Fuzzy logic optimization of hybrid PV-battery system for autonomous robots

Abstract

Most studies on power generation systems have focused on individual components, leaving researchers without a comprehensive understanding of integrated systems. This study addresses this gap by developing a fully self-sufficient photovoltaic (PV) system for a 12 V autonomous mobile robot. We calculated the power and energy requirements of the robot to appropriately size the PV panel and designed a DC–DC buck converter. For energy storage, we used a Li-ion battery and a bidirectional current converter to manage the charging and discharging processes. To optimize performance, we implemented Maximum Power Point Tracking (MPPT) using a fuzzy logic-based control method. Simulation results demonstrate that the proposed fuzzy MPPT controller outperforms the classical P&O algorithm by achieving up to 98% MPPT efficiency, reducing power ripple by over 50%, and improving convergence speed by approximately 30%. The system maintains the output voltage regulated within ±1% of the 12 V target across all tested irradiance and load conditions, confirming both high tracking accuracy and robust stability. During optimal irradiance, the system can simultaneously power the robot and charge the battery, while under low-irradiance conditions, the battery ensures uninterrupted operation. These findings confirm that the proposed hybrid PV system enables mobile robots to operate autonomously and reliably regardless of weather conditions, providing a practical solution for continuous power supply in robotic applications.

Introduction

Mobile robots are indispensable across a wide range of industries, autonomously performing tasks in education, medicine, military operations, rescue missions, space exploration, and agriculture. Their importance became even more evident during the COVID-19 pandemic when their capabilities proved invaluable for critical operations.^1,2 Rapid advancements in robotics technology, coupled with rising concerns regarding energy sustainability, have fueled efforts to develop independent energy systems for mobile robots. However, most mobile robots currently rely on conventional power sources such as batteries and fuel cells, which limit operational flexibility and raise significant sustainability challenges. Although practical, rechargeable batteries require frequent recharging, leading to increased downtime and reduced autonomy.

In contrast, renewable energy sources offer a clean and abundant alternative, making them a promising solution for ensuring uninterrupted robotic operation.^3–5 Among these, solar energy is the most widely utilized and cost-effective option ⁶ Prior research has focused on addressing energy fluctuations in solar systems through power management strategies and Maximum Power Point Tracking (MPPT) techniques. Power management systems optimize energy transfer from solar panels to batteries and onboard components to ensure operational efficiency. For example, Mikołajczyk et al. ⁵ and Hou et al. ⁷ proposed systems that maximize battery life using low-power protocols and energy-saving mechanisms. Initial MPPT approaches, such as operating PV arrays at fixed voltages near the Maximum Power Point (MPP), lacked adaptability to dynamic environmental conditions. ⁸ Later studies categorized MPPT techniques into traditional, smart, enhanced, and hybrid methods.^9,10

Early MPPT algorithms, notably Perturb and Observe (P&O) and Incremental Conductance (InCond), gained popularity for their simplicity and ease of implementation. However, they exhibit performance drawbacks, such as steady-state oscillations around the MPP, reducing overall energy efficiency. To mitigate these limitations, intelligent control techniques particularly fuzzy logic controllers (FLCs) have been introduced in the MPPT domain. Fuzzy logic offers a powerful framework for managing nonlinear behavior and uncertainty by evaluating “degrees of truth” instead of binary logic, enabling more nuanced and adaptive decision-making. ¹¹ An adaptive fuzzy logic-based MPPT has demonstrated improved steady-state performance and robust tracking under sudden irradiance changes. ¹² Similarly, fuzzy logic MPPT combined with InCond techniques showed superior static and dynamic responses, significantly increasing PV output power compared to classical methods.^12,13 Beyond MPPT, fuzzy logic control has also been adopted in broader energy management contexts, such as hybrid PV-battery microgrids, to regulate battery charging/discharging and maintain bus voltage stability effectively.^14,15

Despite its advantages, fuzzy logic control has certain well-documented drawbacks. The implementation of FLCs often involves considerable design complexity, as it depends heavily on expert-defined rules and fine-tuned membership functions, making them sensitive to system parameter variations and computationally intensive.^8,16 Moreover, under rapidly fluctuating environmental conditions such as intermittent shading conventional fuzzy controllers without adaptive enhancements may exhibit suboptimal tracking and increased oscillations around the MPP.^14,17 Nevertheless, fuzzy logic remains particularly advantageous for mobile robotic applications, where operational reliability and dynamic adaptability are crucial. In these contexts, the benefits of fuzzy control including reduced oscillations, improved convergence speed, and superior robustness under variable conditions justify its adoption, particularly when hybridized with classical methods such as P&O.

Alongside improvements at the controller level, researchers have increasingly focused on optimizing PV system integration and power management strategies. In grid-connected or microgrid environments, intelligent control schemes (such as Takagi–Sugeno fuzzy-based strategies for PV–battery DC microgrids) ¹⁴ have demonstrated superior flexibility and stability in the presence of renewable intermittency. ¹⁸ Similarly, recent advances in electric vehicle (EV) charging infrastructures employ fuzzy control combined with hybrid optimization algorithms to address challenges of low inertia and voltage instability in DC microgrids. For instance, a 2024 study proposed an intelligent microgrid controller using embedded fuzzy logic to smooth power fluctuations during fast EV charging, validated through hardware experiments. ¹⁷ These developments highlight broader trend modern PV systems (spanning microgrids, consumer electronics, vehicular systems, and now autonomous robotics) increasingly rely on hybrid intelligent control algorithms (e.g. fuzzy logic, neural networks, and metaheuristics) to achieve high energy efficiency and operational stability under dynamic conditions.^19,20 The study ²¹ introduced a Modified Adaptive Jaya Optimization (MAJO) algorithm for maximum power point tracking, demonstrating superior performance over conventional deterministic and swarm-based MPPT methods—especially in partial shading scenarios, where accurate tracking is most challenging.

