Dynamic UAV Swarm Collaboration for Multi-Targets Tracking under Malicious Jamming: Joint Power, Path and Target Association Optimization (2306.16196v1)

Abstract: In this paper, the multi-target tracking (MTT) with an unmanned aerial vehicle (UAV) swarm is investigated in the presence of jammers, where UAVs in the swarm communicate with each other to exchange information of targets during tracking. The communication between UAVs suffers from severe interference, including inter-UAV interference and jamming, thus leading to a deteriorated quality of MTT. To mitigate the interference and achieve MTT, we formulate a interference minimization problem by jointly optimizing UAV's sub-swarm division, trajectory, and power, subject to the constraint of MTT, collision prevention, flying ability, and UAV energy consumption. Due to the multiple coupling of sub-swarm division, trajectory, and power, the proposed optimization problem is NP-hard. To solve this challenging problem, it is decomposed into three subproblems, i.e., target association, path plan, and power control. First, a cluster-evolutionary target association (CETA) algorithm is proposed, which involves dividing the UAV swarm into the multiple sub-swarms and individually matching these sub-swarms to targets. Second, a jamming-sensitive and singular case tolerance (JSSCT)-artificial potential field (APF) algorithm is proposed to plan trajectory for tracking the targets. Third, we develop a jamming-aware mean field game (JA-MFG) power control scheme, where a novel cost function is established considering the total interference. Finally, to minimize the total interference, a dynamic collaboration approach is designed. Simulation results validate that the proposed dynamic collaboration approach reduces average total interference, tracking steps, and target switching times by 28%, 33%, and 48%, respectively, comparing to existing baselines.

• The paper introduces a joint optimization framework that dynamically coordinates target association, trajectory planning, and power control for UAV swarms under jamming.
• It divides the UAV swarm into sub-swarms using the CETA algorithm, significantly reducing interference and improving tracking performance.
• Simulation results demonstrate reductions of 28% in total interference, 33% in tracking steps, and 48% in target switching times, confirming the method’s efficiency.

This paper (2306.16196) investigates the challenging problem of multi-target tracking (MTT) by a swarm of unmanned aerial vehicles (UAVs) in the presence of malicious jammers. The core challenge lies in the severe interference (both inter-UAV and jamming) that degrades communication quality among UAVs, which is essential for information exchange during tracking. The paper formulates an optimization problem aiming to minimize total interference by jointly optimizing UAV sub-swarm division, trajectory, and transmission power, subject to constraints on tracking quality, collision avoidance, flight capabilities, and energy consumption.

Recognizing that the joint optimization problem is NP-hard due to the coupling between sub-swarm division, trajectory, and power, the authors propose decomposing it into three subproblems and solving them through a dynamic collaboration approach.

The three subproblems and their proposed solutions are:

1. Target Association: This involves dividing the total UAV swarm into multiple sub-swarms and associating each sub-swarm with a specific target. The paper proposes the Cluster-Evolutionary Target Association (CETA) algorithm, inspired by density peak clustering. CETA determines sub-swarm centers based on local density and distance to higher-density points. Remaining UAVs are assigned to the nearest sub-swarm center. Sub-swarms are then matched to targets based on the minimum distance between the sub-swarm's centroid and the target's position. This approach aims for efficient grouping and assignment.
2. Trajectory Planning: Once associated with targets, UAVs need to plan paths to track them while avoiding obstacles, other UAVs, and jammers. The paper develops the Jamming-Sensitive and Singular Case Tolerance (JSSCT)-Artificial Potential Field (APF) algorithm. This algorithm uses attractive forces pushing UAVs towards their targets and repulsive forces pushing them away from potential collision sources (obstacles, other UAVs, jammers). JSSCT-APF specifically addresses two common drawbacks of traditional APF:
   • Local Minima: It introduces an external force to help UAVs escape points where attractive and repulsive forces balance prematurely.
   • Jittering: It includes a mechanism to adjust the turning angle when it exceeds 90 degrees, preventing oscillation. The repulsive force gain coefficients are made sensitive to jamming and inter-UAV interference levels, allowing the trajectory to adapt based on communication conditions.
3. Power Control: UAVs need to control their transmission power for inter-UAV communication while minimizing interference and meeting a minimum SINR requirement. For a large swarm, traditional N-player game theory is computationally intensive. The paper leverages Mean Field Game (MFG) theory to model this interaction. They formulate a Jamming-Aware Mean Field Game (JA-MFG) where the collective behavior of other UAVs and jammers is approximated as mean fields of interference and jamming. The power control problem is transformed into solving coupled Hamilton-Jacobi-BeLLMan (HJB) (for optimal control policy) and Fokker-Planck-Kolmogorov (FPK) (for mean field evolution) partial differential equations. These PDEs are made tractable using a finite difference method, allowing for an alternating update process to find the Mean Field Equilibrium (MFE). The cost function in the MFG balances achieving the target SINR and minimizing total interference (inter-UAV + jamming).

