trajectory by minimizing the magnitude of acceleration inputs over the entire prediction horizon. The parameters $w_g$ and $w_s$ are positive weights that are used to tune the relative importance of the two terms, which have different physical units.

Figure 1.

Goal point projection to ensure path feasibility. If the actual goal ${\mathbf{p}}_{i,g}$ is physically unreachable from the current position ${\mathbf{p}}_i[0]$ , a new target ${\mathbf{p}}_i^{\mathrm{proj}}$ is set by projecting it onto the boundary of the maximum reachable distance $r_{\mathrm{feas}}$ .

All agents must operate within a predefined 3D space. This is expressed as a position constraint for each axis as follows:

$$p_{min,l}\le p_{i,l}[k]\le p_{max,l},l\in \{x,y,z\},\mathrm{\forall }i,k$$

(14)

Furthermore, for the safe operation of the agents, constraints are imposed on velocity and acceleration. Since the dynamic model for the agents in this study allows them to be stationary, the constraint on speed is defined as follows:

$$\sqrt{(v_{i,x}[k]{)}^2+(v_{i,y}[k]{)}^2+(v_{i,z}[k]{)}^2}\le v_{max}$$

(15)

The acceleration constraint is determined by the dynamic performance of each agent, and the magnitude of the acceleration vector is constrained as follows:

$$\sqrt{(a_{i,x}[k]{)}^2+(a_{i,y}[k]{)}^2+(a_{i,z}[k]{)}^2}\le a_{max}$$

(16)

The constraints above can still produce trajectories that include aggressive maneuvers, which are difficult for a real system to follow. To ensure the dynamic feasibility of the trajectory and to allow for smooth tracking by the actuators, a constraint on jerk is also included:

$${\mathbf{j}}_i[k]=({\mathbf{a}}_i[k]-{\mathbf{a}}_i[k-1])/\mathrm{\Delta }t$$

(17)

$$j_{min,l}\le j_{i,l}[k]\le j_{max,l},l\in \{x,y,z\},\mathrm{\forall }i,k$$

(18)

To ensure safety in the multi-agent environment, a minimum safe separation distance $R$ must be maintained between all pairs of agents $(i,j\mathrm{where}\mathit{i}\ne \mathit{j}\mathit{)}$ . This is expressed as the following non-convex constraint for all $k$ :

$$\Vert {\mathbf{p}}_i[k]-{\mathbf{p}}_j[k]{\Vert }_2\ge R,\mathrm{\forall }i,j,i\ne j,\mathrm{\forall }k$$

(19)

CA-AH-MPC algorithm

The constraint equations for velocity (15), acceleration (16), and collision avoidance (19), as defined in the Section “Problem statement,” are either non-linear or non-convex. Even if the non-convex constraints are relaxed, the optimization problem becomes a quadratically constrained quadratic program, which is too computationally complex for on-line path planning. Therefore, to transform the problem into a computationally efficient QP problem, this study linearly approximates the constraints as follows. Typically, the linearization of the non-linear $L_2$ -norm constraints for velocity and acceleration is formulated as follows:

$$v_{min,l}\le v_{i,l}[k]\le v_{max,l},l\in \{x,y,z\},\mathrm{\forall }i,k$$

(20)

$$a_{min,l}\le a_{i,l}[k]\le a_{max,l},l\in \{x,y,z\},\mathrm{\forall }i,k$$

(21)

This approximation transforms the spherical constraint (15) into a conservative, box-shaped constraint inscribed within it.

However, while using axis-wise velocity constraints is computationally efficient, it has an inherent limitation: the coordinate system of the constraints is fixed to the global frame. As illustrated in Figure 2, an axis-wise velocity constraint that is not aligned with the direction vector to the destination, ${\mathbf{p}}_{\mathrm{dir}}$ , results in an inefficient path that cannot achieve maximum speed. To solve this problem, this study applies a dynamic coordinate rotation to the velocity constraint. At each path planning step $\mathrm{\Delta }{t}_p$ , the velocity constraint is rotated by $\psi (t)$ to align with the direction of ${\mathbf{p}}_{\mathrm{dir}}$ . This rotated constraint improves path efficiency by allowing the agent to travel toward the destination with a maximum speed of $v_{max}$ .