Despite these technological advancements, a significant gap remains in the literature regarding photovoltaic-powered autonomous mobile robots. Unlike existing fuzzy-based MPPT schemes that are often designed for static or grid-tied PV systems, our approach is applied for dynamic conditions and embedded operation in fully autonomous mobile robots, offering real-time adaptability with minimal computational burden. In contrast to prior works, the present study proposes a fuzzy logic-enhanced P&O MPPT specifically performed for a 12 V autonomous mobile robot.

This contribution distinguishes itself by integrating intelligent control directly into the robot’s power management system, achieving enhanced dynamic response allowing the MPPT to rapidly adapt to irradiance fluctuations caused by robot movement while significantly reducing steady-state oscillations around the MPP. These improvements translate into higher energy conversion efficiency and a more reliable power supply, critical for sustained robot operation. Therefore, this research extends the current state of the art by demonstrating a robust, hybrid MPPT solution capable of sustaining efficient mobile robotic operation under realistic and variable environmental conditions.

We present a fully autonomous 12 V photovoltaic power system for the mobile robot, including optimal PV panel sizing, a custom DC–DC buck converter, and a Li-ion battery with a bidirectional converter for charge management. This holistic design ensures efficient energy harvesting and reliable power storage for continuous robot operation, in contrast to previous studies that optimize these components in isolation.

Moreover, the proposed hybrid system is rigorously evaluated under diverse environmental conditions (e.g. varying solar irradiance, temperature, and load) using MATLAB/Simulink simulations. The results demonstrate that our fuzzy-P&O controller maintains high tracking efficiency and system stability across dynamic scenarios, where classical MPPT methods often struggle. This validates the controller’s robustness in real-world operating conditions for mobile robots.

The remainder of this paper is organized as follows. The system design and synoptic diagram are outlined, followed by a discussion of the characterization and modeling of the solar power system of the robot. Next, the optimization of the photovoltaic system is explored, and the results are presented and discussed. This paper concludes with a comparative analysis.

Despite significant progress in individual aspects of PV energy systems, few studies have addressed the comprehensive integration, control, and validation of a fully autonomous PV-battery power supply specifically tailored for mobile robots. To address these challenges and bridge the gap in current research, the main contributions of this work are summarized as follows:

• Development of a complete, self-sufficient PV-battery power architecture for autonomous mobile robots, integrating accurate load modeling, system sizing, and robust control for real-world conditions.

• Design and implementation of a fuzzy logic-enhanced MPPT controller based on the P&O algorithm, delivering improved tracking speed, reduced power ripple, and high efficiency under varying irradiance and load disturbances.

• Comprehensive simulation-based validation using MATLAB/Simulink, demonstrating up to 98% MPPT efficiency, more than 50% reduction in power ripple, and approximately 30% faster convergence compared to conventional methods.

• Demonstration of continuous, regulated operation including voltage regulation within ±1% and uninterrupted power delivery under all tested climatic scenarios showcasing the practicality and superiority of the proposed system for real-world mobile robotic applications.

System design

This study comprehensively examines the design, optimization, and performance evaluation of a standalone power system powered by renewable energy, specifically designed for a 12 V mobile robot. ²¹ It focuses on critical components, such as PV panel sizing, DC/DC buck converter design, battery selection, and control strategies for efficient battery charging and discharging. A synoptic diagram of the system is illustrated in Figure 1.

Figure 1.

Synoptic diagram.

Our mobile robot operates using a solar panel with a DC/DC buck converter, efficiently stepping down the high voltage from the panel to the robot’s operating voltage of 12 V. This is achieved through pulse-width modulation (PWM), which rapidly switches the input voltage on and off. By adjusting the duty cycle of the PWM signal, the converter precisely regulates the output voltage while minimizing power losses.

To ensure maximum power output from the solar panel under varying sunlight conditions, we integrated Maximum Power Point Tracking (MPPT) technology. This system continuously adjusts the operating point of the panel to deliver the maximum possible power based on the current sunlight intensity. The robot relies on a lithium-ion battery for operation during cloudy weather or at night.

A bidirectional current transformer manages the battery, enabling both charging and discharging. This transformer efficiently facilitates power transfer between the solar panel, battery, and robot. To maintain a consistent power supply regardless of the weather conditions, a proportional-integral (PI) controller oversees the operation of the two MOSFETs within the bidirectional converter. This always ensures stable and reliable power delivery.

Sizing the PV power system for the mobile robot

The primary advantage of photovoltaic (PV) energy is its ability to generate electricity anywhere on Earth, provided sunlight is available. However, the proper sizing of the PV panel is crucial to meet specific electrical requirements and ensure maximum system efficiency. The sizing of a system involves determining the parameters of its physical components based on well-defined specifications. A PV module, consisting of an array of solar cells, generates direct current (DC), and the combination of multiple modules forms a PV panel. This assembly can be configured in various ways to match the characteristics of the load equipment.

The size of the PV panel plays a key role in evaluating the actual energy consumption of the load. This process typically depends on several factors such as the desired energy output, geographical location, angle, and tilt of the panel. For fixed installations, where the load is constant and well-defined, the sizing is relatively straightforward. However, this process is more complex in mobile systems. These challenges include estimating the energy requirements of the system and accommodating the panel within the physical constraints of the mobile platform.

To appropriately size the PV panel to power the mobile robot, it is necessary to calculate both the power and the energy required for its propulsion. This approach ensures that the robot operates efficiently, while maintaining its mobility and adaptability.

Power and energy required for the mobile robot

Various forces influence the energy consumption of mobile robots; therefore, it is essential to use an energy calculator to account for and overcome these forces. The propulsion power required for the robot must counteract frictional forces arising from gravity, aerodynamic drag, and rolling resistance. These forces are depicted in Figure 2, which illustrates their impact on the energy demand of the robot.

Figure 2.

System voltage and harmonic content.