The Dynamic Collaboration Approach orchestrates these three components. It operates over discrete time slots.

• Target association is initially performed using CETA.
• Trajectory planning is executed using JSSCT-APF based on the current target assignments.
• Power control is updated periodically (at the end of each slot) using the JA-MFG, which takes into account the current positions (and thus distances and channel gains) determined by the trajectory.
• Triggers for Adaptation:
  • Target reassociation is triggered if a sub-swarm's centroid is no longer closest to its assigned target.
  • Trajectory replanning is triggered if the average inter-UAV interference or jamming interference in a slot exceeds predefined thresholds. This allows interference levels calculated by the power control module to influence the spatial arrangement of the UAVs.

Practical Implementation and Applications:

• Real-time System: Implementing this approach in a real-world UAV swarm requires a robust, decentralized control system. Each UAV would need to execute the JSSCT-APF algorithm locally based on its perceived environment (other UAV positions, obstacle locations, target location, jammer location). Inter-UAV communication is needed to share positions and potentially interference measurements for the MFG.
• Computational Load: CETA is computationally efficient (single iteration for initial clustering). JSSCT-APF involves calculating potential fields, which scales with the number of neighbors, obstacles, and jammers within the influence range. The JA-MFG solution using finite difference requires discretizing time and energy states and iterating to find MFE, which adds computational overhead, likely requiring powerful onboard processors or edge computing support.
• Communication Requirements: The approach relies on intermittent communication for target association updates (potentially less frequent) and power control (periodically each slot). The SINR constraint (\ref{P1l}) and the interference minimization objective directly highlight the need for reliable, though potentially low-rate, communication links even under jamming.
• Sensor Fusion: Accurate positions of other UAVs, targets, obstacles, and jammers are crucial inputs. This necessitates robust localization and tracking systems (GPS, visual odometry, radar, etc.) onboard the UAVs and mechanisms for sharing this information.
• Jamming Modeling: The effectiveness of the JA-MFG and the jamming-sensitive APF depends on accurate modeling or estimation of jammer locations and power levels.
• Scalability: The use of MFG for power control addresses scalability challenges compared to N-player games, making it suitable for larger swarms. The decentralized nature of APF for trajectory planning also contributes to scalability.

Simulation Results and Performance:

The simulations validate the effectiveness of the proposed methods.

• CETA is shown to produce more compact sub-swarms with fewer iterations than k-means and FCM, leading to lower average inter-UAV interference.
• JSSCT-APF successfully avoids local minima and jittering issues inherent in traditional APF and provides shorter, smoother trajectories compared to RRT.
• JA-MFG effectively manages power to maintain the desired SINR while considering interference, demonstrating energy level-dependent optimal power policies.
• The overall dynamic collaboration approach is shown to significantly reduce average total interference (by 28%), tracking steps (by 33%), and target switching times (by 48%) compared to baseline methods that do not fully account for jamming or couple the three aspects dynamically. This highlights the performance gains from the joint optimization and adaptive nature of the proposed framework.

In summary, this paper presents a comprehensive framework for coordinated multi-target tracking with a UAV swarm under jamming, providing practical algorithms for target association, robust trajectory planning, and interference-aware power control, all integrated within a dynamic collaboration strategy to adapt to changing conditions and minimize interference.