Figure 2.

Comparison of different velocity constraint formulations. The black dashed circle represents the original non-linear $L_2$ -norm constraint, the red dashed square is the conservative axis-wise linear approximation, and the black solid square shows the proposed rotated constraint aligned with the direction vector ${\mathbf{p}}_{\mathrm{dir}}$ .

The collision avoidance constraint (19), based on the Euclidean distance between agents, is non-convex and cannot be directly applied in a QP problem. To address this, the time instances at which path planning is executed are defined as discrete planning steps $\tau =0,1,2,\dots$ with a time interval of $\mathrm{\Delta }{t}_p$ . Therefore, at each planning step $\tau$ , the non-convex constraint is linearly approximated using a first-order Taylor series expansion around the trajectory obtained from the previous planning step, $\tau -1$ . The resulting linearized constraint is formulated as follows:

$${\eta }^T({\mathbf{p}}_i[k]-{\mathbf{p}}_j^{\tau -1}[k])\ge R$$

(22)

$$\eta =\frac{{\mathbf{p}}_i^{\tau -1}[k]-{\mathbf{p}}_j^{\tau -1}[k]}{\Vert {\mathbf{p}}_i^{\tau -1}[k]-{\mathbf{p}}_j^{\tau -1}[k]{\Vert }_2}$$

(23)

Here, ${\mathbf{p}}^{\tau -1}$ denotes the position computed in the previous planning step and is treated as a constant in the current optimization problem. Since ${\mathbf{p}}_i[k]$ is a linear combination of the acceleration inputs, the above constraint is linear with respect to the decision variables. This constraint creates a half-space separation, with the normal vector defined by the relative position vector ${\mathbf{p}}_i[k]-{\mathbf{p}}_j[k]$ between the two agents, to enforce collision avoidance. All the linearized constraints described above can be aggregated and expressed as a single linear matrix inequality in terms of the control input sequence ${\mathbf{U}}_i=[\mathbf{a}[0{]}^T,\dots ,\mathbf{a}[K-1{]}^T{]}^T$ :

$$\left[\begin{array}{c}{\mathbf{A}}_{\mathrm{dyn}}\\ {\mathbf{A}}_{\mathrm{CA}}\end{array}\right]{\mathbf{U}}_i\le \left[\begin{array}{c}{\mathbf{b}}_{\mathrm{dyn}}\\ {\mathbf{b}}_{\mathrm{CA}}\end{array}\right]$$

(24)

Here, ${\mathbf{A}}_{\mathrm{dyn}}=[{\mathbf{A}}_{\mathrm{pos}}^T{\mathbf{A}}_{\mathrm{vel}}^T{\mathbf{A}}_{\mathrm{acc}}^T{\mathbf{A}}_{\mathrm{jerk}}^T{]}^T$ and ${\mathbf{b}}_{\mathrm{dyn}}=[{\mathbf{b}}_{\mathrm{pos}}^T{\mathbf{b}}_{\mathrm{vel}}^T{\mathbf{b}}_{\mathrm{acc}}^T{\mathbf{b}}_{\mathrm{jerk}}^T{]}^T$ represent the constraints on the agent’s dynamic limits, and ${\mathbf{A}}_{\mathrm{CA}}$ and ${\mathbf{b}}_{\mathrm{CA}}$ denote the matrices for the linearized collision avoidance constraints.