The motion of the robot follows Newton’s law, which states that the sum of the forces acting on it is equal to the product of its mass and acceleration, as shown in (1).

$$M\overrightarrow{a}={\overrightarrow{F}}_m+{\overrightarrow{F}}_f+{\overrightarrow{F}}_a+{\overrightarrow{F}}_p$$

(1)

According to Newton’s second law, the term M.a represents the resultant force acting on the robot, which is the vector sum of all the forces applied to it. This resultant force dictates the acceleration or deceleration of the robot depending on its direction and magnitude. When the forces are projected onto the axis of motion, the traction force $F_m$ emerges. The traction force $F_m$ can be calculated as the sum of the components of all the forces acting along the direction of motion, as expressed in (2).

$$F_m=\mathrm{M}.\mathrm{a}+{\mathrm{F}}_f+{\mathrm{F}}_a+{\mathrm{F}}_p$$

(2)

When the robot climbs a slope, the friction force $F_f$ consists of two main components: one parallel to the slope surface, commonly referred to as rolling resistance, and another perpendicular to the slope surface, which is caused by gravity but is generally negligible. The parallel component of friction ( $F_f$ ) primarily arises from the resistance of the robot’s wheels or tracks as they move along the inclined surface. This force is calculated similarly to that on a horizontal surface; however, the inclination of the slope must be considered. If the slope’s inclination angle is $\beta$ , then the rolling resistance force $F_f$ is determined using (3).

$$F_f=C_r.M.g.\cos \left(\beta \right)$$

(3)

The aerodynamic resistance force $F_a$ is proportional to several factors, including the air density, the square of the relative velocity (accounting for wind), the robot’s frontal area S, and its drag coefficient C _x . This relationship is described by equation (4).

$$F_a\frac{1}{2}.\rho .S.C_x.V^2$$

(4)

The slope force $F_p$ represents the component of the robot’s weight acting along an inclined surface due to gravity. This force resists the robot’s motion when ascending a slope and assists it when descending. The slope force depends on the slope’s inclination angle ( $\beta$ ), the robot’s mass ( $M$ ), and the gravitational acceleration ( $g$ ). It is calculated as the weight component along the slope. When the robot ascends, $F_p$ acts upward and is determined to use (5). Conversely, when the robot descends, $F_p$ acts downward, and its sign is reversed.

$$F_p=\mathrm{M}.g.\sin \left(\beta \right)$$

(5)

By summing these components, we determine the total driving force required to overcome all resistive forces and achieve the desired acceleration or deceleration along the direction of motion. This equation provides a comprehensive framework for analyzing and understanding the dynamics of the robot’s motion.

When the acceleration is positive, the robot is in an acceleration phase, resulting in an increase in speed. Conversely, a negative acceleration value indicates a deceleration phase, during which the robot’s speed decreases.

Additionally, the power of the robot at a given velocity is defined as the product of the traction force $F_m$ and the velocity, as expressed in (6).

$$P_{\mathrm{Robot}}={\mathrm{F}}_m.V$$

(6)

Thus, the power of the mass at a given velocity can be expressed using (7).

$$P_{\mathrm{Robot}}=(M\frac{\mathrm{dV}}{\mathrm{dt}+{\mathrm{C}}_r}\mathrm{Mgcos}\left(\beta \right)+\frac{1}{2}\mathrm{\rho }{\mathrm{SC}}_x{V}^2+\mathrm{Mgsin}\left(\beta \right))V$$

(7)

Here, $\mathrm{dV}/\mathrm{dt}$ represents the rate of in the velocity of the robot, which corresponds to its acceleration $a=\mathrm{dV}/\mathrm{dt}$ . From this power, the energy required to propel the robot can be calculated using (8).

$$\mathrm{E}=\frac{A_r}{V}.P_{\mathrm{Robot}}$$

(8)

The total energy consumption is determined by the robot’s power and speed, scaled by its autonomy. This reflects the energy required to propel the robot over a specific distance or duration at a given velocity, accounting for its operational autonomy. The term $A_r/V$ represents the time or distance over which the robot’s autonomy extends. Multiplying this term by the robot’s power $P_{\mathrm{Robot}}$ yields the energy required for propulsion over that distance or time period. This equation is essential for estimating the energy demands of the robot’s propulsion system and for designing systems that enhance energy efficiency based on desired velocities and operational autonomy.

Sizing of the PV panel

To determine the size of the PV panel for our robot, we first calculated the daily electrical consumption, as previously mentioned. After obtaining the daily energy requirements in watt-hours ( $\mathrm{Wh}$ ), we calculated the required size of the PV panel to generate this energy. When sizing the PV panel, we need to consider factors such as the panel’s efficiency, the average solar insolation at our location (which depends on latitude, weather conditions, and time of year), and any system loss.

Model of a PV cell

A PV cell can be modeled using an equivalent circuit that characterizes its electrical behavior. The most widely used model is the equivalent diode model, which includes a photoelectric current source (representing the current generated by sunlight) in parallel with a diode. To account for electrical losses in the cell, this model was extended by adding series and parallel resistance.^22,23 The equivalent circuit of the single-diode model is represented in Figure 3.

Figure 3.

Equivalent model of the PV cell.

By applying Kirchhoff’s law, the output current of the cell can be expressed by (9)^24,25:

$$I_{\mathrm{pv}}={\mathrm{I}}_{\mathrm{ph}}-I_D-I_{\mathrm{sh}}$$

(9)

Where $I_{\mathrm{ph}}$ is not dependent on the voltage across the cell or series resistance $R_s$ . It is primarily generated by the absorption of sunlight by the PV cells. The photocurrent is proportional to the intensity of the incident light flux on the PV cell and is influenced by the carrier diffusion length in the semiconductor material of the cell. Thus, the photocurrent can be expressed by (10).

$$I_{\mathrm{ph}}=(I_{\mathrm{cc}}+{\mathrm{K}}_i.[T_r-T_{\mathrm{ref}}]).\frac{G}{G_n}$$

(10)

The current flowing through the parallel resistance ( $I_{\mathrm{sh}}$ ) in the PV cell is the current flowing through the parallel resistance $R_{\mathrm{sh}}$ of the cell. It is expressed by (11).

$$I_{\mathrm{sh}}=\frac{V_{\mathrm{pv}}+{\mathrm{R}}_S.I_{\mathrm{pv}}}{R_{\mathrm{sh}}}$$

(11)

