Fusing Deep Learning and Predictive Control for Safe Operation of Manned–Unmanned Aircraft Systems

Highlights

What are the main findings?

• An EKF–LSTM fusion model for manned–unmanned collaborative flight trajectory prediction reduces ADE, FDE, and RMSE by 21.2%, 50.7%, and 24.9% compared with an LSTM baseline, and remains accurate under typical and nonlinear flight states.
• A trajectory dispersion cone (TDC) with Monte Carlo sampling uses EKF-LSTM prediction errors to estimate collision probability, while the VO-MPC strategy increases minimum separation, raises avoidance success from 91.2% to 99.8%, and lowers mean collision probability by 66.7% in low noise, with further reductions to 27.7% and 34.2% of MPC in medium- and high-noise cases.

What are the implications of the main findings?

• Integrating EKF-LSTM prediction, TDC-based uncertainty quantification, and VO-MPC forms a unified safety assurance framework that addresses safety challenges in manned–unmanned collaborative flight.
• The framework shows high feasibility and practical value in civil aviation and can be extended to more complex multi-aircraft cooperative scenarios.

Abstract

With the rapid development of the low-altitude economy, the deployment of unmanned aircraft vehicles (UAVs) in many fields is increasing continuously, and the demand for collaborative flights is also growing. However, the issue of flight safety in complex airspace remains a pressing concern. Precise flight path prediction, collision detection, and avoidance are paramount for secure collaborative operations. This study proposes an integrated framework that combines an EKF-LSTM model for trajectory prediction, a Trajectory Dispersion Cone (TDC) method for probabilistic collision risk assessment, and a Velocity Obstacle-Model Predictive Control (VO-MPC) strategy for dynamic collision avoidance. Experimental results demonstrate the advantages of our approach: the EKF-LSTM model reduces prediction errors in complex flight states. Furthermore, the VO-MPC method achieves a 99.8% collision avoidance success rate under low-noise conditions—an 8.6% improvement over traditional MPC—while reducing the average collision probability by 66.7%. It also maintains stable performance under medium- and high-noise conditions, reducing the collision probability to only 27.7% and 34.2% of that of conventional MPC, respectively. The proposed framework offers a solution for safe manned–unmanned collaboration in complex environments. Future work will extend these methods to multi-aircraft cooperative scenarios.

1. Introduction

In recent years, UAVs have been playing an increasingly important role in various fields such as agricultural plant protection, disaster response, and environmental monitoring [1,2]. However, the intelligent autonomy of UAVs remains limited by constraints on algorithmic maturity, computational resources, and payload capacity. These limitations often necessitate human intervention, reducing their adaptability to dynamic environments [3].

To address this challenge, Manned–Unmanned Aircraft System (M-UAS) collaborative flight modes have been proposed as a promising solution. In M-UAS frameworks, manned aircraft assume command and decision-making roles, while UAVs perform high-risk missions. This synergy leverages their complementary strengths to enhance operational efficiency and resource utilization in complex scenarios [4]. The architecture of a typical M-UAS collaborative flight system (shown in Figure 1) comprises a ground mission control center, which connects multiple command aircraft-equipped mission planning systems. Each system deploys several manned/unmanned collaborative groups, supporting multi-formation M-UAS mission operations.

Although manned–unmanned collaborative flight has demonstrated potential, collision avoidance in complex operational environments remains a critical challenge and a core bottleneck limiting further deployment [5]. Recent work on prediction-informed autonomous trajectory planning in crowded and unknown dynamic environments also emphasizes collision avoidance as a central requirement for safe UAV operations [6]. Moreover, a comprehensive survey on multi-UAV collision avoidance summarizes existing solution families and highlights collision avoidance as a persistent challenge for multi-agent airspace operations [7]. To improve safety assurance, existing research has explored mission-driven autonomous perception and information fusion for enhanced situational awareness [8], as well as swarm-level collision-avoidance control and optimization strategies [9]. Meanwhile, progress in intent-aware and data-driven motion prediction has provided stronger prerequisites for downstream avoidance, including multi-agent intention-guided prediction [10], vision-based planning with dynamic obstacle trajectory prediction [11], and UAV-based moving-target trajectory prediction in cluttered environments [12]. Recent studies have further explored integrating predicted/estimated intentions into receding-horizon optimization frameworks (e.g., prediction-driven MPC) to support safe UAV navigation in dynamic environments [13]. These studies collectively indicate that trajectory prediction and collision/conflict detection are not only the technical foundations of collision avoidance algorithms, but also key enablers for ensuring overall flight safety of collaborative systems.

Aircraft trajectory prediction serves as the cornerstone for ensuring safe coordination between manned and unmanned aircraft, as it directly underpins the reliability of collision detection and safety assessments. Existing prediction methodologies can be broadly categorized into three groups: dynamics-based methods (relying on aerodynamics and aircraft performance models), state estimation methods, and machine learning techniques [14].

Dynamics-based methods rely on dynamic and kinematic equations to simulate aircraft parameters for trajectory prediction. Kang et al. [15] proposed a path prediction method based on attitude estimation of fixed-wing aircraft, and the results show that the performance of the proposed algorithm is superior to that of the prediction method based only on position data. Sahbon et al. [16] compared two aerodynamic models in trajectory simulations, highlighting the impact of model selection on prediction precision. Although dynamics-based methods analyze aircraft from the perspective of force interactions, most studies are conducted under idealized assumptions to simplify the model. Due to insufficient consideration of real-world constraints, the actual prediction results fail to meet practical requirements.

State estimation methods use statistical analysis of historical trajectory data to construct probabilistic distribution models, making them suitable for processing uncertain data in dynamic environments [17]. Hematulin et al. [18] proposed a multi-UAV trajectory planning and hierarchical collision avoidance approach based on nonlinear Kalman filtering, achieving real-time trajectory prediction through sensor data fusion, ideal for multi-target tracking scenarios. Li et al. [19] used dynamic models for coupled motion and leveraging Kalman filtering to fuse scene context information, this approach achieves accurate and feasible multi-step multimodal trajectory prediction by combining the advantages of learning-based and physics-based models. Despite their advantage in uncertainty handling, these methods fail to capture complex nonlinear and time-varying trajectory characteristics, leading to decreased accuracy in highly dynamic scenarios.