A CBF is a control technique that prevents a system from leaving a predefined safe set $\mathcal{C}$ . This is achieved by guaranteeing set invariance, which ensures the system always remains within the set $\mathcal{C}$ . The safe set $\mathcal{C}$ , its boundary $\mathrm{\partial }\mathcal{C}$ , and its interior $\mathrm{Int}(\mathcal{C})$ are defined using a continuously differentiable function $h(\mathbf{x})$ as follows:

$$\mathcal{C}=\{\mathbf{x}\in {\mathbb{R}}^n:h(\mathbf{x})\ge 0\}$$

(25)

$$\mathrm{\partial }\mathcal{C}=\{\mathbf{x}\in {\mathbb{R}}^n:h(\mathbf{x})=0\}$$

(26)

$$\mathrm{Int}(\mathcal{C})=\{\mathbf{x}\in {\mathbb{R}}^n:h(\mathbf{x})>0\}$$

(27)

According to Ames et al., ²⁰ if the control input satisfies the following zeroing CBF condition for all states, the forward invariance of the set $\mathcal{C}$ is guaranteed:

$$\dot{h}(\mathbf{x})\ge -\alpha (h(\mathbf{x}))$$

(28)

Here, $\alpha$ is an extended class $\mathcal{K}$ function, which is a strictly increasing function that satisfies $\alpha (0)=0$ . For discrete-time systems, as in this study, the following linearized condition proposed by Zeng et al. ¹⁹ can be used:

$$h({\mathbf{x}}_{k+1})\ge (1-\gamma )h({\mathbf{x}}_k)$$

(29)

Based on the previously defined linearized collision avoidance constraint (23), the barrier function $h({\mathbf{x}}_k)$ is formulated as follows:

$$h({\mathbf{x}}_k)={\eta }^T({\mathbf{p}}_i[k]-{\mathbf{p}}_j^{\tau -1}[k])-R$$

(30)

This constraint enforces a lower bound on how much the relative distance between agents can decrease as they approach the safety boundary $\mathrm{\partial }\mathcal{C}$ . Here, the parameter $\gamma$ regulates the conservativeness of the safety margin; a smaller value of $\gamma$ induces the generation of a more conservative path.

As shown in the flowchart in Figure 3, the proposed CA-AH-MPC algorithm operates in the following steps. The algorithm begins with an Initialization step, where each agent generates an initial trajectory toward its destination without considering collision avoidance constraints. At each planning step $\tau$ , agents exchange their planned trajectories and verify if the following condition is satisfied for all $k$ (Collision Check):

$$\Vert {\mathbf{p}}_i[k]-{\mathbf{p}}_j[k]\Vert <R,\mathrm{\forall }i,j\in \{1,\dots ,N\},i\ne j$$

(31)

The prediction horizon length for the next planning instance, $K_{\tau +1}$ , is adjusted based on the outcome of this collision check. If a potential collision is detected, the agent’s prediction horizon is extended to its maximum length, $K_{max}$ to ensure safety. Conversely, if no collision is detected, the prediction horizon is incrementally shortened to $K_{\tau +1}=K_{\tau }-1$ for computational efficiency, subject to a minimum length constraint $(K_{\tau }\ge K_{min})$ . Based on this determined prediction horizon length, each agent generates an optimal path that satisfies the given constraints. However, the linearized CBF constraints used in this process can excessively restrict the solution space. This can lead to a failure to find a feasible solution for the QP problem or result in a deadlock. To prevent this, the algorithm confirms if the QP solver has found a feasible solution through a Feasibility Check, and initiates a Detour if no solution was found.

Figure 3.

Flowchart of the CA-AH-MPC’s planning and conflict resolution logic. The algorithm first adapts the prediction horizon based on the outcome of a Collision Check to balance safety and efficiency. If the resulting optimization problem is infeasible, a Detour is attempted. If the problem remains infeasible even after the Detour, Emergency Stop is executed to guarantee safety. CA-AH-MPC: collision-aware adaptive horizon model predictive control.