This equation indicates that the parallel resistance current depends on the voltage across the cell (V), the total cell current (I), the series resistance ( $R_s$ ), and the parallel resistance ( $R_{\mathrm{sh}}$ ). The parallel resistance current contributes to the total cell current and can affect overall performance. $I_d$ is the current flowing through the $p-n$ junction diode in the PV cell and is determined using (12).

$$I_D={\mathrm{I}}_{0.}(e^{\left(\frac{q.V_D}{A.K.T_r}\right)}-1)$$

(12)

The reverse saturation current ( $I_{\mathrm{sat}}$ ) of the diode in a PV cell is often derived from the Shockley diode equation, which considers the several parameters, including temperature, and may vary depending on the model used to represent the diode. This is expressed by (13):

$$I_0={\mathrm{I}}_{\mathrm{sat}}.{\left(\frac{T_r}{T_{\mathrm{ref}}}\right)}^3.e^{\left[\left(\frac{q.E_{g0}}{A.K}\right)\left(\frac{1}{T_{\mathrm{ref}}-\frac{1}{T_r}}\right)\right]}$$

(13)

Based on the parameters, the output current of the PV cell was computed according to (14).

$$I_{\mathrm{pv}}={\mathrm{I}}_{\mathrm{ph}}-I_{0.}[e^{\left(\frac{q.V_{\mathrm{pv}}}{A.K.T_r}\right)}-1]-\left[\frac{V_{\mathrm{pv}}+{\mathrm{R}}_S.I_{\mathrm{pv}}}{R_{\mathrm{sh}}}\right]$$

(14)

Equation (14) represents the current-voltage characteristics of the PV cell, which is the fundamental component of the PV solar panels. These semiconductor devices, typically made of silicon, generate a voltage that can range from 0.3 to 0.7 V, depending on factors such as the material used, configuration, temperature, and cell aging. A PV module is composed of multiple cells connected in series ( $N_s$ ) and in parallel ( $N_p$ ). Connecting cells in series increases the output voltage, whereas connecting cells in parallel increases the output current. The behavior of a PV module composed of several cells is described by (15).

$$\mathrm{I}={\mathrm{N}}_p.I_{\mathrm{ph}}-N_p.I_{0.}[e^{\frac{q.(V_{\mathrm{pv}}+{\mathrm{R}}_s.I_{\mathrm{pv}})}{N_s.A.K.T}}-1]-\left[\frac{V_{\mathrm{pv}}+{\mathrm{R}}_s.I_{\mathrm{pv}}}{R_{\mathrm{sh}}}\right]$$

(15)

The shunt resistance $R_{\mathrm{sh}}$ is typically very high, making the shunt current $I_{\mathrm{sh}}$ negligible. Therefore, the equation can be simplified to neglect the $I_{\mathrm{sh}}$ term, leading to (16).

$$\mathrm{I}={\mathrm{N}}_p.I_{\mathrm{ph}}-N_p.I_{0.}[e^{\frac{q.(V_{\mathrm{pv}}+{\mathrm{R}}_s.I_{\mathrm{pv}})}{N_s.A.K.T}}-1]$$

(16)

Sizing DC/DC buck converters

The Buck converter used in this study is a step-down DC–DC converter employed to reduce the DC input voltage to a lower DC output voltage. The duty cycle of the buck converter is given by (17).

$$\alpha =\frac{V_{\mathrm{Robot}}}{V_{\mathrm{pv}}}=\frac{12}{17.88}=0.671$$

(17)

The equivalent resistance is given by (18).

$$R_{\mathrm{eq}}=\frac{V_{\mathrm{Robot}}^2}{P}=\frac{{12}^2}{30}=4.8\Omega$$

(18)

The inductance $L$ is determined using (19).

$$L⪰\frac{V_{\mathrm{pv}}}{4\mathrm{\Delta }{\mathrm{I}}_{\mathrm{Lmax}}.f}$$

(19)

With $\mathrm{\Delta }{I}_L=400\mathrm{mA}$ , $f=100\mathrm{kHz}$ ,we get $L⪰\frac{17.88}{{4.0.4.10}^5}\approx 112\mu H.$

Adding a safety margin of 20%, we choose $L=140\mu H$ .

The capacitor $C_2$ is determined using (20).

$$C_2⪰\frac{\mathrm{\Delta }{\mathrm{I}}_{\mathrm{Lmax}}}{8.\mathrm{\Delta }{\mathrm{V}}_{C2.\max }.f}$$

(20)

With $\mathrm{\Delta }{V}_{C_2}=10\mathrm{mV}$ , we get $C_2\approx 50\mu F$ .

Adding a safety margin, we choose $C_2=100\mu F.$

For the capacitor $C_1$ , it is computed using (21).

$$C_1⪰\frac{I_{\mathrm{pv}}}{\mathrm{\Delta }\mathrm{Vpvmax}.f}$$

(21)

With $\mathrm{\Delta }{V}_{C_1}=100\mathrm{mV}$ , we get $C_1\approx 170\mu F$ .

Adding a safety margin, we choose $C_1=300\mu F$ . The buck converter specifications for the proposed application are listed in Table 1.

Table 1.

Buck converter specifications.

Setting	Value
Input voltage	$17.8\pm 4V$
Output voltage	$12V$
Maximum power	$30W$
Switching frequency	$100\mathrm{KHz}$
Yield	$93\%$
Output voltage ripple	$⪯1\%$
Inductance $L$	$140\mathrm{\mu }\mathrm{H}$
Capacitance $C_2$	$100\mathrm{\mu }\mathrm{F}$
Capacitance $C_1$	$300\mathrm{\mu }\mathrm{F}$

These specifications allow for the design of an efficient buck converter for our application and provide a stable output voltage of 12 V to power our robot.

Battery design for the mobile robot

Batteries play a crucial role in storing the collected solar energy, ensuring continuous operation of the robot even when solar energy is unavailable (e.g. at night or during cloudy weather). Efficient energy storage systems such as lithium-ion batteries are ideal for providing extended autonomy to robots. ²⁶ These batteries are widely used in solar applications and autonomous robots owing to their high energy density, long lifespan, low self-discharge rate, and fast charging capabilities.^27,28 By enhancing autonomy and ensuring a continuous energy supply, the robot can operate reliably and efficiently throughout its working cycle, even under varying weather conditions.