Machine learning-based methods, particularly neural networks, have been widely applied in trajectory prediction due to their strong temporal modeling capabilities. Yoon et al. [20] introduced a deep learning framework employing gated recurrent units (GRUs) for real-time, precise, and scalable UAV trajectory prediction, showcasing its effectiveness in managing temporal data. Li et al. [21] proposed the MFAN model, which integrates mixed feature attention mechanisms to enhance trajectory prediction performance and improve the accuracy of motion forecasting. Shi et al. [22] developed a UAV trajectory prediction system that integrates multiple flight modes, leveraging diverse flight states to improve prediction accuracy. Machine learning methods exhibit exceptional nonlinear modeling capabilities and do not rely on physical models, thereby eliminating the need for certain unavailable aircraft performance parameters, data, and unrealistic assumptions. However, they struggle to quantify uncertainty and suffer from black-box characteristics. Thus, this study integrates state estimation with machine learning methods. The integrated model can not only analyze long-term trends and high-level intentions to provide global observational predictions but also perform local optimization and correction based on accurate physical models, ensuring trajectory smoothness and physical rationality. This makes the model an intelligent predictor that understands both physics and intentions.

Beyond trajectory prediction, collision detection is another core technology ensuring safe M-UAS collaboration, as it directly determines the effectiveness of subsequent collision avoidance strategies [23]. Roberto et al. [24] proposed a vision -based method for obstacle detection, tracking and conflict detection, enabling small UAS to achieve non-cooperative sense-and-avoid capabilities. Zou et al. [25] developed a small UAV collision probability approach integrating navigation errors; they further proposed a rapid algorithm [26] with an average computation time of <0.001 s for real-time performance. Although these methods are effective in specific scenarios, they generally rely on high-quality perceptual data or precise knowledge of system errors. In dynamic and uncertain mixed M-UAS airspace, their resilience faces challenges. To address the above challenges, this paper introduces the Trajectory Dispersion Cone (TDC) method. By constructing a probabilistic safety space that accommodates uncertainties, this method breaks away from the reliance on continuous high-quality external observations and provides a more fundamental solution for the safe operation of manned–unmanned collaborative flight in complex environments.

Collision detection is a prerequisite for identifying risks in Manned–Unmanned Aerial Collaborative Flight, while collision avoidance serves as the core guarantee to fundamentally mitigate such risks and ensure operational safety. These techniques are primarily categorized into tactical and strategic approaches.

Tactical methods respond rapidly to collision threats by analyzing the relative geometry and dynamic characteristics between aircraft in real time [27]. Wakabayashi et al. [28] developed a Chance Constrained Model Predictive Control (CCMPC) method that provides more robust collision avoidance against changes in obstacle speed. Zhang et al. [29] proposed a velocity obstacle-based method for multi-agent systems, constructing RHC chance constraints to plan at velocity level for collision-free trajectories.

Strategic methods prioritize global path planning to minimize collision risks throughout the flight. Wang et al. [30] proposed a D3QN path planning algorithm customized for UAVs—with novel designs of state space, action space and reward mechanism to reflect objectives and constraints—achieving low collision rates and high adaptability in tests. Wei et al. [31] modeled aircraft collision avoidance as a POMDP and solved it via MCTS, with the algorithm showing good performance in effectiveness, robustness, convergence and constraint handling.

In summary, while strategic methods provide globally optimized solutions for complex mission profiles, real-time safety in dynamic M-UAV shared airspace hinges on robust tactical-layer solutions. To address the critical need for both instantaneous reactivity and predictive foresight, this study focuses on the tactical layer, proposing a novel collision avoidance method by seamlessly merging the Velocity Obstacle (VO) approach with Model Predictive Control (MPC).

Building upon existing literature, this study proposes an integrated framework for manned–unmanned collaborative flight. The main contributions are threefold: (1) developing an EKF-LSTM hybrid model that combines the strengths of machine learning for nonlinear sequence modeling and Kalman filtering for state estimation, to reduce trajectory prediction errors during complex flight maneuvers; (2) constructing a trajectory uncertainty and collision risk assessment method based on Monte Carlo sampling for probabilistic collision detection in 3D airspace; and (3) designing a VO-MPC strategy to improve collision avoidance performance under varying noise conditions. The novelty lies in integrating EKF-LSTM’s predictive accuracy, TDC’s uncertainty quantification, and VO-MPC’s reliable collision avoidance performance under noisy conditions into a unified safety assurance system for manned–unmanned collaborative flight.

The remainder of this paper is organized as follows. Section 2 presents the proposed framework, including the EKF-LSTM trajectory prediction model, the TDC-based probabilistic collision risk assessment method, and the VO-MPCVO-MPCVO-MPC collision avoidance strategy. Section 3 reports the experimental setup and results, and analyzes the performance of the proposed approach under different flight scenarios and noise conditions. Finally, Section 4 concludes the paper and outlines directions for future work.

2. Materials and Methods

2.1. EKF-LSTM Fusion Prediction Model for Trajectory Prediction

2.1.1. Model Basics

The Kalman Filter (KF) is a recursive state estimation algorithm that integrates system dynamics models with observational data to achieve optimal state estimation in environments with Gaussian noise. It is particularly effective for linear systems where the noise is Gaussian. However, the KF’s assumption of linearity limits its applicability in nonlinear maneuvering scenarios, which are common in UAV operations. To address this, the Extended Kalman Filter (EKF) extends the KF framework to nonlinear systems by linearizing the nonlinear functions using a first-order Taylor expansion. This makes the EKF a widely used method for aircraft trajectory prediction. Nevertheless, in scenarios with strong nonlinearities or high dynamics, the linear approximation can lead to significant errors due to model mismatch.

Long Short-Term Memory (LSTM) networks, an advanced form of recurrent neural networks (RNNs), are designed to capture long-term dependencies in sequential data through gating mechanisms. LSTMs excel at learning nonlinear dynamic features from historical trajectory data, making them a powerful tool for trajectory prediction. However, their purely data-driven nature means they lack the constraints of physical models, which can lead to predictions that deviate from actual dynamic characteristics, especially when data is scarce or when there are abrupt changes in the environment.

2.1.2. Model Architecture and Fusion Mechanism

The EKF-LSTM fusion prediction model integrates the Extended Kalman Filter’s (EKF) capability to model physical systems with the Long Short-Term Memory (LSTM) network’s strength in capturing temporal features. The LSTM analyzes time series data to extract long-term dependencies from flight trajectories, providing its output as observational input to the EKF algorithm. Leveraging a model of aircraft dynamics, the EKF extracts local characteristics from flight data and refines the LSTM’s predictions. This combined approach enhances the accuracy of flight trajectory predictions. Figure 2 presents the principle block diagram of this method.

