The rapid advancement of artificial intelligence and automation has propelled distributed multi-Unmanned Aerial Vehicle (UAV) systems into the forefront of applications across diverse fields such as defense, precision agriculture, emergency response, and logistics. Compared to a single UAV, a distributed multi-UAV system exhibits superior robustness, flexibility, scalability, and adaptability, offering more comprehensive and integrated capabilities. While significant research has been conducted on autonomous navigation, planning, and control for these systems, ensuring their safe operation in complex environments fraught with multi-source risks remains a paramount challenge. This is particularly critical for tasks like cable-suspended payload transport in disaster relief or mountainous delivery, where systems are susceptible to disturbances from the swinging load and collision risks from both static and dynamic obstacles.
This paper addresses the safety challenge for multi-UAV systems during cable-suspended payload transportation. We propose a novel risk-triggered distributed safety cooperative control framework. The core innovation lies in a two-pronged approach: the quantitative characterization of multi-source risks and the design of a risk-aware controller. Firstly, we model the payload-induced disturbance as an exogenous system and design a disturbance observer for its precise estimation and compensation. The resulting positional tracking error under this disturbance is statistically characterized. Furthermore, we integrate this with uncertainties in state estimation and obstacle perception to model the coupled collision risk. This risk is rigorously quantified using the Conditional Value-at-Risk (CVaR) metric, providing a probabilistic safety guarantee. Secondly, building upon this risk quantification, we develop a distributed controller that seamlessly integrates robust formation tracking, a risk-triggered collision/obstacle avoidance strategy, and active disturbance compensation. The avoidance maneuvers are activated only when the assessed CVaR exceeds a dynamic safety threshold, thereby reducing conservatism and unnecessary maneuvers compared to traditional methods that rely on constant safety margins.
1. System Modeling and Risk Quantification Foundation
1.1 UAV Dynamics with Payload Disturbance
Consider a team of N quadrotor UAVs performing a cooperative transport task with cable-suspended payloads. The translational dynamics of the i-th UAV in the world frame can be described by:
$$ m_i \dot{\mathbf{v}}_i = m_i g \mathbf{e}_3 + \mathbf{R}_i F_i \mathbf{e}_3 + \mathbf{D}_{ai} $$
where \( \mathbf{p}_i, \mathbf{v}_i \in \mathbb{R}^3 \) are the position and velocity vectors, \( m_i \) is the total mass, \( g \) is gravity, \( \mathbf{R}_i \in SO(3) \) is the rotation matrix, \( F_i \) is the total thrust, and \( \mathbf{D}_{ai} \in \mathbb{R}^3 \) is the external disturbance force induced by the cable-suspended payload. This disturbance is a key risk factor impacting control accuracy.
1.2 Disturbance Modeling and Observer Design
The payload-induced disturbance \( \mathbf{D}_{ai} \) is modeled as an output of a linear exogenous system with partially known dynamics, representing its oscillatory nature:
$$ \begin{cases} \dot{\boldsymbol{\xi}}_i(t) = \mathbf{A} \boldsymbol{\xi}_i(t) \\ \mathbf{D}_{ai}(t) = \mathbf{B} \boldsymbol{\xi}_i(t) \end{cases} $$
where \( \boldsymbol{\xi}_i(t) \in \mathbb{R}^6 \) is the state of the exogenous system, and \( \mathbf{A} \in \mathbb{R}^{6\times6} \), \( \mathbf{B} \in \mathbb{R}^{3\times6} \) are known matrices. To estimate and cancel this disturbance, a nonlinear disturbance observer (DOB) is designed:
$$ \begin{aligned} \dot{\boldsymbol{\eta}}_i &= (\mathbf{A} – \mathbf{L}_i(\mathbf{p}_i, \mathbf{v}_i)\mathbf{G}\mathbf{B})\boldsymbol{\eta}_i + \mathbf{A}\boldsymbol{\lambda}_i(\mathbf{p}_i, \mathbf{v}_i) – \mathbf{L}_i(\mathbf{p}_i, \mathbf{v}_i)(\mathbf{G}\mathbf{f}_i(\mathbf{v}_i) + \dot{\boldsymbol{\lambda}}_i(\mathbf{p}_i, \mathbf{v}_i)) \\ \hat{\boldsymbol{\xi}}_i &= \boldsymbol{\eta}_i + \boldsymbol{\lambda}_i(\mathbf{p}_i, \mathbf{v}_i) \\ \hat{\mathbf{D}}_{ai} &= \mathbf{B} \hat{\boldsymbol{\xi}}_i \end{aligned} $$
Here, \( \hat{\cdot} \) denotes estimated values, \( \boldsymbol{\eta}_i \) is an auxiliary state, \( \boldsymbol{\lambda}_i \) is a designed auxiliary function, \( \mathbf{G} = [\mathbf{0}_{3\times3}; (1/m_i)\mathbf{I}_{3\times3}] \), and \( \mathbf{L}_i(\cdot) \) is the observer gain matrix chosen to make \( (\mathbf{A} – \mathbf{L}_i\mathbf{G}\mathbf{B}) \) Hurwitz. The estimation error \( \tilde{\boldsymbol{\xi}}_i = \boldsymbol{\xi}_i – \hat{\boldsymbol{\xi}}_i \) converges exponentially to zero.