Control of the battery charging and discharging

To ensure the optimal performance of our system, we require a control system that manages the battery-charging and discharging processes.

Bidirectional current converter

To charge or discharge the battery, a change in the direction of the energy flow is associated with a change in the current direction, while the voltage remains constant. Thus, the converter used to recharge the battery is a bidirectional-current converter. It has a dual purpose: it can either power the robot with solar energy or with the energy stored in the battery. The duty cycle ${\alpha }_B$ controlling this converter ranges from 0 to 1, which is depicted in Figure 4.

Figure 4.

Bidirectional current converter.

To control the two MOSFETs of the bidirectional converter and ensure a stable power supply for the robot ( $V_{\mathrm{charge}}$ ) regardless of weather conditions, we will use two conventional Proportional-Integral (PI) controllers. These controllers will regulate the voltage and current to maintain the desired performance of the power system.

State of charge and discharge of the battery

Using the SimpowerSystems toolbox in MATLAB, we conducted two tests, discharge and charge. Figure 5(a) depicts the discharge state, while Figure 5(b) shows the charge state of the battery.

Figure 5.

State of charge and discharge of the battery: (a) battery discharge from 45% to 0% and (b) battery charge from 45% to 100%.

It should be noted that the battery discharged from 45% to 0% over 30,000 s, approximately 8 h. Conversely, the battery charge reached 100% after 20,000 s, which is approximately 5 h.

A lithium-ion (Li-ion) battery was selected for the simulation due to its high energy density, long cycle life, low self-discharge rate, and widespread use in mobile robotics and embedded systems. Compared to alternatives like lead-acid or nickel-metal hydride (NiMH), Li-ion offers superior efficiency and reduced weight both critical for autonomous robotic platforms. This choice aligns with current industrial and academic trends in mobile energy storage.

MPPT algorithm

The concept of the maximum power point (MPP) in PV systems is essential for optimizing energy generation. This refers to the point at which the solar panel operates at peak efficiency, delivering the maximum power output for a given set of conditions. To ensure that PV systems operate at this optimal point and maximize energy production, various Maximum Power Point Tracking (MPPT) algorithms have been used. In literature, different types of algorithms such as the Constant Current Algorithm, Constant Voltage Algorithm (CV), Incremental Conductance Algorithm (IncCond), and Perturb and Observe Algorithm (P&O) ²⁹ are commonly employed. These algorithms adjust the operating parameters of the PV system, such as the voltage or current, to continuously search for and maintain the MPP, ensuring that the system extracts the maximum available power from the solar panels. In this study, we used the Perturb and Observe (P&O) method.

Perturbation and Observation (P&O) algorithm

The Perturbation and Observation (P&O) method is a widely used MPPT algorithm for PV systems. It is known for its simplicity and effectiveness, as it does not require prior knowledge of the PV panel’s characteristics. This method works by perturbing the system and observing its effect on power. It only requires measurements of the voltage ( $V_{\mathrm{pv}}$ ) and current ( $I_{\mathrm{pv}}$ ) of the panel to track the maximum power point when there are changes in illumination and temperature. The algorithm perturbs the voltage ( $V_{\mathrm{pv}}$ ) by a small amplitude around its initial value and analyzes the resulting power variation. Figure 6 illustrates the variation in power as a function of the PV panel voltage.

Figure 6.

Operating principle of the P&O MPPT algorithm.

As shown, if the operating voltage is perturbed in each direction and the power increases (p > 0), the perturbation moves the operating point closer to the MPP. The P&O algorithm continues to perturb the voltage in the same direction and adjusts the operating point until the MPP is reached. However, if the power decreases (p < 0), the perturbation moves the operating point away from MPP. In this case, the algorithm reverses the direction of the next perturbation, as shown in Table 2.

Table 2.

P&O algorithm.

Perturbation	Change in power	Next perturbation
Positive	Positive	Positive
Positive	Negative	Negative
Negative	Positive	Negative
Negative	Negative	Positive

A flowchart of the P&O method is presented in Figure 7, ³⁰ illustrating the process of analyzing power evolution after each voltage perturbation. This control method typically requires two sensors: one to measure the voltage and another to measure the current, allowing for the determination of PV power at each moment.

Figure 7.

Flowchart of the perturb and observe (P&O) method.

Optimization of the perturbation and observation method by fuzzy logic

In this study, a fuzzy-logic controller was developed to enhance the accuracy and efficiency of the MPPT in our PV system. This approach addresses the limitations of the basic P&O method, including its slow response to changing environmental conditions and the oscillations around the Maximum Power Point (MPP). ³⁰

Fuzzy logic controller

The functional diagram of our fuzzy logic controller (FLC) includes three parts (fuzzification, inference based on rules, and defuzzification), as shown in Figure 8.

Figure 8.

Diagram of a fuzzy logic controller.

The reasoning behind the chosen fuzzy-logic control approach is based on the relationship between the last change in the control signal $\alpha$ (duty cycle) and the resulting power variation. If the change in α increases power, the controller continues moving in the same direction. Conversely, if the change reduces the power, the controller shifts to the opposite direction. The fuzzy controller uses two input variables: $\mathrm{\Delta }{P}_{\mathrm{pv}}\left(k\right)$ (power variation) and $\mathrm{\Delta }{V}_{\mathrm{pv}}\left(k\right)$ (voltage variation), as defined in equation (22). The single output variable is the duty cycle $\alpha$ . ³¹

$$\begin{array}{c}\mathrm{\Delta }{\mathrm{P}}_{\mathrm{pv}}\left(k\right)={\mathrm{P}}_{\mathrm{pv}}\left(k\right)-P_{\mathrm{pv}}(k-1)\hfill \\ \mathrm{\Delta }{\mathrm{V}}_{\mathrm{pv}}\left(k\right)={\mathrm{V}}_{\mathrm{pv}}\left(k\right)-V_{\mathrm{pv}}(k-1)\hfill \end{array}$$

(22)

The power variation values $P_{\mathrm{pv}}\left(k\right)$ and output voltage variation $V_{\mathrm{pv}}\left(k\right)$ of the PV generator can be stabilized before the fuzzification process to simplify the control calculation.