At time $t$, the LSTM leverages historical trajectory information to produce a one-step-ahead prior state estimate ${\widehat{x}}_{t\mid t-1}$. Specifically, $\left\{X_1,X_2,\dots ,X_t\right\}$ denotes the ordered trajectory input sequence up to time $t$, where each $X_i$ represents the trajectory feature vector at time step $i$ (i.e., the measured kinematic quantities used as the LSTM input; the sequence is fed in chronological order). The LSTM output ${\widehat{x}}_{t\mid t-1}$ is then used as the observation-related input for the EKF, which performs iterative “prediction–update” refinement. The EKF first propagates the prior uncertainty through the state transition model and the error covariance update, and then incorporates observation information via the Kalman gain to correct the state estimate. Sequential rolling prediction generates a complete flight trajectory. The specific equations governing this process are detailed below:

$$\{\begin{array}{ll}{\widehat{x}}_{t|t-1}=\mathrm{L}\mathrm{S}\mathrm{T}\mathrm{M}\left(X_1,X_2,\cdots ,X_t\right)& \\ P_{t|t-1}=F_t{P}_{t-1|t-1}{F}_t^T+Q_t& \end{array}$$

(1)

In Equation (1), ${\widehat{x}}_{t\mid t-1}$ is the predicted (prior) state estimate at time tobtained from the LSTM based on the historical sequence $\left\{X_1,\dots ,X_t\right\}$. $P_{t\mid t-1}$ is the prior error covariance matrix, which quantifies the uncertainty associated with the prior estimate. The term $F_t{P}_{t-1\mid t-1}{F}_t^T$ describes how the previous posterior uncertainty $P_{t-1\mid t-1}$ is propagated through the state transition at time $t$, where $F_t$ is the state transition matrix (capturing the local mapping of state perturbations across time). $Q_t$ is the process noise covariance matrix, which models uncertainty introduced by unmodeled dynamics, disturbances, and maneuvering effects. Therefore, Equation (1) corresponds to the EKF prediction (time-update) stage, where uncertainty is propagated forward before incorporating the current observation.

In the update step, the observed data is used to correct the predicted results, and the Kalman gain $K_t$ is used to calculate the corrected state estimate. The update equation is:

$$\{\begin{array}{ll}{K}_t=P_{t|t-1}{H}_t^T{\left(H_t{P}_{t|t-1}{H}_t^T+R_t\right)}^{-1}& \\ {\widehat{x}}_t={\widehat{x}}_{t|t-1}+K_t\left(z_t-h\left({\widehat{x}}_{t|t-1}\right)\right) & \\ P_t=\left(I-K_t{H}_t\right)P_{t|t-1}& \end{array}$$

(2)

In Equation (2), $z_t$ denotes the observation at time $t$, and $h(\cdot )$ is the measurement function that maps a state estimate to the predicted observation. Accordingly, $H_t$ is the measurement matrix that maps state-space uncertainty into the observation space (or equivalently the local linearization of $h(\cdot )$). The innovation term $z_t-h\left({\widehat{x}}_{t\mid t-1}\right)$ represents the residual between the actual observation and the predicted observation implied by the prior estimate. The Kalman gain $K_t$ weights this residual to fuse observation information with the prior prediction in an uncertainty-aware manner: $R_t$ characterizes the observation noise level (measurement reliability), while $P_{t\mid t-1}$ reflects the prior uncertainty. The updated state estimate ${\widehat{x}}_t$ is the posterior result after correction, and $P_t$ is the corresponding posterior error covariance reflecting the updated uncertainty. Overall, Equation (2) corresponds to the EKF update (measurement-correction) stage.

2.1.3. Implementation Details and Reproducibility

To improve reproducibility,

Table 1. LSTM predictor and EKF fusion filter settings used in this work.

Module	Parameter Name	Symbol/Notation	Setting
LSTM	Input	–	3D position [x, y, z]
	Look-back window	L	10 steps
	Layers	–	2
	Hidden units	–	1000
EKF	State	–	[x, y, z, vx, vy, vz, ax, ay, az]ᵀ
	Measurement matrix	H	[I3×3, 03×6]
	Initial covariance	P0	diag ([1, 1, 1, 400, 400, 400, 1, 1, 1])
	Process noise	Qekf	diag ([10, …, 10])
	Initial measurement noise	Rekf,0	120 I3

summarizes the key implementation parameters of the LSTM predictor and the EKF fusion filter.

The LSTM is trained with one-step supervision using MSE loss and the Adam optimizer (lr = 10⁻⁴) for 100 epochs with batch size 32. Training data are shuffled each epoch, and the checkpoint with the lowest validation loss is selected. All experiments use a fixed random seed for determinism.

2.2. Trajectory Dispersion Cone (TDC) for Collision Detection

2.2.1. Theoretical Foundation

In complex three-dimensional airspace, aircraft trajectories are subject to significant uncertainty due to measurement errors, environmental disturbances, and other factors [32]. To address this, this study proposes a collision detection method based on the Trajectory Dispersion Cone (TDC), which integrates trajectory prediction with the geometric properties of a conical region and employs Monte Carlo sampling to assess collision risks between aircraft.

The TDC constructs a conical spatial region defined by the aircraft’s predicted trajectory, heading, and root mean square error (RMSE), which quantifies trajectory deviation and maps uncertainty to a three-dimensional cone for quantitative risk assessment.

This conical region encapsulates the range of possible aircraft movements within a predicted time frame, enabling the evaluation of intersections with obstacles or other aircraft. The TDC approach effectively manages movement uncertainty and offers distinct advantages in multi-target or dynamic obstacle environments by not only predicting future positions but also quantifying uncertainty through a rigorous geometric model.

2.2.2. Construction of the Trajectory Dispersion Cone Model

Let the starting point of the aircraft’s predicted trajectory be $\left(x_0,y_0,z_0\right)$, and the trajectory over the next Tc time steps be:

$$P\left(t\right)=\left\{\left(x_t,y_t,z_t\right)|t=\mathrm{1,2},\cdots ,Tc\right\}$$

(3)

The cone has its vertex at the predicted starting point $\left(x_0,y_0,z_0\right)$, the cone axis direction is the unit vector $d={\displaystyle \frac{d_{Tc}}{\parallel d_{Tc}\parallel }}$ pointing from the starting point to the predicted endpoint $\left(\begin{array}{c}{x}_T,y_T,z_T\end{array}\right)$, where $d_{Tc}=\left(x_{Tc}-x_0,y_{Tc}-y_0,z_{Tc}-z_0\right)$, and the cone axis length is the total length of the future trajectory $L=\parallel d_{Tc}\parallel$. The cone radius function is denoted as $r={\displaystyle \frac{t}{Tc}}\cdot \mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\left(\mathrm{t}\right)$, which varies with time t and is related to the prediction uncertainty (i.e., the RMSE value), reflecting the range of prediction uncertainty. As RMSE increases, the radius of the cone base increases, indicating increased prediction uncertainty; conversely, a decrease in RMSE means more precise predictions, with the cone base radius correspondingly decreasing. The distance between the base circles of the two aircraft’s TDCs dynamically changes with time t. Through the three-dimensional cone model, the predicted trajectory can be visually displayed and uncertainty quantified.