1.3 Quantifying Uncertain Collision Risk with CVaR
Despite disturbance compensation, residual tracking errors and sensor uncertainties (e.g., in ego-state and obstacle position estimation) create probabilistic collision risks. We define the tracked position as a random variable \( \mathbf{P}_i \sim \mathcal{N}(\hat{\mathbf{p}}_i, \boldsymbol{\Sigma}_i) \), where \( \boldsymbol{\Sigma}_i = \boldsymbol{\Sigma}_{ei} + \boldsymbol{\Sigma}_{pi} \). \( \boldsymbol{\Sigma}_{ei} \) comes from state estimation noise, and \( \boldsymbol{\Sigma}_{pi} \) is derived from the distribution of the residual tracking error under payload disturbance, which can be fitted from flight data (e.g., \( \boldsymbol{\Sigma}_{pi} = \text{diag}(0.02^2, 0.03^2, 0.02^2) \)). Similarly, an obstacle’s position is \( \mathbf{P}_k \sim \mathcal{N}(\hat{\mathbf{p}}_k, \boldsymbol{\Sigma}_k) \).
The safety distance between UAV i and obstacle k is defined using an ellipsoidal metric to account for downwash and payload swing:
$$ D_{ik} = \| \boldsymbol{\Psi}^{-1/2} (\mathbf{P}_k – \mathbf{P}_i) \|, \quad \text{with} \quad \boldsymbol{\Psi} = \text{diag}(1, 1, L_s) $$
where \( L_s > 1 \) is a scaling factor. A collision occurs if \( D_{ik} < D_{ik,\min} \), the minimum permitted distance. We define a safety loss function \( \mathcal{L}_{ik} = D_{ik,\min} – D_{ik} \). A positive value indicates a safety violation. To quantify the tail risk beyond a confidence level \( \alpha \in (0,1) \), we employ Conditional Value-at-Risk (CVaR). CVaRα(\( \mathcal{L}_{ik} \)) represents the expected loss in the worst \( (1-\alpha) \times 100\% \) of cases (e.g., the average of losses exceeding the 95th percentile). Formally, with Value-at-Risk \( \text{VaR}_\alpha(\mathcal{L}) = \inf\{z \in \mathbb{R}: P(\mathcal{L} > z) \leq 1-\alpha\} \),
$$ \text{CVaR}_\alpha(\mathcal{L}_{ik}) = \mathbb{E}[\mathcal{L}_{ik} \mid \mathcal{L}_{ik} \geq \text{VaR}_\alpha(\mathcal{L}_{ik})] $$
Calculating CVaR for nonlinear \( \mathcal{L}_{ik} \) involving the norm of Gaussian variables can be done via sampling or approximation methods. The condition \( \text{CVaR}_\alpha(\mathcal{L}_{ik}) < 0 \) provides a probabilistic guarantee of safety with confidence \( \alpha \). The same formulation applies to inter-UAV collision risk \( \mathcal{L}_{ij} \) between UAV i and j.
