Safe and Energy-Aware Decentralized PDE-Constrained Optimization-Based Control of Multi-UAVs for Persistent Wildfire Suppression

Safe and energy-aware decentralized PDE-constrained optimization-based control of multi-UAVs for persistent wildfire suppression addresses the need for autonomous, long-term wildfire management by developing a framework that integrates UAV motion, water deployment, spatial safety, and energy sufficiency under uncertainty. The core contribution is a novel decentralized optimization approach that guarantees safety and energy feasibility in large-scale operations using only local information.

The gist: A decentralized optimization-based control framework is proposed to manage multi-UAV wildfire suppression by coupling a density-based Partial Differential Equation (PDE) model of fire dynamics with Control Barrier Functions (CBFs) for spatial safety and energy constraints, enabling persistent suppression under localization and motion uncertainties.

Problem Formulation

The problem is formulated as a multi-UAV wildfire mitigation problem over a bounded domain where the objective is to limit the spatial growth of the fire region itself. The fire dynamics are modeled by a temperature–fuel field, governed by equations describing temperature evolution and fuel consumption, with suppression input defined as:

us(r, t) = X N i=1 − fi(t)Kspray(r, xi), where Kspray is a Gaussian shaping function representing the suppressant spray shape at robot position xi.

Centralized Control Framework

The initial approach involves a centralized controller using a Control Lyapunov Function (CLF) coupled with the PDE framework. The task objective is defined by minimizing control effort while driving the swarm toward a target density PDF, where:

V (ρw, t) = 1/2 Z Ω ρd(r, t) − ρw(r, t) 2 dr.

The CLF drives the swarm to transport and deploy water towards the target density ρd concentrated over the deployment zone D, while simultaneously enforcing spatial safety through a CBF constraint: hs(ρ) ≥ 0, which bounds the allowed residual belief mass within an unsafe region A.

Decentralized Control Extension

To adapt this to large-scale operations, the framework is decentralized by replacing the global density with a local detectable density ρNi(r, t) based on a detection radius d. The safety and energy constraints are enforced locally using neighborhood sets defined by a distance-based communication graph. This ensures that each robot operates with only locally available information within a detection radius d.

Decentralized Optimization Controller

The proposed decentralized controller extends the centralized model by localizing the CLF and incorporating energy awareness. The control objective is formulated as:

min ui∈U, s ui squared + γs s.t. αvVi + V˙ i − s ≤ 0, αhhs,i + h˙s,i ≥ δi, αEhEi(xi) + h˙ Ei(xi, ui) ≥ 0.

Here, the safety CBF hs is replaced by its local counterpart hs,i. Furthermore, neighboring robots are treated as stationary in planning, and the initial predicted velocities uj (0) are assigned to induce a worst-case motion prediction ρ˙ worst Ni used in the safety constraint δi.

Validation and Results

The effectiveness of both controllers is validated through simulations and real quadcopter experiments. Simulations show that while centralized control generally outperforms decentralized control in the main suppression phase by prioritizing larger fires, the decentralized controller react[s] to these smaller hot spots much earlier. The experiment with four quadcopters demonstrated that the decentralized deployment nearly halves the peak fire area, confirming its effectiveness using only local sensing and neighbor information while respecting safety and energy constraints. Crucially, the computational demand of the centralized controller increases significantly with team size, making it impractical for large teams, whereas the decentralized controller remains practical for deployment.

Conclusion

The work introduces a decentralized density-based PDE-constrained control framework that successfully combines fire-aware target generation, local information sharing, water deployment, spatial safety via CBFs, and energy-aware charging within a unified optimization-based controller. The results demonstrate the practical feasibility of this framework for persistent wildfire suppression under localization and motion uncertainty. Future work will focus on extending the framework to include water-refill planning for fully autonomous operations.

How it works

The system models the fire dynamics using a temperature–fuel field governed by a PDE, where fuel consumption follows an Arrhenius law. The UAV suppression input is modeled as:

us(r, t) = X N i=1 − fi(t)Kspray(r, xi), where Kspray is a Gaussian shaping function representing the suppressant spray shape at robot position xi.

The spatial density of the multi-robot system evolves according to the Fokker-Planck equation (3), which provides a deterministic macroscopic model of the system density despite the presence of uncertainties. This framework governs the deterministic evolution of the entire team’s probabilistic spatial distribution under control input u.

Here are specific improvements to AI systems derived from this research, along with what those improved systems can achieve:

1. Improved Fire Response System: The proposed decentralized density-based control framework allows AI systems to perform coordinated wildfire suppression in large-scale, remote environments using only local sensing and neighbor information. This system can actively reduce the active fire area by dynamically adjusting UAV trajectories to move toward active fire fronts, deploy suppressants based on localized temperature maps, and avoid high-temperature zones while ensuring every agent maintains sufficient battery for return to charging stations.

2. Energy-Aware Autonomous Swarms: By integrating a formal energy sufficiency constraint into the control law (via Control Barrier Functions), the AI system can execute long-duration missions under strict operational limits. This means UAV swarms can sustain persistent wildfire monitoring and suppression operations over multiple charge cycles without succumbing to energy depletion, making them viable for extended, autonomous response scenarios where recharging infrastructure may be sparse.

3. Robust Safety Guarantees in Uncertain Environments: The use of Control Barrier Functions (CBFs) provides formal mathematical guarantees for spatial safety (avoiding thermal damage zones) and motion constraints even when facing localization and motion uncertainties. This allows the AI system to operate reliably in real-world, noisy conditions where perfect state knowledge is impossible, ensuring that the collective swarm never enters a dangerous thermal region or violates hard physical limits.

4. Scalable Decentralized Control for Large Teams: The framework is designed to scale from centralized control (for high coordination) to decentralized control (for large numbers of robots). Specifically, the decentralized controller can be implemented by each robot using only local information and worst-case neighbor predictions. This enables the AI system to effectively manage thousands of UAVs in a dynamic fire scenario without requiring constant, high-bandwidth communication across the entire team, ensuring fast reaction times that are computationally feasible for onboard processing.

5. Adaptive Task Prioritization: The framework utilizes a unified density-based Partial Differential Equation (PDE) model and a task Lyapunov function that couples fire dynamics with water deployment targets. This allows the AI system to dynamically prioritize its actions—balancing the need to eliminate large, dominant fire regions versus responding quickly to smaller, emerging hot spots—leading to optimized suppression strategies tailored to the current state of the wildfire.

6. Real-Time Deployment Strategy: The controller explicitly models and optimizes both water transportation (moving water from drones) and deployment (spraying it at the target zone). This allows the AI system to calculate an optimal, coordinated sequence for deploying suppressant resources, minimizing waste while maximizing suppression efficiency by ensuring suppressants reach the most critical areas as quickly as possible.