2.2.3. Collision Detection Model Construction

Cone Point Set Distribution: In order to reflect the uncertainty of the aircraft trajectory, the point set distribution inside the cone must be defined. The position of any point inside the cone can be expressed as:

$$q\left(t,u,v\right)=v_0+td+uR\left(e_1\right)+vR\left(e_2\right)$$

(4)

where $t\in \left[0,L\right]$ is the distance along the cone axis; $u,v\in \mathbb{R}$ satisfy $u^2+v^2\le r^2\left(t\right)$; $e_1,e_2$ are the transformed bases of the standard orthogonal basis under the action of the rotation matrix $R$, which describe the two orthogonal directions of the cone base, respectively.

Monte Carlo sampling: At each time step, we generate a finite set of sample points inside the trajectory dispersion cone using an axially stratified sampling procedure. Specifically, we first discretize the axial coordinate $t\in [0,L]$ into $N$ uniformly spaced levels $\{t_i{\}}_{i=1}^N$ as in Equation (5). This step ensures that the samples cover the cone consistently along its full axial extent (i.e., the entire look-ahead length). Conditioned on each axial level $t_i$, we then draw a random point $(u_i,v_i)$ uniformly within the cross-sectional circular disk $u^2+v^2\le r^2\left(t_i\right)$ using two independent random variables ${\xi }_1,{\xi }_2\sim U(0,1)$, as given in Equation (6) and (7). Therefore, “uniform along the cone axis” refers to the uniform spacing of the axial levels $\left\{t_i\right\}$, while the randomness is introduced through the in-disk sampling at each axial level. Repeating the above process for the cones of the two aircraft yields the corresponding point sets used for collision checking and probability estimation.

Distribute sampling points uniformly along the cone axis:

$$t_i={\displaystyle \frac{i}{N}}L,i=\mathrm{1,2},\cdots ,N$$

(5)

Among them, $L$ is the axial length of the cone.

For each axial sampling point $t_i$, sampling points are uniformly distributed on the circular disk with radius $r\left(t_i\right)$ corresponding to the cone. The sampling points $u_i,v_i$ satisfy:

$$u_i=r\left(t_i\right)\sqrt{{\xi }_1}\mathit{cos}\left(2\pi {\xi }_2\right)$$

(6)

$$v_i=r\left(t_i\right)\sqrt{{\xi }_1}\mathit{sin}\left(2\pi {\xi }_2\right)$$

(7)

Among them, ${\xi }_1,{\xi }_2\sim U\left(\mathrm{0,1}\right)$.

Perform the above sampling process on the cones of the two aircraft to obtain the point sets:

$$Q_A\left(t\right)={\left\{q_{A,i}\left(t\right)\right\}}_{i=1}^N$$

(8)

$$Q_B\left(t\right)={\left\{q_{B,j}\left(t\right)\right\}}_{j=1}^N$$

(9)

Collision conditions and probability estimation: For any pair of sampling points $\left(q_{A,i},q_{B,j}\right)$, in three-dimensional space, calculate their Euclidean distance:

$$d_{ij}\left(t\right)=\Vert q_{A,i}\left(t\right)-q_{B,j}\left(t\right)\Vert$$

(10)

Set the system safety threshold $D_s=40 \mathrm{m}$, which is selected as a moderate tactical separation within the commonly reported baseline separation range (typically 30–80 m) in low-altitude UAV conflict management studies, and lies between representative fixed baselines (e.g., 30 m and 50 m) frequently used in simulations to balance safety margin and operational burden [33]. The system collision risk conditions is as follows:

$$\exists i,j d_{ij}\left(t\right)<D_s$$

(11)

That is, when the distance between any two sampling points is less than $D_s$, a potential collision risk is deemed to exist. At each time step, 1000 independent Monte Carlo trials are conducted to estimate the collision probability for that time step:

$$P_c\left(t\right)={\displaystyle \frac{Number of collisions detected}{1000}}$$

(12)

In order to make the detection results more accurate, multi-time step joint detection is used to combine the collision probabilities of the next k time steps:

$$P_c^{\mathrm{total}}\left(t\right)=1-{\prod }_{t=1}^k\left(1-P_c\left(t\right)\right)$$

(13)

Set the threshold $P_t=0.1$. Here, $P_t$ is an alerting (decision) threshold for triggering collision warning and avoidance rather than a regulatory target probability; in detect-and-avoid practice, such thresholds are chosen by trading off missed detections and nuisance alerts (often characterized via SOC-type analyses relating alert rate to residual risk). In addition, since $P_c^{\mathrm{total}}\left(t\right)$ aggregates risk over the next $k$ steps in Equation (13), $P_t=0.1$ corresponds to a smaller per-step risk level, and together with 1000 Monte Carlo trials per step it provides a more stable online trigger under finite-sample estimation noise. If $P_c^{\mathrm{total}}\left(t\right)>0.1$, determine that the system is at risk of collision, trigger a collision warning, and execute obstacle avoidance.

Existing collision detection models can be broadly grouped into (i) deterministic separation or geometry-based checks that assess conflicts on nominal predicted trajectories, (ii) velocity-space/geometric formulations (e.g., VO-type methods) that characterize conflicts efficiently in the velocity domain, and (iii) probabilistic risk models that typically assume an explicit sensing/navigation error model or bounded error sets. Deterministic/geometric checks are computationally efficient but can underestimate risk when prediction uncertainty is significant unless conservative buffers are introduced. Probabilistic models provide risk quantification but often depend on how uncertainty is parameterized. In contrast, the proposed TDC explicitly converts trajectory prediction residual statistics into a 3D uncertainty envelope and estimates conflict risk via Monte Carlo sampling inside the dispersion cones, producing a collision-probability output that aligns with the warning/decision threshold used by the downstream avoidance module. Therefore, TDC can be viewed as a lightweight probabilistic layer bridging trajectory prediction uncertainty and tactical-level collision warning, and it is complementary to the geometric constraints used later in the VO-MPC controller.

2.3. Collision Avoidance Method Based on Velocity Obstacle-Model Predictive Control (VO-MPC)

2.3.1. Theoretical Basis and Problem Modeling

To ensure safe collaborative flight between manned aircraft and UAVs in complex airspace, this study proposes a collision avoidance method integrating the velocity obstacle (VO) approach with model predictive control (MPC), termed VO-MPC. The VO technique identifies potential collision zones, while MPC optimizes control inputs, making this method highly effective for dynamic environments. Figure 3 illustrates the implementation process of this approach.