In this model, the membership functions of the output and input variables, as presented in Figure 9, use triangular functions. Six linguistic terms are defined: three for the input (N for negative, Z for zero, and P for positive) and three for the output (S for small, M for medium, and B for big).

Figure 9.

Membership functions of the input variables, and the output variable alpha.

In the context of fuzzy logic control methods for MPPT in PV systems, the fuzzy rule base is a set of if-then rules that dictate the system’s behavior. These rules are designed based on professional expertise and the operational characteristics of the control system. Each rule in the fuzzy rule base consists of an if-part (antecedent), which defines conditions based on the input variables, and a then-part (consequent), which specifies the corresponding output control action. The rules of inference for this controller are summarized in Table 3.

Table 3.

Inference rules.

Rule No.	$\mathrm{\Delta }{\mathrm{V}}_{\mathrm{pv}}$	$\mathrm{\Delta }{\mathrm{P}}_{\mathrm{pv}}$	Alpha
1	P	P	S
2	N	P	B
3	Z	P	M
4	Z	Z	M
5	N	Z	M
6	P	Z	M
7	P	N	B
8	N	N	S
9	Z	N	M

The output of a fuzzy controller is always a fuzzy set, which necessitates a defuzzification process to produce a crisp output for the proposed fuzzy control system. Various defuzzification techniques have been suggested in the literature. Among these, the most commonly used method is the center of gravity or centroid method.^32,33 This technique calculates the center of gravity of the fuzzy set and uses its value as the output of the fuzzy logic controller (FLC). In this study, the single output variable is the duty cycle $\alpha$ .

Results and discussion

To validate the proposed fuzzy-P&O MPPT controller across realistic operating conditions, we evaluated system performance under multiple representative case scenarios. These include: (i) steady-state operation under full irradiance, (ii) dynamic irradiance fluctuations simulating cloud cover transitions, (iii) low irradiance conditions reflecting evening or shaded environments, and (iv) variable temperature conditions. In all cases, the fuzzy controller consistently tracked the maximum power point faster and with reduced oscillation compared to the classical P&O method. These scenarios reflect typical challenges faced by autonomous mobile robots operating outdoors, where weather variability and changing light angles are common.

Figures 10(a) and 11(a) illustrate the simulation results of the classic P&O algorithm, a traditional method for MPPT in PV systems. The power curves depict the relationship between the power output of the PV system and constant illumination levels ( $1000,W/m^2$ in Figure 10(a) as well as varying irradiation levels in Figure 11(a), while maintaining a fixed temperature of ${25}^{o}C$ . These results provide insights into how the power output changes with different irradiation levels under stable temperature conditions when the classic P&O algorithm is employed.

Figure 10.

Comparison of output power behavior under fixed climatic conditions: (a) classic P&O algorithm and (b) fuzzy logic-enhanced P&O algorithm.

Figure 11.

Output power response under variable irradiance conditions at constant temperature (25°C): (a) classic P&O algorithm and (b) fuzzy logic-enhanced P&O algorithm.

Figures 10(b) and 11(b) present the simulation results of the P&O algorithm optimized using a fuzzy logic controller. By incorporating linguistic rules and fuzzy sets, the fuzzy logic controller addresses uncertainties and imprecisions in the MPPT process, thereby enhancing the performance of the P&O algorithm. The power curves in Figure 10(b) show the relationship between the power output and constant illumination levels ( $1000,W/m^2$ ), while Figure 11(b) illustrates the performance under varying irradiation levels ( $500W/m^2,800W/m^2$ , and $1000W/m^2$ ), all at a fixed temperature of ${25}^{o}C$ . These figures demonstrate how fuzzy-logic optimization significantly improves the P&O algorithm’s performance under different irradiation conditions.

In both steady-state and dynamic irradiance conditions, the fuzzy controller exhibits markedly higher efficiency, faster response, and greater stability than the classical approach. A detailed comparison of the methods is provided in Table 4, highlighting the key performance metrics and showcasing the advantages of our approach in terms of efficiency, adaptability, and stability under varying environmental conditions.

Table 4.

Comparison between the classical P&O algorithm and our fuzzy-optimized P&O.

Performance metric	Classical P&O	Fuzzy P&O (proposed)	Improvement
MPPT tracking efficiency	∼78% Of available power	∼98% Of available power	≈+20 Percentage points (≈+26% relative)
Steady-state power ripple (peak-to-peak)	≈10 W (≈10% of output)	≈4 W (≈4% of output)	≈60% Reduction in oscillation amplitude
Response time to MPP	∼0.50 s (to settle)	∼0.35 s (to settle)	≈30% Faster (shorter settling time)

The fuzzy logic-optimized controller consistently achieves a much higher tracking efficiency than the classical P&O. For example, under standard test conditions (1000 W/m², 25°C), the fuzzy controller harvested approximately 98% of the available PV power, whereas the classical P&O captured only about 78%–80%. This corresponds to roughly a 20+ percentage point increase in absolute efficiency (approximately 25% more energy captured relative to the classical method). The superior efficiency of the fuzzy controller is attributed to its ability to minimize deviations from the true MPP. In steady-state operation at fixed irradiance, the classical P&O tends to oscillate around the MPP, causing the operating point to wander and average out at a lower power output. By contrast, the fuzzy-enhanced P&O quickly fine-tunes the duty cycle with adaptive step sizes, virtually eliminating any sustained deviation from the MPP. As a result, the fuzzy controller delivers near-optimal power to the load consistently, even under conditions where the conventional algorithm would suffer tracking losses.