Detour aims to solve the problem of solution space reduction caused by linearized constraints. This is accomplished by modifying the initial trajectory guess for the collision avoidance constraints. Figure 4 illustrates a head-on scenario where agent $i$ encounters agent $j$ while moving toward its goal position ${\mathbf{p}}_{i,g}$ . The linearized collision avoidance constraint $\eta$ , derived based on the predicted position of agent $j$ as shown in (23), forms a half-space constraint region indicated by the red line. This constraint hinders the agent from executing lateral maneuvers to reach the goal, directly resulting in a deadlock state. Therefore, the detour strategy is essential to resolve this infeasibility problem.

Figure 4.

Deadlock caused by a linearized constraint in a head-on approach. The linearized collision avoidance constraint (red line) forms perpendicular to the path exploration direction, which hinders the optimizer from exploring lateral maneuvers and results in a deadlock.

The detour strategy proposed in this study is implemented by modifying the trajectory based on the right-of-way rule, which is widely used for collision avoidance maneuvers in fixed-wing aircraft. According to this strategy, each agent generates a new trajectory by turning at a predefined angle $\theta$ while maintaining its current speed. The Rodrigues’ rotation formula ²³ is used to perform this rotation in a 3D space. As an explicit attitude is not defined, it is assumed to be based on the velocity vector, $\mathbf{v}(t)$ . The rotation axis $\mathbf{n}[k]$ is defined by the cross product of the vector from the current position $\mathbf{p}[k]$ to the goal and the current velocity vector $\mathbf{v}(t)$ :

$$\mathbf{n}[k]=\frac{({\mathbf{p}}_g-\mathbf{p}[k])\times \mathbf{v}[k]}{\Vert ({\mathbf{p}}_g-\mathbf{p}[k])\Vert \Vert \mathbf{v}[k]\Vert }$$

(32)

However, if the current velocity vector is parallel to the vector ${\mathbf{p}}_g-\mathbf{p}[k]$ , the rotation axis is undefined. In this case, the rotation is performed around the $z$ -axis. From the defined rotation axis, the skew-symmetric matrix $\mathbf{K}$ is formed to construct the rotation matrix $\mathbf{R}$ . This is then used to calculate the desired acceleration command, ${\mathbf{a}}_{\mathrm{des}}[k]$ , required for the turn:

$$\mathbf{K}=\left[\begin{array}{ccc}0& -n_z[k]& n_y[k]\\ n_z[k]& 0& -n_x[k]\\ -n_y[k]& n_x[k]& 0\end{array}\right]$$

(33)

Once ${\mathbf{a}}_{\mathrm{des}}[k]$ is calculated, an acceleration command that satisfies the jerk constraints relative to the current acceleration, $\mathbf{a}[k]$ , must be computed:

$${\mathbf{a}}_{\mathrm{des}}[k]=\mathbf{R}\mathbf{v}[k]-\mathbf{v}[k]$$

(34)

Here, $\mathrm{\Delta }\mathbf{a}[k]$ represents the required change in acceleration to achieve ${\mathbf{a}}_{\mathrm{des}}[k]$ from the current acceleration. To achieve this, the change in acceleration, $\mathrm{\Delta }\mathbf{a}[k]$ , from the current to the target acceleration is calculated. A final acceleration command is then generated such that the resulting jerk, calculated as $\mathrm{\Delta }\mathbf{a}[k]/\mathrm{\Delta }t$ , satisfies the system’s maximum allowable jerk constraint (18). The rate of change of acceleration, $\mathrm{\Delta }\mathbf{a}[k]/\mathrm{\Delta }t$ must satisfy the system’s jerk constraints.

After the optimization with the new initial path from the detour strategy, the algorithm performs another Feasibility Check to determine if a solution exists. If a feasible solution is still not found during this second verification step, the Emergency Stop phase is initiated to prevent a collision. The emergency stop is a fail-safe maneuver aimed at rapidly dissipating the agent’s momentum to bring it to a hovering state. To this end, a desired acceleration ${\mathbf{a}}_{\mathrm{des}}$ is set in the opposite direction of the current velocity vector $\mathbf{v}(t)$ to induce braking. Similar to the detour strategy, this process is also regulated within the system’s physical limits, adhering to the acceleration and jerk constraints.