2.3.2. UAV Dynamics Model

The state of a UAV consists of its position and velocity. The dynamics model is represented by a nonlinear discrete-time system:

$$x_A^{k+1}=g_A\left(x_A^k,u_A^k\right)+{\omega }_A^k$$

(14)

Among these, $x_A={\left[p_A^T,v_A^T\right]}^T$ denotes the state vector composed of position and velocity, and $u_A$ is the control input vector. $k$ denotes the $k$th time step of the UAV, and $g_A$ is the nonlinear discrete-time dynamic model of the UAV.

Considering the Gaussian process noise of velocity ${\omega }_A\sim N\left(0,W_i\right)$, where the covariance matrix $W_i$ is a diagonal matrix.

2.3.3. Velocity Obstacle Model Construction

The VO method is a mature collision detection technique that identifies potential collision risks by calculating the projection area of obstacles in the velocity space [34]. Suppose that UAV A is located at $p_A$, with a velocity of $v_A$ and a radius of $r_A$; manned aircraft B is located at $p_B$, with a velocity of $v_B$ and a radius of $r_B$. The Minkowski sum of the two aircraft is defined as:

$$O_A\oplus O_B=\left\{m_A+m_B|m_A\in O_A,m_B\in O_B\right\}$$

(15)

Among them, $O_A=\left\{p_A+\mu r_A|{\Vert \mu \Vert }_2\le 1\right\}$, $O_B=\left\{p_B+\mu r_B|{\Vert \mu \Vert }_2\le 1\right\}$. The relative velocity $v_{AB}=v_A-v_B$, and the collision cone $C_{AB}$ is expressed as:

$$C_{AB}=\left\{v_{AB}|\left(O_A\oplus O_B\right)\cap \lambda \left(v_{AB}\right)\ne \mathrm{\varnothing }\right\}$$

(16)

Among them, $\lambda \left({\mathrm{v}}_{\mathrm{A}\mathrm{B}}\right)=\left\{{\mathrm{p}}_{\mathrm{A}}+\lambda {\mathrm{v}}_{\mathrm{A}\mathrm{B}}|\lambda \ge 0\right\}$. The velocity obstacle $V_{AB}$ is:

$$V_{AB}=\left\{v_A|\left(v_A-v_B\right)\in C_{AB}\right\}=v_B+C_{AB}$$

(17)

For object A, any velocity $v_A\in V_{AB}$ will result in a collision, so the composite obstacle velocity and collision cone are:

$$V_A=\underset{B\ne A}{\cup }{V}_{AB}$$

(18)

$$C_A=\underset{B\ne A}{\cup }{C}_{AB}$$

(19)

2.3.4. VO-MPC Optimization Framework

VO-MPC generates collision avoidance trajectories by solving optimization problems. The objective function comprehensively considers trajectory tracking error and control input penalties:

$$\begin{array}{c}J=\sum _{k=0}^{N-1} \left[{\parallel p_k-p_{r,k}\parallel }_Q^2+{\parallel {\nu }_k-{\nu }_{r,k}\parallel }_Q^2+{\parallel u_A^k\parallel }_R^2\right]\hfill \\ =\sum _{k=0}^{N-1} [{\parallel x_A^k-x_{r,A}^k\parallel }_Q^2+{\parallel u_A^k\parallel }_R^2]\hfill \end{array}$$

(20)

Among them, $x_A^k={\left[{p_A^k}^T{{\nu }_A^k}^T\right]}^T$ denotes the state vector of agent A at time k, where $p_A^k$ and ${\nu }_A^k$ are the actual position and velocity of agent A at time k, respectively; $x_{r,A}^k={\left[{p_{r,A}^k}^T{{\nu }_{r,A}^k}^T\right]}^T$ represents the reference state vector for agent A at time k, where $p_{r,A}^k$ and ${\nu }_{r,A}^k$ are the target position and velocity of the reference trajectory for agent A at time k, respectively. Q and R are weighting matrices that adjust the weights of state error (position and velocity) and control input, respectively; $N$ is the prediction time domain length. The constraints include:

Dynamic constraints:

$$\begin{array}{c}{x}_A^{k+1}=g\left(x_A^k,u_A^k\right)\end{array}$$

(21)

$$\begin{array}{c}{\underset{̱}{x}}_A^{k+1}\le x_A^{k+1}\le {\stackrel{̱}{x}}_A^{k+1}\end{array}$$

(22)

Among them, ${\underset{̱}{x}}_A$, ${\stackrel{̱}{x}}_A$ are the lower and upper limits of the state variables.

Collision probability constraints:

Considering noise ${\mathbf{v}}_A^k\sim \mathcal{N}({\widehat{\mathbf{v}}}_A^k,{\mathbf{W}}_i)$, the chance constraint is:

$$\begin{array}{c}\mathit{Pr}\left(v_{AB}^{k+1}\notin C_A^{k+1}\right)\ge 1-{\delta }_A\end{array}$$

(23)

Lemma 1

(Deterministic reformulation of a Gaussian chance constraint). Let $X\left(t\right)\sim \mathcal{N}\left(\mu \right(t),\mathsf{\Sigma }(t\left)\right)$ be a multivariate Gaussian random variable. For any vector $A$ and scalar $b$, the chance constraint

$$Pr\left(A^{T}X\left(t\right)<b\right)\le \phi$$

is equivalent to the deterministic linear constraint

$$A^T\mu (t)-b\ge \eta$$

where

$$\eta =\sqrt{2 A^{\mathsf{T}}\mathsf{\Sigma }\left(t\right)A} {\mathrm{e}\mathrm{r}\mathrm{f}}^{-1}(1-2\phi )$$

and $\mathrm{e}\mathrm{r}\mathrm{f}(x)={\displaystyle \frac{2}{\sqrt{\pi }}}{\int }_0^x\mathrm{e}\mathrm{x}\mathrm{p}(-s^2) \mathrm{d}s$.

By using Lemma 1, the probability constraint is transformed into a deterministic linear constraint:

$$\begin{array}{c}{N}_{AB,1}^{kT}{\widehat{v}}_A^k-N_{AB,1}^{kT}{v}_B^k\ge {\kappa }_{AB,1}\end{array}$$

(24)

$$\begin{array}{c}{N}_{AB,2}^{kT}{\widehat{v}}_A^k-N_{AB,2}^{kT}{v}_B^k\ge {\kappa }_{AB,2}\end{array}$$

(25)

where ${\kappa }_{AB,1}=\sqrt{2N_{AB,1}^{kT}{W}_i{N}_{AB,1}^k}er{f}^{-1}\left(1-2{\delta }_{AB,1}\right)$, ${\kappa }_{AB,2}=\sqrt{2N_{AB,2}^{kT}{W}_i{N}_{AB,2}^k}er{f}^{-1}\left(1-2{\delta }_{AB,2}\right)$.