2. Risk-Triggered Distributed Safety Cooperative Controller
The proposed control scheme follows an inner-outer loop structure. The inner loop stabilizes attitude. The outer loop position controller synthesizes three components: formation tracking, risk-triggered avoidance, and disturbance compensation.
2.1 Robust Distributed Formation Tracking
For the i-th UAV communicating with neighbors over a directed graph \( \mathcal{G} \), a robust distributed formation controller is designed:
$$ \begin{aligned} \mathbf{u}_{f,i} = & \sum_{j \in \mathcal{N}_i} a_{ij}[\mathbf{K}_p((\hat{\mathbf{p}}_j – \boldsymbol{\delta}_j) – (\hat{\mathbf{p}}_i – \boldsymbol{\delta}_i)) + \mathbf{K}_v(\hat{\mathbf{v}}_j – \hat{\mathbf{v}}_i)] \\ & + a_{i0}[\mathbf{K}_p(\mathbf{p}_d – \hat{\mathbf{p}}_i – \boldsymbol{\delta}_i) + \mathbf{K}_v(\dot{\mathbf{p}}_d – \hat{\mathbf{v}}_i)] \end{aligned} $$
where \( \mathbf{K}_p, \mathbf{K}_v > 0 \) are diagonal gain matrices, \( a_{ij} \) are adjacency weights, \( \boldsymbol{\delta}_i \) is the desired formation offset, and \( \mathbf{p}_d(t) \) is the desired trajectory of the virtual leader.
2.2 Risk-Triggered Collision Avoidance
Avoidance control is not always active but triggered based on real-time risk assessment. We define a dynamic safety threshold \( T_{ik} \) for UAV i against obstacle k:
$$ T_{ik} = \frac{\mathbf{v}_{ik} \cdot \mathbf{p}_{ik}}{\|\mathbf{p}_{ik}\|} – \delta_1 – \delta_2 D_{ik,s} $$
where \( \mathbf{v}_{ik} = \mathbf{v}_i – \mathbf{v}_k \), \( \mathbf{p}_{ik} = \hat{\mathbf{p}}_k – \hat{\mathbf{p}}_i \), \( \delta_1, \delta_2 > 0 \), and \( D_{ik,s} > 0 \) is a safety buffer. This threshold considers relative velocity: it decreases when vehicles approach, making triggering more likely.
The risk-triggered obstacle avoidance control \( \mathbf{u}_{a,i}^k \) is then:
$$ \mathbf{u}_{a,i}^k = \begin{cases} \mathbf{0}, & \text{if } \text{CVaR}_\alpha(\mathcal{L}_{ik}) \leq T_{ik} \\ (u_{r,ik} + u_{d,ik}) \mathbf{K}_s \frac{\mathbf{p}_{ik}}{\|\mathbf{p}_{ik}\|}, & \text{if } \text{CVaR}_\alpha(\mathcal{L}_{ik}) > T_{ik} \end{cases} $$
where \( \mathbf{K}_s \) is a gain matrix. The repulsive term \( u_{r,ik} \) and a rotational guiding term \( u_{d,ik} \) are designed as:
$$ u_{r,ik} = k_1 (D_{ik,c} – \|\boldsymbol{\Psi}^{-1/2}\mathbf{p}_{ik}\|), \quad u_{d,ik} = -k_2 \mathbf{R}(\Theta_i) \mathbf{v}_i $$
The rotation matrix \( \mathbf{R}(\Theta_i) \) helps the UAV navigate around obstacles, preventing local minima (“deadlock”). The inter-UAV avoidance control \( \mathbf{u}_{s,i}^j \) is designed similarly, triggered by \( \text{CVaR}_\alpha(\mathcal{L}_{ij}) > T_{ij} \).
2.3 Integrated Safety Control Law
The final distributed position control input for UAV i integrates all components with the disturbance estimate for feedforward compensation:
$$ \mathbf{u}_i = k_f \mathbf{u}_{f,i} + \sum_{j \in \mathcal{N}_i} k_{sj} \mathbf{u}_{s,i}^j + \sum_{k \in \mathcal{O}_i} k_{sk} \mathbf{u}_{a,i}^k – \hat{\mathbf{D}}_{ai} $$
where \( k_f, k_{sj}, k_{sk} \) are weighting coefficients, and \( \mathcal{O}_i \) is the set of obstacles detected by UAV i.