At each synchronized planning period $\mathrm{\Delta }{t}_p$ , each agent updates its collision avoidance constraints based on the trajectory shared in the previous iteration, as described in (23), and computes a new trajectory using the CA-AH-MPC algorithm. The computed trajectory is then shared with the other agents for their subsequent planning steps. To ensure that each agent receives the most recent trajectories of the others before each planning step, the sum of the computation time required to generate a trajectory, $t_{\mathrm{comp}}$ , and the communication delay for transmitting the trajectory through the network, $t_{\mathrm{delay}}$ , must be smaller than $\mathrm{\Delta }{t}_p$ . If, for a given agent $j$ at a specific planning step $\tau$ , $t_{\mathrm{comp}}+t_{\mathrm{delay}}\ge \mathrm{\Delta }{t}_p$ , the other agents must plan their trajectories based on the $(\tau -1)$ -th trajectory of agent $j$ (or an even earlier one). Therefore, both the trajectory computation time and the communication delay can affect the performance and safety of the algorithm, and their effects are analyzed in detail in the Section “Performance evaluation against communication delay.”

Numerical simulation

This section describes the simulation results conducted to verify the performance of the proposed CA-AH-MPC algorithm. The simulations were performed using UAVs, a representative 3D multi-agent system, in a crossing scenario designed to increase the frequency and complexity of inter-agent interactions. The effects of the algorithm’s core components were analyzed and quantitatively evaluated: the CBF, the adaptive prediction horizon, and the detour strategy for deadlock avoidance. The simulations were conducted in the MATLAB 2023a environment. From the Sections “Analysis of conflict resolution in an example scenario” to “Performance analysis of the detour strategy,” the fundamental performance of the algorithm was assessed without considering time delays, using the quadprog solver in MATLAB for its numerical accuracy. In contrast, the Section “Performance evaluation against communication delay” presents simulation results that take trajectory computation time and communication delays into consideration in order to emulate imperfect information-sharing scenarios. To account for practical computational overhead and ensure real-time feasibility, the OSQP ²⁴ solver was employed in this analysis. All computations were executed on a PC equipped with a 24-core Intel i9 CPU and 32 GB of RAM.

All agents are homogeneous, with the parameters set as $v_{max}=5$  m/s, $a_{max}=10$  m/s ${}^2$ , and $j_{max}=30$  m/s ${}^3$ . The minimum separation distance is $R=2$  m, and the parameters are set to $\kappa =15,w_g=1.5,w_s=1$ . Furthermore, the length of the prediction horizon dynamically varies between $K_{min}=20$ and $K_{max}=30$ , the discretization time step is $\mathrm{\Delta }t=0.1$  s, and the path planning period is $\mathrm{\Delta }{t}_p=0.2$  s.

Analysis of conflict resolution in an example scenario

In this section, the effects of the dynamic adjustment of the prediction horizon and the CBF, which are core elements of CA-AH-MPC, were analyzed through an example scenario. Six agents are placed at equal intervals on the circumference of a circle with a radius of 15 m, and each navigates toward its diametrically opposite target point at the same altitude. First, with $\gamma$ set to 0.2, the results from the simulation using CA-AH-MPC are described, including the generated path, the minimum separation distance, and the variation of the horizon. Subsequently, comparisons are made with fixed-horizon MPC (FH-MPC, $K=25$ ) simulations using different $\gamma$ values, presenting the minimum separation distance, computation time, and mission completion time. This scenario is primarily used to evaluate the performance in maintaining the minimum separation distance between UAVs and the dynamic adjustment capability of the prediction horizon.