Position distance constraint:

Ensure that the minimum distance over the next N time steps is greater than the safety threshold $d_{\min }$:

$$\begin{array}{c}{\Vert p_A-p_B^k\Vert }_2\ge {d\left\{\mathrm{1,2},\cdots ,N\right\}}_{min}\end{array}$$

(26)

Control input and boundary constraints:

$$\begin{array}{c}{\underset{̱}{u}}_A\le u_A\le {\stackrel{̱}{u}}_A{,p}_{\min }\le p\left(t\right)\le p_{\max },v_{\min }\le v\left(t\right)\le v_{\max }\end{array}$$

(27)

For reproducibility, we report the VO-MPC implementation settings as follows. The MPC state is x = [p_x, p_y, p_z, v_x, v_y, v_z]ᵀ and the control is u = [a_x, a_y, a_z]ᵀ. We use Δt = 0.1 s and horizon N = 20 (2.0 s). The weighting matrices are Q_mpc = diag (1000, 1000, 1000, 100, 100, 100) and R_mpc = 10⁻⁶ I₃, with an additional vertical penalty w_z = 100. Control bounds are u ∈ [−100, 100] per axis. The VO activation range is 75 m and the risk threshold is δ = 0.1. The resulting nonlinear program is solved using CasADi + IPOPT (max_iter = 1000, tol = 10⁻⁸, obj_tol = 10⁻⁶).

2.3.5. Deterministic VO-MPC Formulation and Solution

At each time step t, VO-MPC solves the following optimization problem to obtain the control input:

$$\begin{array}{c}\underset{x_A^{1:N},u_A^{0:N-1}}{min}{\displaystyle \sum _{k=0}^{N-1}}{\Vert x_A^k-x_{ref,A}^k\Vert }_Q+{\Vert u_A^k\Vert }_R\end{array}$$

(28)

Subject to the above constraints, the optimal control sequence $u_A^{\mathrm{*}}={\left[{\left(u_A^{\mathrm{*}0}\right)}^T{\left(u_A^{\mathrm{*}1}\right)}^T\cdots {\left(u_A^{\mathrm{*}\left(N-1\right)}\right)}^T\right]}^T$ is generated, and the first control input $u_A^{*0}$ is executed. By this method, the probabilistic constraints can be converted into deterministic linear constraints, which facilitates the solution.

2.4. Fusion Logic Between EKF-LSTM Prediction and VO-Based Avoidance

The proposed safety-assurance pipeline couples trajectory prediction, probabilistic risk assessment, and tactical-level avoidance in a closed loop. While Section 2.1, Section 2.2 and Section 2.3 introduce the EKF-LSTM predictor, the TDC-based collision risk assessment, and the VO-MPC controller, the information flow between these modules was not explicitly described. This section therefore summarizes how EKF-LSTM prediction is fused with VO-based avoidance during online operation.

At each time step $t$, the onboard navigation system provides measurements of each aircraft state (position and velocity). The EKF-LSTM module uses a window of historical trajectory states to generate a one-step-ahead state prediction ${\widehat{x}}_{t\mid t-1}$ and then produce the updated (filtered) state estimate after correction. The resulting predicted trajectory over the next few steps constitutes the nominal future motion used by the downstream collision-risk evaluation. Meanwhile, EKF-LSTM prediction residuals provide an empirical description of forecast uncertainty, which is later leveraged by the risk assessment module.

Based on the predicted nominal trajectories, the TDC method constructs a three-dimensional uncertainty envelope for each aircraft and performs Monte Carlo sampling inside the dispersion cones to estimate the collision probability over a finite look-ahead window. The resulting risk value is compared with the alerting threshold $\delta$; when the estimated collision probability exceeds $\delta$, a potential conflict is declared and the avoidance controller is triggered. In this way, the EKF-LSTM predictor does not directly command avoidance actions; instead, it provides both the nominal motion forecast and the uncertainty evidence that enable risk-aware decision triggering.

Once activated, the VO-MPC controller uses the latest filtered state estimate as the initial condition for optimization, improving resilience against measurement noise. The other aircraft is treated as a moving obstacle, and the relative position and velocity derived from the most recent state estimates are used to construct the corresponding velocity obstacle region in the velocity space. The MPC optimization then searches for a control sequence that maintains trajectory tracking while enforcing VO-based collision-free constraints together with the vehicle dynamics and the probabilistic/deterministic constraints defined in Section 2.3. The first control input of the optimal sequence is applied, and the overall procedure repeats at the next time step, forming an iterative loop.

3. Results

3.1. Flight Trajectory Prediction Results

3.1.1. Dataset and Preprocessing

The dataset utilized in this study for trajectory prediction in manned–unmanned aircraft collaboration was constructed from actual flight data of a specific manned aircraft model and simulation data from a six-degree-of-freedom aircraft model. The dataset covers five representative maneuver types—S-shaped maneuver, dive, roll, circling, and level flight—with 500 complete trajectories for each maneuver. Each training sample is generated using a sliding window with an input history length of 10 time steps. Using this process, a total of 285,396 samples were obtained. Data preprocessing involved cleaning and Min–Max normalization (scaling to [0, 1]) to eliminate dimensional differences. Following model prediction, denormalization was applied to restore the predicted values to their original scale. To ensure the model’s generalization capability, the dataset was split into training, validation, and test sets, comprising 70%, 15%, and 15% of the samples, respectively. This split follows common practice in supervised learning for trajectory prediction, aiming to balance sufficient training data for learning representative maneuver patterns, an independent validation subset for model selection and hyper-parameter tuning, and a sufficiently large held-out test subset for stable and unbiased performance reporting. If other reasonable splits are adopted, the main effect is a trade-off between the amount of training data and the statistical stability of validation/test evaluation: allocating more data to training may slightly improve fitted accuracy but reduces validation/test reliability, whereas allocating more data to testing strengthens evaluation reliability but may marginally reduce training performance due to fewer training samples.

3.1.2. Introduction to Evaluation Metrics

Evaluation metrics are critical for assessing the performance of prediction models, facilitating the comparison and selection of the optimal model, detecting overfitting and underfitting, and guiding optimization strategies. They ensure consistency and comparability in evaluations while supporting decision-making in practical applications, such as UAV navigation and control. In this study, Root Mean Squared Error (RMSE), Average Displacement Error (ADE), and Final Displacement Error (FDE) are adopted as evaluation metrics for the model.