On the other side, the fuzzy controller also greatly improves the stability of the PV output by suppressing oscillations around the MPP. The classical P&O exhibited noticeable power and voltage ripple in both the fixed and variable irradiance tests. In the simulations, the conventional algorithm’s output oscillated with a peak-to-peak amplitude of up to about 10 W (approximately 10% of the 100 W panel capacity in our test scenario). These oscillations indicate wasted energy and increased stress on the power electronics. In sharp contrast, the fuzzy logic-optimized P&O reduced the ripple by well over 50%, limiting the peak-to-peak power fluctuation to roughly 4 W (about 4% of output). This ∼60% reduction in steady-state ripple reflects the fuzzy controller’s better adaptability: it intelligently decreases perturbation step size as the operating point nears the MPP, avoiding the continuous hunting behavior inherent to the fixed-step P&O. Consequently, the PV output with fuzzy MPPT is much smoother and more stable. The reduction in oscillatory behavior not only means higher average power (contributing to the efficiency gains noted above) but also implies less voltage stress and more stable operating conditions for the downstream hardware and the robot’s electrical system.

Moreover, the fuzzy MPPT controller demonstrates a faster response to changing environmental conditions, improving the system’s adaptability to irradiance transients. When the irradiation level was varied (as shown in Figure 11, with steps from 500 to 800 to 1000 W/m²), the classical P&O controller showed a noticeable delay in reaching the new MPP after each change, and its power output exhibited overshoot and undershoot around the transitions. Quantitatively, the conventional P&O required on the order of 0.5 s to settle to the new steady state after a large irradiance step. In contrast, the fuzzy-enhanced controller settled in approximately 0.35 s under the same conditions. This represents roughly a 30% reduction in settling time. The improved transient response is due to the fuzzy controller’s adaptive step size adjustment: it accelerates the perturbation step when a large change in conditions is detected, allowing it to swiftly climb toward the new MPP, then refines the step size to avoid overshooting the peak. The outcome is a faster tracking of the MPP with minimal overshoot, which means the system spends less time in suboptimal operating states during irradiance transitions. This rapid convergence is crucial for maintaining high energy capture when sunlight conditions fluctuate, as it reduces the energy lost during the tracking process by a significant margin.

The simulation model depicted in Figure 12 represents a comprehensive standalone power system designed to independently provide a reliable energy supply.

Figure 12.

Complete simulation system.

A detailed analysis reveals key insights into the system’s behavior under varying radiation conditions, as illustrated in Figure 13. The voltage at the load terminals ( $V_{\mathrm{load}}$ ) consistently aligns with the reference voltage ( $V_{\mathrm{load}.\mathrm{ref}}$ ) of 12 V, irrespective of the radiation levels. This demonstrates the system’s robust voltage regulation and stability, ensuring a steady and reliable power supply to the robot.

Figure 13.

Simulation results of the complete standalone PV power system with variable irradiance.

A dynamic relationship is observed between the radiation levels and the reference current ( $I_{B.\mathrm{ref}}$ ), which in turn influences the battery current ( $I_B$ ). The polarity of the current plays a critical role, with a positive polarity indicating battery discharge and a negative polarity signifying charging. This polarity shift highlights the flow of energy within the system, providing insights into the battery’s operational states.

Under low-radiation conditions (e.g. $900W/m^2$ ), the system depends on the battery, reflecting a discharge state. As radiation levels reach $900W/m^2$ , the PV panel becomes the primary power source, disconnecting the battery from the load. When radiation exceeds $900W/m^2$ , the system operates solely on the PV panel, simultaneously charging the battery. This transition demonstrates the system’s adaptability and efficient energy management across varying environmental scenarios.

To examine the effect of temperature on the system, a constant radiation level of $1000W/m^2$ was maintained while the temperature was varied, as shown in Figure 14. The results revealed that temperature had only a minor influence on the system’s overall behavior. The load terminal voltage ( $V_{\mathrm{load}}$ ) remained consistently regulated at $12V$ , highlighting the system’s robust voltage regulation.

Figure 14.

Simulation results of the complete standalone PV power system with variable temperature.

Additionally, the battery stayed in a charging state throughout the temperature variations, indicating that these fluctuations did not significantly affect the battery’s charging behavior. A slight impact of temperature on the power output was observed, suggesting that temperature changes had a limited effect on the system’s overall performance. This analysis underscores the system’s stability and resilience under varying thermal conditions

The fuzzy logic-enhanced P&O MPPT controller provides substantial improvements over the classical P&O method for 12 V solar-powered mobile robots, including 20%–25% higher power extraction, a 50% reduction in steady-state power ripple, and ∼30% faster response to irradiance changes. These enhancements translate to more stable, reliable power for both the battery and the robot, maximizing available solar energy under optimal and fluctuating conditions, and enabling sustained autonomous operation.

Crucially, comprehensive simulations confirm the stability of the proposed controller across all tested scenarios, including rapid irradiance changes, temperature fluctuations, and load variations. As evidenced in Figures 10–14, the system’s voltage, current, and power all converge quickly after disturbances, with no sustained oscillations, overshoot, or instability. Voltage regulation is consistently maintained within ±1% of the 12 V setpoint. The reduction in power ripple by over 50% further demonstrates superior damping and oscillation suppression relative to the classical P&O. The adaptive fuzzy controller reliably prevents limit cycles or hunting behavior and ensures bounded-input, bounded-output (BIBO) stability, with no performance degradation or divergence observed throughout all simulation scenarios. This confirms that the system remains robust and predictable, providing high performance and resilience even in the face of environmental disturbances.

Comparative study

A review of recent MPPT studies published between 2024 and 2025 including, PSO/metaheuristics, hybrid intelligent controllers, and classical approaches demonstrates that the proposed fuzzy logic-enhanced P&O controller achieves superior performance in efficiency, stability, and convergence speed. Conventional methods such as P&O and Incremental Conductance achieve only about 85%–88% tracking efficiency under challenging conditions, with greater oscillations at steady state. ³⁴ ANN-based MPPT approaches may reach 98.16% efficiency, but typically require longer tracking times (e.g. 1.3 s), while metaheuristic strategies such as DA, GOA, and MFOA often fall below the 98% efficiency mark and can suffer from higher ripple or longer settling times.^35,36 Even advanced hybrid controllers, including fuzzy logic combined with Incremental Conductance or deep reinforcement learning (DDPG), generally report lower efficiency (97.7% and 95%, respectively) or higher ripple.^34,37 Table 5 summarizes other comparisons between 2018 and 2025, highlighting that our approach consistently delivers up to 98% MPPT efficiency, more than 50% reduction in power ripple, and approximately 30% faster convergence than the latest published alternatives.