Figure 5 illustrates the flight path of each UAV generated through the simulation, while Figure 6 shows the maximum and minimum envelopes of the distance between all UAV pairs over time. As confirmed in Figure 6, all UAVs navigate safely while adhering to the minimum safe separation distance ( $R=2$  m), even in the high-density intersection area (around 4 s). Figure 7 demonstrates the dynamic variation of the prediction horizon, a key feature of the proposed algorithm. At the beginning of the simulation, the prediction horizon gradually decreases as no collision risk with other agents is detected. When the agents approach the center and a collision risk is predicted, the collision-aware mechanism activates and immediately extends the prediction horizon length to its maximum. The extended prediction horizon allows for the consideration of potential collisions further into the future, enabling the search for a safe and optimized avoidance path from a long-term perspective. After safely passing the intersection and the collision risk is resolved, the length of the prediction horizon gradually decreases again to its minimum, maintaining the minimum prediction horizon length of $K_{min}=20$ . This dynamic change in the prediction horizon confirms that the proposed CA-AH-MPC actively balances the trade-off between computational efficiency and safety.

Figure 5.

Flight paths of the six agents generated by the CA-AH-MPC algorithm in the example scenario. CA-AH-MPC: collision-aware adaptive horizon model predictive control.

Figure 6.

Variation of the minimum and maximum distances between all agent pairs over time in the simulation from Figure 1 (the dashed line indicates the minimum safe separation distance $R=2$  m).

Figure 7.

Comparison of the prediction horizon length variation for each agent in the simulation from Figure 5 (blue solid line) and the fixed horizon length of FH-MPC (red dashed line). FH-MPC: fixed-horizon model predictive control.

The proposed CA-AH-MPC algorithm is designed to enhance the two objectives of computational efficiency and path safety. From the results in Table 1, it can be observed that dynamically adjusting the prediction horizon reduces computation time compared to the fixed-horizon approach ( $K=25$ ), except for the case where $\gamma =1$ . When $\gamma =1$ , the computation time tends to increase because paths close to the minimum separation distance are generated, leading to frequent extensions of the prediction horizon. However, the overall reduction in computation time observed when $\gamma <1$ is possible because the CBF safety constraint ensures a sufficient safety margin even when the prediction horizon is shortened. Furthermore, it is observed that setting the CBF parameter $\gamma$ closer to 0 makes the system react more sensitively to collisions, thereby securing a larger minimum separation distance. The impact of the interaction between computational efficiency and safety on the mission success rate is analyzed in detail in the following section.

Table 1.

Performance comparison between CA-AH-MPC and FH-MPC.

	Computation time (s)		Minimum distance (m)
$\gamma$	CA-AH-MPC	FH-MPC	CA-AH-MPC	FH-MPC
0.2	19.6	21.4	2.48	2.36
0.6	18.3	18.9	2.02	2.04
1	20.6	18.3	2.0	2.0

CA-AH-MPC: collision-aware adaptive horizon model predictive control; FH-MPC: fixed-horizon model predictive control.

Computation time: CPU time per agent, FH-MPC: fixed prediction horizon length ( $K=25$ ).

Ablation study in a high-density crossing environment

In this section, an ablation study is conducted to evaluate the performance of the proposed CA-AH-MPC algorithm and its core components: the CBF and the detour strategy. The simulation environment consists of a $30\mathrm{m}\times 30\mathrm{m}\times 30\mathrm{m}$ box-shaped space. Each agent is randomly initialized on one of the four side faces of this space and is tasked with navigating to a random point on the diametrically opposite face. This setup is suitable for evaluating collision avoidance and deadlock resolution capabilities, as it compels all agents to fly toward the center of the space, thereby increasing the probability of their paths intersecting. The following metrics are used for the quantitative evaluation of this simulation:

Success rate (%): The percentage of agents that reach their destination within a limited time (15 s) while maintaining the minimum separation distance.

Average flight time (s): The average flight time of agents that successfully reached their destination.

Flight length ratio: The ratio of the actual distance traveled by an agent to the straight-line distance between its initial position and destination. A value greater than 1 indicates a more significant detour. This is also recorded only for agents that successfully reach their target.