RMSE quantifies the square root of the mean of squared prediction errors, thereby imposing a greater penalty on larger deviations. This metric is particularly well-suited for tasks demanding high precision, such as trajectory prediction in aerial systems. A lower RMSE value signifies reduced prediction errors and, consequently, enhanced model performance. The mathematical expression for RMSE is:

$$\mathit{RMSE} =\sqrt{ {\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\left({\widehat{x}}_i-x_i\right)}^2}$$

(29)

ADE assesses the overall deviation between the predicted and actual trajectories by calculating the average Euclidean distance across all time steps in the prediction horizon. This metric comprehensively reflects the model’s prediction accuracy over the entire trajectory. Its mathematical expression is:

$$\mathit{ADE}={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N\Vert {\widehat{x}}_i-x_i\Vert$$

(30)

FDE measures the Euclidean distance between the predicted and actual positions at the final time step, serving as an indicator of the model’s accuracy at the trajectory’s endpoint. Its mathematical expression is:

$$\mathit{FDE}=\Vert {\widehat{x}}_N-x_N\Vert$$

(31)

3.1.3. Comparison and Analysis of Experimental Results

The experimental setup included various flight scenarios (such as level flight, S-shaped maneuver flight, etc.). The prediction task used a window of 10 time steps, and the evaluation metrics included RMSE, ADE, FDE. The results are shown in

Table 2. Prediction error results for EKF, CNN, LSTM, and EKF-LSTM methods.

Flight States	Metric	LSTM	CNN	EKF	LSTM-EKF
S-shaped Maneuver Flight	ADE (m)	145.79	236.14	249.57	122.67
	FDE (m)	342.39	773.98	249.84	221.28
	RMSE (m)	116.99	180.90	145.04	95.75
Dive Flight	ADE (m)	69.69	295.95	277.49	65.06
	FDE (m)	80.06	269.51	312.11	15.14
	RMSE (m)	57.09	225.66	161.93	42.89
Circling Flight	ADE (m)	59.12	528.60	267.31	53.09
	FDE (m)	40.09	808.91	289.33	30.77
	RMSE (m)	46.35	387.17	154.75	39.40
Roll Flight	ADE (m)	168.21	793.43	224.34	113.36
	FDE (m)	86.10	362.34	223.33	8.24
	RMSE (m)	175.47	1251.41	129.53	115.06
Level Flight	ADE (m)	45.03	420.22	339.81	30.07
	FDE (m)	99.15	304.55	339.81	44.16
	RMSE (m)	34.51	369.51	196.19	30.04
Average	ADE (m)	97.57	454.87	271.71	76.85
	FDE (m)	129.56	503.86	282.88	63.92
	RMSE (m)	86.08	486.93	157.49	64.63

:

The experimental results demonstrate that the EKF-LSTM fusion model outperforms standalone methods across all evaluated metrics, achieving reductions of approximately 21.2%, 50.7%, and 24.9% in ADE, FDE, and RMSE, respectively, compared to the LSTM alone. To more intuitively verify the prediction performance of the EKF-LSTM model, we plot the three-dimensional diagrams of the predicted trajectories and actual trajectories of the four models under various typical flight states. Under approximately linear and stable horizontal flight (Figure 4), all models yield marginally differing predictions. However, notable X-direction errors emerge for CNN and EKF, stemming from their inherent limitations: CNN lacks long-term temporal modeling capacity, while EKF is constrained by linearization assumptions.

As illustrated in Figure 5, Figure 6, Figure 7 and Figure 8, significant disparities in predictive performance are evident across different model types for complex flight states, including circling flight (Figure 5), S-shaped maneuvering flight (Figure 6), dive flight (Figure 7), and roll flight (Figure 8). These maneuvers are characterized by stronger nonlinearity and higher dynamics than level flight, which places greater demands on both temporal modeling and state estimation.

In circling flight (Figure 5), the aircraft follows a continuously curved path. The CNN model shows a large deviation from the actual trajectory due to its insufficient ability to model long-term temporal dependence. The LSTM model follows the turning trend better and captures the curved pattern, but it still exhibits a certain degree of mismatch over the horizon. The EKF model performs well in maintaining the overall turning shape; however, constrained by the linearization assumption, it may present a noticeable lag/offset along the trajectory. In contrast, the EKF-LSTM model yields the closest trajectory to the ground truth throughout the turn.

For the S-shaped maneuver (Figure 6), the trajectory contains successive turns with an evident direction switch. The LSTM model captures the overall “S” trend, yet local deviations can be observed near the turning points. Compared with LSTM, EKF-LSTM further reduces these deviations, producing a trajectory that aligns more consistently with the ground truth across both turns and the transition region. Meanwhile, CNN shows the largest mismatch around the direction-change segments, and EKF may exhibit lag/offset when the trajectory changes direction rapidly.

During dive flight (Figure 7), the motion involves a pronounced altitude change and strong 3D coupling. The LSTM model provides a reasonable partial fit of the dive trend, but it may deviate in the steep descent segment due to the lack of real-time correction. The EKF-LSTM model remains the closest to the actual trajectory throughout the entire dive process, demonstrating the best overall performance in nonlinear scenarios. CNN shows significant deviation under this maneuver, while EKF also exhibit mismatch around the transition segment under rapidly changing dynamics.

In roll flight (Figure 8), the trajectory contains a short transition segment, where prediction errors are most noticeable. The EKF prediction is consistent with the overall trend and aligns closely with the ground-truth trajectory, although a visible deviation can be observed around the transition segment. The CNN prediction exhibits the largest error, producing an evident detour and failing to remain on the true 3D path. The LSTM prediction generally follows the overall trajectory but shows a local mismatch near the transition. In contrast, the EKF-LSTM prediction almost overlaps with the ground truth throughout the entire roll maneuver and further reduces the transition deviation, demonstrating the most stable and accurate performance in this highly dynamic scenario.

Comparative analysis reveals that the EKF-LSTM model exhibits superior accuracy across diverse dynamic scenarios, particularly in complex flight phases such as dives and rolls. In contrast, standalone methods struggle in these phases due to their limited ability to capture long-term temporal dependencies or manage significant prediction biases during dynamic maneuvers. By integrating the LSTM’s capability to model nonlinear sequences with the EKF’s resilience, the proposed model delivers stable, accurate, and interpretable predictions, making it well-suited for trajectory forecasting in challenging aerial environments.

3.2. Collision Detection and Avoidance Results

3.2.1. Collision Detection Based on Trajectory Dispersion Cones

In this section, we evaluate a representative two-aircraft manned–unmanned collaborative flight scenario to validate the complete pipeline The trajectories of UAV A and manned aircraft B during the potential collision phase are selected as the objects of study. First, the root mean square error (RMSE) is calculated for each time step based on the predicted three-dimensional trajectory, and a three-dimensional trajectory dispersion cone model is constructed using the RMSE, as shown in Figure 9. The trajectory dispersion cone model fully considers the uncertainty of the prediction and can clearly describe the movement range of the aircraft and their deviation distribution.

