Development of LPV-MPC and LQR control strategies for multi-uav formation with battery-awareweight matrix optimization

Abstract

Unmanned aerial vehicles (UAVs) have become indispensable in a wide range of civilian and military applications such as surveillance, logistics, disaster response, and precision agriculture. With the growing demand for cooperative UAV missions, the design of reliable and efficient formation control strategies has gained substantial importance. One of the primary challenges in this field is energy management, as UAVs are strictly limited by their onboard battery capacity. Neglecting this factor can cause premature mission termination, uneven performance across agents, and even safety-critical failures. This thesis addresses the challenge by developing a battery-aware control methodology that incorporates the state of charge (SoC) of UAVs directly into the control framework of multi-UAV formations. The proposed control architecture integrates Linear Parameter-Varying (LPV) Model Predictive Control (MPC) and Linear Quadratic Regulator (LQR) strategies with battery-dependent weight matrix optimization. The novelty lies in dynamically adapting the aggressiveness of control inputs based on the available battery levels of each UAV. Vehicles with depleted batteries are assigned smoother, less demanding trajectories to conserve energy, while those with higher reserves take on more aggressive maneuvers to maintain formation performance. The adaptive tuning of weight matrices is performed using the Nelder–Mead algorithm, a derivative-free optimization method that provides fast convergence and is suitable for real-time applications. The dynamic model is based on a nonlinear six-degree-of-freedom quadrotor representation described by Newton–Euler equations, incorporating both translational and rotational dynamics. The control structure is organized into two hierarchical loops: an outer loop that handles position and trajectory tracking, and an inner loop that stabilizes orientation and angular rates. The MPC predicts system behavior over a finite horizon, enforcing constraints and optimizing control actions, while the LQR provides stabilizing feedback gains by solving the Riccati equation. This hybrid configuration achieves a balance between optimal prediction and efficient stabilization, ensuring reliable tracking under different mission and environmental conditions. A comprehensive set of simulations validates the effectiveness of the proposed approach. In the single-UAV case, the framework demonstrated accurate trajectory tracking with smooth control signals, proving the stability and feasibility of the design. The study was then extended to a multi-UAV formation scenario. Under nominal conditions where all UAVs started with equal SoC, the formation maintained coordinated flight with high accuracy. When battery-aware weight optimization was activated, the results showed a clear redistribution of control efforts: UAVs with lower battery reserves produced smoother control inputs, while UAVs with higher reserves executed more aggressive actions. This adaptation preserved formation integrity and prolonged overall mission endurance by preventing early depletion of individual UAVs. To further evaluate robustness, additional experiments introduced mass variations and external disturbances. These changes caused temporary oscillations, but the LPV-based MPC effectively adapted to parameter variations, restoring formation stability. The findings highlight the resilience of the proposed control scheme in dynamic environments where system properties may change unpredictably. The contributions of this thesis are threefold. First, it proposes a hybrid formation control framework that combines MPC and LQR, leveraging the predictive capabilities of MPC with the efficiency of LQR for inner-loop stabilization. Second, it introduces a novel battery-aware weight optimization mechanism, enabling UAVs to adjust their level of control aggressiveness according to their energy state, thus ensuring fair energy distribution across the swarm. Third, it provides simulation-based validation demonstrating that the approach improves both energy efficiency and trajectory tracking performance in realistic multi-agent scenarios. The broader implication of this research is the potential for practical applications in missions where both endurance and coordination are critical. Examples include long-duration surveillance, cooperative delivery operations, and search-and-rescue missions in resource-constrained environments. By extending the operational lifetime and maintaining coordinated performance, the proposed framework addresses two fundamental requirements for next-generation UAV swarms. In conclusion, this thesis presents a promising step toward energy-aware and adaptive multi-UAV formation control. By embedding battery-awareness directly into the control framework and employing lightweight optimization, the method achieves an effective balance between performance and endurance. Future work will focus on hardware-in-the-loop experiments, real-world flight tests, and the integration of fault-tolerant mechanisms to handle actuator or sensor failures. These directions will strengthen the applicability of the proposed framework in large-scale and safety-critical missions.