Computation time (s): The recorded CPU time for each agent to travel to its destination.

Average minimum distance (m): The average minimum distance of agents

Analysis of the adaptive horizon’s computational efficiency

In this section, to verify the effectiveness of the adaptive prediction horizon, which is central to the proposed CA-AH-MPC, its performance was compared and analyzed against a FH-MPC model using a fixed prediction horizon ( $K=25$ ). The fixed horizon length used for comparison was set to the midpoint of the proposed algorithm’s adaptive horizon operating range $[20,30]$ , intended to represent the algorithm’s average performance. Simulations were conducted by varying the number of agents from 15 to 25, performing 100 runs for each agent count, while the parameter $\gamma$ was set to 1 to exclude the influence of the CBF. As shown by the computation time metric in Figure 8, the CA-AH-MPC recorded, on average, 35% lower computation times than the FH-MPC under all conditions. This demonstrates that the strategy of dynamically adjusting the prediction horizon significantly reduces unnecessary computations, leading to a substantial decrease in computation time. Conversely, in Figure 8, the CA-AH-MPC exhibited a lower success rate compared to the simulation that maintained a constant prediction horizon, owing to the shortened horizon. This underscores the necessity of the CBF constraint to secure a safety margin even with dynamic adjustment of the prediction horizon.

Figure 8.

Performance comparison between FH-MPC and CA-AH-MPC showing the average computation time and mission success rate versus the number of agents (15–25). Results are averaged over 100 simulation runs per condition. FH-MPC: fixed-horizon model predictive control; CA-AH-MPC: collision-aware adaptive horizon model predictive control.

Analysis of safety enhancement from the CBF

In this section, simulations are performed to examine the relationship between the safety margin and path efficiency according to the key CBF parameter, $\gamma$ . The parameter $\gamma$ regulates the strictness of the CBF constraint (29). When the value of $\gamma$ is close to 1, the constraint is relatively relaxed, restricting the next state ( $h({\mathbf{x}}_{k+1})$ ) only when in proximity to the safety boundary ( $h({\mathbf{x}}_k)=0$ ). Conversely, as the value of $\gamma$ approaches 0, the constraint becomes stricter, strongly limiting the decrease of $h({\mathbf{x}}_k)$ even when far from the safety boundary, thereby inducing preemptive avoidance maneuvers and enhancing the safety margin. To verify this characteristic, the performance variation with respect to the number of agents was analyzed while changing $\gamma$ to 1.0 (representing a traditional collision avoidance constraint), 0.6, and 0.2. The success rate was improved by approximately 13% on average due to the CBF. This is because the CBF enhances the safety of the path by recognizing potential collision risks early and ensuring an adequate safety margin for the path. On the other hand, a trade-off relationship was observed in terms of travel efficiency. Preemptive maneuvers for a higher safety margin inherently mean generating wider detour paths, so as the value of $\gamma$ decreases, the travel efficiency metric is inevitably sacrificed as shown in Figure 9. Accordingly, the mission time also increases, as depicted in Figure 9, which can be interpreted as a reasonable cost for enhanced safety. It was also observed that computation time increases as $\gamma$ decreases. This suggests that smaller values of $\gamma$ make the feasible region of the QP problem narrower and more complex, potentially requiring the solver to perform more iterations to find a solution.

Figure 9.

Performance comparison of CA-AH-MPC with varying $\gamma$ : success rate, average mission completion time, average flight length ratio, and average computation time versus the number of agents (15–25). Results are averaged over 100 simulation runs per condition ( $\gamma =1.0,0.6,0.2$ ). CA-AH-MPC: collision-aware adaptive horizon model predictive control.

Performance analysis of the detour strategy

In this section, to analyze the performance of the detour strategy, simulations were performed for 50 runs under each condition in the same scenario with $\gamma =1$ , while the number of agents was increased from 30 to 60. Figure 10 compares the success rate and average computation time with and without the application of the detour strategy. Without a significant increase in computation time, the detour strategy improves the success rate by modifying the initial trajectory guess to escape from deadlocks when a feasible solution cannot be found.

