Optimizing Energy Efficiency in Agricultural Spraying Drones Through Fractional-Order PID Controllers and Genetic Algorithm

OTIMIZAÇÃO DA EFICIÊNCIA ENERGÉTICA EM DRONES DE PULVERIZAÇÃO AGRÍCOLA ATRAVÉS DE CONTROLADORES PID FRACIONÁRIOS E ALGORITMO GENÉTICO OPTIMIZING ENERGY EFFICIENCY IN AGRICULTURAL SPRAYING DRONES THROUGH FRACTIONAL-ORDER PID CONTROLLERS AND GENETIC ALGORITHM Authors: Heictor Alves de Oliveira Costa¹; Fernando José Von Zuben² ¹Universidade Estadual de Campinas (UNICAMP), [email protected] ²Universidade Estadual de Campinas (UNICAMP), vonzub[email protected] Abstract RESUMO A viabilidade da agricultura de precisão na agricultura familiar está intrinsecamente ligada à eficiência operacional e energética dos equipamentos, especialmente quando dependem de fontes renováveis no local, como painéis fotovoltaicos. Este trabalho aborda o desafio de maximizar a eficiência energética de drones de pulverização através de uma otimização de controle avançada. A metodologia emprega um Algoritmo Genético (AG) para otimizar e comparar dois tipos de controladores: um Proporcional-Integral-Derivativo (PID) convencional e um PID de Ordem Fracionária (FOPID). A otimização visa minimizar uma função de custo que modela o consumo de energia e o tempo de voo. Os resultados da simulação demonstram que o controlador FOPID alcança uma redução de 3,1% no custo operacional por hectare em comparação com o PID convencional. Análises dos perfis de aceleração revelam que o FOPID, apesar de exibir um comportamento de alta frequência, evita os picos de grande amplitude característicos do PID, resultando em um menor esforço de controle geral e, consequentemente, menor consumo de energia. O estudo conclui que a otimização de software avançada, especificamente com controladores FOPID, oferece uma solução energeticamente eficiente que promove a sustentabilidade na agricultura familiar. Palavras-chave: Eficiência Energética; Drone Agrícola; Controle de Ordem Fracionária; Algoritmo Genético; Agricultura de Precisão. Abstract ABSTRACT The viability of precision agriculture in family farming is intrinsically linked to the operational and energy efficiency of equipment, especially when relying on on-site renewable sources like photovoltaic panels. This paper addresses the challenge of maximizing the energy efficiency of spraying drones through advanced control optimization. The methodology employs a Genetic Algorithm (GA) to optimize and compare two controller types: a conventional Proportional-Integral-Derivative (PID) and a Fractional-Order PID (FOPID). The optimization aims to minimize a cost function that models energy consumption and flight time. Simulation results demonstrate that the FOPID controller achieves a 3.1% reduction in operational cost per hectare compared to the conventional PID. Analysis of the acceleration profiles reveals that the FOPID, despite exhibiting high-frequency behavior, avoids the large-amplitude peaks characteristic of the PID, resulting in lower overall control effort and, consequently, reduced energy consumption. The study concludes that advanced software optimization, specifically with FOPID controllers, offers an energy-efficient solution that promotes sustainability in family farming. Keywords: Energy Efficiency; Agricultural Drone; Fractional-Order Control; Genetic Algorithm; Precision Agriculture. 1 INTRODUCTION The agricultural sector is a cornerstone of the global economy but also a significant consumer of energy (MAJEED et al., 2023). The increasing integration of renewable energy sources, such as on-farm photovoltaic (PV) systems, is pivotal for enhancing sustainability and reducing operational costs, particularly for family farming operations (GORJIAN et al., 2020). In this context, Unmanned Aerial Vehicles (UAVs), or drones, have emerged as a transformative technology in precision agriculture (SETIAWAN et al., 2025). However, the operational viability of these drones is intrinsically linked to their energy efficiency and power consumption, as limited battery life poses a significant constraint (REZOUG; IQBAL; NEMRA, 2025). The central challenge this paper addresses is the optimization of a drone’s flight dynamics to minimize energy expenditure during agricultural spraying missions. This is not merely an economic consideration but a crucial factor for sustainability, as higher efficiency translates to less demand on limited, locally-generated renewable energy. While Proportional-IntegralDerivative (PID) controllers are widely used for UAV stabilization, their integer-order structure can be restrictive when fine-tuning for optimal energy use (BAHARUDDIN; BASRI, 2023; ALMAHTURI et al., 2020). Abrupt and aggressive control actions can lead to inefficient power usage and mechanical wear (SHANKARAN et al., 2022). This study explores the potential of Fractional-Order PID (FOPID) controllers, which generalize the integral and derivative terms to non-integer orders (λand µ), offering additional degrees of freedom (PODLUBNY, 1999). This enhanced flexibility allows for a more precise shaping of the system’s dynamic response. The scientific gap lies in applying this advanced control strategy, optimized via a Genetic Algorithm (GA) and guided by an intelligent path planner (Probabilistic Roadmap), to specifically target energy efficiency in an agricultural context. We hypothesize that this software-driven approach can yield a more efficient control system, characterized by smoother behavior and reduced control effort. 2 METHODOLOGY The methodology integrates path planning and control optimization within a high-fidelity simulation environment. The objective is to create an energy-efficient flight plan for a drone operating in a complex agricultural setting. 