Building on the trajectory dispersion cone model, collision detection and risk assessment were conducted by calculating the Euclidean distance between points within the dispersion cones of UAV A and manned aircraft B. In a three-dimensional flight scenario, UAV A maintained a level flight phase while manned aircraft B performed an S-shaped maneuver, introducing a potential collision risk. The predicted three-dimensional flight trajectories, generated using the EKF-LSTM fusion method, are presented in Figure 10.

In the simulation, a collision probability threshold of 0.1 was established. This value indicates that if the collision probability exceeds 0.1 at any time step, a potential collision risk is detected, triggering a collision warning. The threshold was chosen to reflect the aircraft’s operational environment—such as altitude, speed, and surrounding traffic—ensuring sensitive detection of collision risks while minimizing false alarms that might arise from an overly conservative threshold. This approach enhances safety without sacrificing system stability. Figure 11 illustrates the trend of collision probability across time steps, highlighting the threshold’s effectiveness in identifying critical risk moments.

Collision probability fluctuations are directly driven by the spatial relationship between aircraft, specifically their separation distance and the overlap of trajectory dispersion cones. From the 2nd to 3rd time steps, the UAV’s high-speed flight expands its trajectory cone, increasing overlap with the manned aircraft’s cone and elevating collision risk. As the aircraft subsequently move apart, reduced overlap lowers collision probability accordingly. Between the 22th and 25th time steps, their re-approach causes maximum cone overlap and a renewed risk increase. Outside these intervals, collision probability remains low (mostly near zero), indicating sustained safe separation with no significant convergence trend. Flight conflict experiments show close alignment between model predictions and actual outcomes, validating the trajectory dispersion cone-based collision detection model’s effectiveness in accurately identifying potential risks. This method demonstrates resilience in complex environments, providing a reliable basis for collision avoidance decision-making.

3.2.2. Collision Avoidance Based on VO-MPC

To comprehensively evaluate the performance of the VO-MPC method proposed in this paper, its performance is compared with that of the traditional MPC method under different noise levels. The core performance metrics of the two methods are compared under low-noise (σ = 0.5 m), medium-noise (σ = 1.0 m), and high-noise (σ = 2.0 m) conditions. Here, the noise level $\sigma$ denotes the standard deviation of additive Gaussian position measurement noise used to emulate imperfect sensing/communication. Specifically, the position observation is generated as $\mathit{z}\left(t\right)=\mathit{p}\left(t\right)+\mathit{v}\left(t\right)$, where $\mathit{v}\left(t\right)\sim \mathcal{N}(\mathbf{0},{\sigma }^2{\mathit{I}}_3)$. The noisy observations are fed to the prediction/risk module at the measurement-update instants (with $\Delta t=0.1 \mathrm{s}$ in our simulations). The primary metrics include minimum distance (the shortest horizontal distance between aircraft), collision avoidance success rate (the proportion of aircraft that safely pass each other), and average collision probability (a measure of collision risk probability). These metrics evaluate the model’s overall success rate from different perspectives. The experimental results are shown in Figure 12.

The simulation results presented in

Table 3. Comparison of safety performance indicators between MPC and VO-MPC under different noise conditions.

Noise Level	Method	Minimum Distance (m)	Collision Avoidance Success Rate (%)	Average Collision Probability (%)
0.5 m	MPC	12.3	91.2	0.12
	VO-MPC	15.6	99.8	0.04
1.0 m	MPC	10.2	88.5	0.65
	VO-MPC	14.7	96.5	0.18
2.0 m	MPC	7.8	75.3	2.4
	VO-MPC	12.4	89.7	0.82

illustrate that the VO-MPC method introduced in this study outperforms traditional Model Predictive Control (MPC) methods in complex airspace environments, particularly in enhancing safety across varying noise levels. Under low-noise conditions, VO-MPC achieves a minimum separation distance of 15.6 m, marking a 27% improvement over traditional MPC. The collision avoidance success rate reaches 99.8%, an 8.6% increase, while the average collision probability drops to 0.04%, reflecting a 66.7% reduction. In medium-noise scenarios, VO-MPC sustains stable performance with a minimum distance of 14.7 m and a collision avoidance success rate of 96.5%, reducing the average collision probability to 27.7% of that observed with traditional MPC. Similarly, under high-noise conditions, the method maintains a minimum distance of 12.4 m and a success rate of 89.7%, with the collision probability reduced to 34.2% of the traditional MPC value. This approach excels in capturing dynamic interactions between aircraft and environmental shifts, demonstrating exceptional adaptability in high-density airspace and intricate obstacle settings. Notably, VO-MPC’s ability to mitigate collision risks and enhance flight path safety margins, even in challenging high-noise contexts, highlights its potential to substantially elevate flight safety standards in operational environments.

4. Conclusions

This paper presented a unified safety-assurance framework for manned–unmanned collaborative flight by integrating (i) an EKF-LSTM predictor for intent-aware yet physically consistent trajectory forecasting, (ii) a trajectory dispersion cone (TDC) model for probabilistic conflict assessment, and (iii) a VO-MPC controller for collision avoidance under uncertainty. The proposed pipeline explicitly connects prediction, risk quantification, and control, enabling the downstream avoidance module to react not only to nominal future states but also to the estimated uncertainty envelope inferred from prediction residuals.

From the trajectory forecasting experiments under representative maneuvers, the EKF-LSTM fusion consistently outperformed standalone predictors and achieved notable reductions in ADE, FDE, and RMSE compared with the LSTM baseline.

These improvements indicate that combining data-driven temporal modeling with model-based filtering can better accommodate nonlinear flight dynamics while maintaining physically plausible state evolution. Building upon these predictions, the TDC-based Monte Carlo risk evaluation provided a direct mechanism to translate prediction errors into probabilistic collision estimates, which supports the timely triggering of avoidance actions and avoids relying solely on deterministic separation checks.

For collision avoidance, the VO-MPC strategy increased safety margins and remained effective across different noise levels. In the reported experiments, VO-MPC improved minimum separation and raised the avoidance success rate from 91.2% to 99.8% in low-noise settings, while reducing the mean collision probability by 66.7%; it also maintained lower collision risk than conventional MPC in medium- and high-noise cases.

These results suggest that incorporating velocity-obstacle constraints into the MPC formulation can provide more reliable tactical-level avoidance decisions in uncertain and dynamically changing airspace.

Despite these encouraging results, the current study focuses on pairwise encounter scenarios and is evaluated primarily in simulation. Future work will extend the proposed pipeline to multi-aircraft cooperative settings by developing scalable conflict-detection and resolution mechanisms (e.g., coordination and prioritization among multiple agents) while preserving real-time feasibility. We will also investigate more realistic uncertainty representations and perform sensitivity analyses with respect to key safety parameters. In addition, we plan hardware-in-the-loop and flight-test validation, together with computational profiling on representative onboard hardware, to quantify real-time performance and deployment readiness.