Figure 10.

Performance comparison of CA-AH-MPC with and without the detour strategy. The mission success rate and average computation time are shown versus the number of agents (30–60). Results are averaged over 50 simulation runs per condition. CA-AH-MPC: collision-aware adaptive horizon model predictive control.

To analyze the reason for the higher success rate, mission failure cases were investigated and categorized as either collisions or deadlocks. Figure 11 shows the number of failures based on their cause. Without the detour strategy, failures due to deadlocks occur frequently as the number of agents increases. In contrast, when the detour strategy is applied, failures caused by deadlocks are reduced. This indicates that the detour strategy effectively helps agents escape from the local minima created by the linearized constraints. Furthermore, it was observed that by proactively resolving deadlocks, the strategy also has the secondary effect of partially reducing the incidence of collisions.

Figure 11.

Failure cause analysis for the simulation in Figure 10. Comparison of failure frequencies due to collisions and deadlocks versus the number of agents.

Performance evaluation against communication delay

In this section, the robustness of the proposed algorithm against communication delays was evaluated. With the number of agents fixed at 30, the mission success rate and minimum separation distance were analyzed by varying $\gamma$ and incrementally increasing $t_{\text{delay}}$ from 0.05 to 0.5 s. For ease of analysis, the communication delay was assumed to have the same value for all agents under each test condition. The trajectory computation time, $t_{\mathrm{comp}}$ , using the OSQP solver showed no significant variation across the test conditions, with a mean of $1.465\times {10}^{-2}$  s and a standard deviation of $2.842\times {10}^{-2}$  s.

As illustrated in Figure 12, both the success rate and minimum separation distance decreased in the region where $t_{\text{delay}}\ge \mathrm{\Delta }{t}_p$ . This performance degradation is attributed to the delay in updating the trajectories of other agents, which reduces the quality of the optimal solution. Conversely, in the region where $t_{\text{delay}}<\mathrm{\Delta }{t}_p$ , a partial increase in the success rate was observed. This can be interpreted as the communication delay effectively mitigating the reciprocal dance phenomenon by introducing a subtle desynchronization, which prevents agents from obstructing each other during simultaneous avoidance maneuvers in distributed planning. This effect was particularly pronounced when generating paths close to the minimum separation distance, such as when $\gamma =1$ . In conclusion, the results demonstrate that even in unstable environments with communication delays, the system’s overall robustness can be effectively enhanced by generating conservative paths through the integration of CBF constraints.

Figure 12.

Performance evaluation of CA-AH-MPC against varying communication delays ( $t_{\mathrm{delay}}$ from 0.05 to 0.5 s). The results illustrate the success rate and average minimum separation distance for a fixed number of 30 agents. Results are shown for different CBF parameter values ( $\gamma =0.2,0.6,1.0$ ), with each data point averaged over 100 simulation runs per condition. CA-AH-MPC: collision-aware adaptive horizon model predictive control; CBF: control barrier function.

Conclusions and future works

This article proposed a distributed path planning algorithm, the CA-AH-MPC, for the cooperative mission execution of multi-agent systems, considering both computational efficiency and safety. The proposed algorithm ensures computational efficiency by dynamically adjusting the prediction horizon based on whether a collision is predicted, while simultaneously guaranteeing safety by integrating a CBF as a constraint, even when the prediction horizon is shortened. Furthermore, the deadlock issue caused by linearized constraints in the QP formulation was addressed with a detour strategy. Through numerical simulations, including an ablation study, it was demonstrated that the proposed algorithm reduces computation time compared to a fixed-horizon approach while also increasing the mission success rate and safety margin through the use of the CBF and the detour strategy. While this study focuses on the algorithmic and conceptual verification of the CA-AH-MPC framework, practical validation using high-fidelity simulators to assess the algorithm’s performance under realistic communication constraints is planned for our future investigation.