3. Simulation and Experimental Validation
The proposed framework is validated through both real-world flight tests and extensive numerical simulations, highlighting its performance in disturbance rejection and safety-critical obstacle avoidance.
3.1 Flight Test: Anti-Disturbance Performance
A flight experiment was conducted using a quadrotor UAV carrying a 100g payload (60cm cable) tracking an 8-shaped trajectory. The proposed controller (with DOB) was compared against a baseline robust formation controller without disturbance compensation.
The results demonstrated a significant improvement in tracking accuracy under payload disturbance. The Root Mean Square Error (RMSE) of position tracking is summarized below:
| Controller Type | Position RMSE (m) | Improvement |
|---|---|---|
| Baseline (without DOB) | 0.103 | – |
| Proposed (with DOB) | 0.043 | 58.25% |
The residual tracking error distribution under the proposed controller was collected and fitted to a Gaussian model \( \mathcal{N}(\mathbf{0}, \boldsymbol{\Sigma}_{pi}) \), which is used for the subsequent risk quantification. This demonstrates the effectiveness of the composite anti-disturbance strategy for China UAV drone platforms in realistic scenarios.
3.2 Multi-UAV Simulation: Safe Navigation in Cluttered Environment
A simulation of five UAVs navigating through a dense obstacle field was performed. The UAVs started in a formation and were required to reach a target 35 meters away. Sensor noise and the characterized tracking error distribution were injected to model uncertainties (\( \boldsymbol{\Sigma}_i = \text{diag}(0.0404, 0.0409, 0.0404) \)). The confidence level was set to \( \alpha = 0.95 \).
Key Results:
- Safety: All UAVs successfully avoided all static obstacles and each other. The minimum recorded distance between any UAV and any obstacle was 1.27m, above the collision threshold of 1.25m.
- Performance & Conservatism: The average path length traveled was 36.70m, only 4.9% longer than the ideal straight-line path (35m). This indicates low conservatism and efficient trajectories. The formation was well-maintained during transit.
- Comparison: A comparison with a bio-inspired flocking algorithm showed that the proposed method achieved similar safety but with 14.2% lower average clearance from obstacles (1.51m vs 1.76m), meaning it navigates closer to obstacles when safe to do so, and with faster task completion.
The following table compares key performance metrics between the proposed method and the baseline flocking algorithm:
| Performance Metric | Proposed Method | Flocking Algorithm |
|---|---|---|
| Collision-Free Operation | Yes | Yes |
| Avg. Path Length (m) | 36.70 | 37.92 |
| Avg. Min. Obstacle Distance (m) | 1.51 | 1.76 |
| Avg. Speed (m/s) | ~1.02 | ~0.98 |
| Formation Keeping | Excellent | Good |
4. Conclusion
This paper presented a comprehensive distributed safety cooperative control framework for multi-UAV systems operating under multi-source risks, specifically focusing on cable-suspended payload transport in complex environments. The core contribution is the integration of quantitative risk assessment into the control loop. By modeling and observing the payload disturbance, statistically characterizing the resulting tracking uncertainty, and employing CVaR to quantify probabilistic collision risks, the controller gains a predictive understanding of safety. The risk-triggered mechanism ensures that aggressive avoidance maneuvers are employed only when necessary, as dictated by the real-time risk assessment. This achieves an optimal balance between safety assurance and operational efficiency (low conservatism).
Experimental and simulation results validate the framework’s effectiveness. The disturbance observer-based compensation significantly improved trajectory tracking accuracy for a China UAV drone under payload swing. In cluttered environments, the multi-UAV system maintained safety guarantees while exhibiting smooth, efficient, and formation-preserving flight paths. This work provides a principled approach towards building resilient and intelligent multi-agent systems capable of operating safely in uncertain, real-world conditions. Future directions include extending the risk model to dynamic obstacles, integrating communication delays into the risk assessment, and implementing the framework on fully distributed swarms of China UAV drones for large-scale cooperative tasks.