Table 5.

Comparison of MPPT methods.

Aspect	Previous research	Our research	Strength of our results
Energy source	Predominantly battery-powered systems with limited renewable integration, leading to frequent recharging and downtime, 3 some works integrate PV panels and storage in micro-grids to improve reliability, but full autonomy in mobile robots remained unrealized 38	Fully autonomous 12 V photovoltaic (PV) system powering a mobile robot, supplemented by a lithium-ion battery for energy storage. The design meets all the robot’s power needs using solar energy, eliminating reliance on external charging.	Achieves complete off-grid autonomy using renewable energy, enabling continuous robot operation without manual recharges. The system reliably powered the robot (and charged its battery) under optimal sun and maintained operation under low sunlight, ensuring uninterrupted mobility
MPPT algorithm	Classical MPPT techniques (e.g., Perturb & Observe and Incremental Conductance) have been widely used for their simplicity. More advanced “smart” algorithms (neural networks, meta-heuristics, etc.) have been explored to improve performance, though often at the cost of greater complexity and tuning effort. 39	An improved P&O-based algorithm enhanced with a fuzzy logic controller. The fuzzy logic layer dynamically adjusts the perturbation step size based on linguistic rules, providing adaptive decision-making that better handles changing irradiance and load conditions.	Delivers higher tracking efficiency and robustness across varying conditions. In testing, our fuzzy-enhanced MPPT achieved faster convergence and ∼20% greater energy harvesting efficiency than the standard P&O algorithm, while effectively managing partial shading and other non-ideal conditions.
Tracking speed	Many conventional algorithms exhibit slow convergence to the MPP, especially during rapid changes in irradiance. In fact, traditional fixed-step methods can be “confused” by fast transient, sometimes drifting or lagging before locking onto the new MPP.16,40	The fuzzy-P&O controller responds more quickly to changes by using adaptive step adjustments. The integration of fuzzy logic accelerates the MPPT response, allowing the system to swiftly track the MPP under both steady-state and rapidly changing environmental conditions.	Significantly improved dynamic response. Our MPPT reaches the new MPP much faster (about 30% quicker than the unoptimized P&O) when irradiance levels fluctuate, ensuring efficient energy capture during transient conditions and minimizing the time spent away from peak power.
Oscillations around MPP	Basic MPPT methods tend to settle with noticeable oscillations around the MPP in steady state, which leads to small but continual power losses. These oscillations occur as the controller hunts around the optimum, and reducing this effect has been a key challenge in prior research. 41	Our fuzzy logic optimization of the P&O algorithm dramatically dampens these oscillations. As the operating point nears the MPP, the fuzzy controller fine-tunes the perturbation step, preventing overshoot and undershoot and thereby smoothing out the power output around the maximum point.	Yields a more stable power output with minimal oscillatory deviation at MPP. Experiments showed that the oscillation amplitude was reduced by more than 50% compared to the conventional P&O file-mr7gcrjqtsnyr5telxbyzn. This stability not only minimizes energy loss at the MPP but also reduces stress on the power electronics
Implementation complexity	Traditional algorithms (like standard P&O or InCond) are straightforward to implement on microcontrollers and require few resources. By contrast, some high-performance schemes (e.g., using AI or evolutionary optimization) demand more computation and sensors, which can complicate implementation or require specialized hardware 42	The proposed MPPT controller adds only a lightweight fuzzy logic layer to the simple P&O framework. It uses a small rule base and basic arithmetic operations, so it remains computationally efficient. Only standard PV voltage and current measurements are needed, keeping the hardware requirements minimal.	Maintains a low complexity design suitable for embedded systems. Our method does not require significant processing power or memory and can run on a modest microcontroller in real time. This ease of implementation means the improved MPPT can be deployed without upscale hardware or major modifications to the robot’s power unit.

Comparative analysis underscores the significant advancements achieved in the development of MPPT algorithms for solar energy systems. Unlike earlier research that primarily employed conventional MPPT methods, such as the Perturb and Observe (P&O) or Incremental Conductance algorithms, our approach enhances the traditional P&O method through the integration of fuzzy logic control. This innovative enhancement delivers notable improvements, including increased efficiency under variable environmental conditions, faster tracking speeds, and reduced oscillations at the Maximum Power Point (MPP).

These advancements, combined with the deployment of a fully autonomous photovoltaic system, enable our solution to consistently achieve maximum energy efficiency while maintaining stability in real-world scenarios, such as partial shading or abrupt changes in irradiance. This study highlights the transformative potential of incorporating intelligent control mechanisms like fuzzy logic into traditional MPPT techniques, addressing the limitations of earlier methods and paving the way for more reliable and sustainable energy management systems.

Future work will involve rigorous quantitative benchmarking against other advanced MPPT methods through detailed simulations and practical experiments to further solidify the comparative performance benefits of the proposed approach.

Conclusion

This paper proposed a fuzzy logic-enhanced Perturb and Observe (P&O) MPPT controller applied for photovoltaic-powered autonomous mobile robots. The objective was to improve energy harvesting efficiency, dynamic responsiveness, and operational stability under fluctuating environmental conditions, using a lightweight and real-time compatible control strategy. Simulation results confirmed that the proposed method outperforms the classical P&O algorithm, achieving up to 98% MPPT efficiency, reducing power ripple by over 50%, and improving convergence speed by approximately 30%. The system maintained regulated output within ±1 % of the 12 V target across all tested irradiance scenarios, demonstrating both tracking accuracy and output stability.

Future work will focus on real-time hardware implementation and broader testing under varying load and environmental conditions. These steps will further establish the proposed method’s practical applicability in mobile, energy-constrained embedded systems.