2.1 Path Planning in a Simulated Environment The process begins in the CoppeliaSim environment, which hosts a virtual agricultural terrain complete with cultivation areas and non-navigable obstacles, as shown in Figure 1. An initial reconnaissance flight allows onboard sensors to gather data, from which a map of the area is constructed. Figure 1: Simulation environment in CoppeliaSim showing agricultural terrain. Using this map, the Probabilistic Roadmap (PRM) algorithm (‘mobileRobotPRM‘ in MATLAB) generates a graph of all possible safe paths, as seen in Figure 2. The PRM is highly effective for environments with complex obstacle geometries (KAVRAKI et al., 1996; ARNALDO et al., 2024). A specific flight path is then calculated from this roadmap. Figure 3 shows a partial segment of a trajectory, while Figure 4 illustrates a complete coverage path synthesized from multiple such segments. Figure 2: Probabilistic Roadmap (PRM) generated over the free space. Figure 3: A partial path segment calculated using the PRM. Figure 4: The complete, synthesized coverage path on the grid map. 2.2 Controller Design and Optimization With a defined trajectory, a Genetic Algorithm (GA) optimizes the drone’s control system for energy efficiency (KHUWAJA et al., 2018). The GA tunes the parameters for two different controllers for comparison: a conventional PID and a Fractional-Order PID (FOPID). The FOPID controller’s PIλDµstructure offers greater tuning flexibility, which can lead to smoother responses and improved robustness (ZHUO-YUN et al., 2020; FAREH, 2019). The GA’s goal is to minimize a cost function, J, that models the trade-offs of a mission: J=ZT 0w1p˙x(t)2+ ˙y(t)2+ ˙z(t)2+w2t+w3P(p(t)) + w4 m(t) B(t)dt (1) The terms in the function represent weighted costs for path length (energy), flight time, obstacle risk, and battery usage. Critically, the drone’s mass, m(t), decreases as it sprays, and the battery level, B(t), is depleted by control effort, making the simulation physically realistic. 3 RESULTS AND DISCUSSION The optimization process yielded distinct performance profiles for the PID and FOPID controllers. The analysis focuses on both the overall mission cost and the specific characteristics of the control effort. 3.1 Energy Efficiency and Operational Cost The GA was executed to minimize the cost function Jfor both controllers. The resulting dimensionless costs were: •Regular PID Controller: JP ID = 2.256916 ×104 •Fractional-Order PID Controller: JF OP ID = 2.186916 ×104 Using a conversion methodology calibrated against the real-world operational costs of a drone (including energy, battery depreciation, and maintenance), these abstract values were translated into a tangible metric. The analysis, detailed in Table 1, shows that the FOPID controller achieves a 3.1% reduction in operational cost per hectare. Table 1: Cost conversion from dimensionless J to $/Hectare. Metric Regular PID FOPID Optimized J Cost (adimensional) 22,569.16 21,869.16 Real Mission Cost [$] $2.66 $2.58 Operational Cost [$/ha] $0.89 $0.86 Improvement vs. PID — 3.1% 3.2 Control Effort and Acceleration Profile Analysis To understand the source of this efficiency gain, the acceleration profiles of both controllers were analyzed. Figure 5 shows the acceleration and velocity for the PID controller, while Figure 6 shows the same for the FOPID controller. Figure 5: Acceleration and velocity profiles for the standard PID controller. Figure 6: Acceleration and velocity profiles for the FOPID controller. A visual comparison reveals a critical difference in control strategy. The standard PID controller (Figure 5) exhibits a noisy and aggressive acceleration profile, characterized by large, high-amplitude peaks. These correspond to abrupt control actions as the drone attempts to correct its path, leading to significant overshoot and sustained periods of acceleration and deceleration. This style of control is mechanically stressful and electrically inefficient, demanding high peak currents from the battery. In contrast, the FOPID controller’s acceleration profile (Figure 6) is visibly much smoother. While both controllers produce very similar velocity profiles over the course of the mission, the acceleration performed by the FOPID requires far less abrupt effort from the drone’s mechanical components. This prevents the large-scale oscillations seen in the PID response. This behavior, characteristic of a well-tuned fractional-order system, results in lower total control effort. The energy saved by avoiding aggressive acceleration peaks leads to the observed 3.1% improvement in overall efficiency. 4 CONCLUSIONS This paper successfully demonstrated that an advanced, software-driven approach can significantly enhance the energy efficiency of agricultural drones. By employing a Genetic Algorithm to optimize a Fractional-Order PID controller and guiding it with a path from a Probabilistic Roadmap planner, we achieved a more efficient and smoother flight control system compared to a conventional PID controller. The primary finding is that the FOPID controller yields a 3.1% reduction in operational cost per hectare. This is not just a theoretical improvement; it is a direct consequence of a more intelligent control strategy. The analysis of acceleration profiles showed that the FOPID controller avoids energy-intensive, high-amplitude corrections in favor of more subtle, highfrequency adjustments, resulting in less mechanical stress and lower overall power consumption. For the family farmer relying on renewable energy, this efficiency gain is critical. It translates to more area covered per battery charge, greater operational autonomy, and reduced strain on local energy systems. This study validates that focusing on software intelligence, particularly advanced control theory, is a powerful pathway to creating sustainable, efficient, and accessible technology for modern agriculture. References AL-MAHTURI, A. et al. Pid controller tuning for a quadcopter using meta-heuristic algorithms. 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