Implementing Wireless Charging System for Semi-Autonomous Agricultural Robots

Abstract

The modernization of agriculture can help humanity address major challenges such as population growth, climate change, and labor shortages. Semi-autonomous agricultural robots offer clear advantages in automating tasks and improving efficiency. However, in open-field conditions, their autonomy is limited by the size and weight of onboard batteries. Wireless charging is a promising solution to overcome this limitation. This work proposes a methodology for the design, modeling, and experimental validation of a wireless power transfer (WPT) system for battery recharging of agricultural robots. A brief review of WPT technologies is provided, followed by key design considerations, co-simulation, and testing results. The proposed WPT system uses a resonant inductive power transfer topology with series–series (SS) compensation, a high-frequency inverter (85 kHz), and optimized spiral planar coils, enabling medium-range operation under agricultural conditions. The main contribution lies in the first experimental assessment of WPT performance under real agricultural environmental factors such as soil moisture and water presence, combined with electromagnetic safety evaluation and robust component selection for harsh conditions. Results highlight both the potential and limitations of this approach, demonstrating its feasibility and paving the way for future integration with intelligent alignment and adaptive control strategies.

1. Introduction

Agricultural activities are undergoing a profound transformation to address demographic and environmental challenges such as population growth, increasing energy demands, climate change, labor shortages, population aging, and pandemic-related risks [1,2]. In this context, the new paradigm of smart agriculture incorporates the use of semi-autonomous agricultural robots, known as Smart Agribots, characterized by their hybrid electric drivetrain. These technologies offer significant advantages for automating agricultural processes and improving the energy efficiency of operations [2,3,4]. These robots can be deployed in greenhouses or open fields, with the ability to perform various tasks in different agricultural environments.

In outdoor applications, Smart Agribots must operate for long periods, often several hours, while being limited by the amount of available energy. Even when a hybrid configuration is used, it is crucial to recharge these robots automatically, with minimal human intervention, in order to extend their operating time without increasing the size or weight of the onboard energy storage systems [5]. Indeed, increasing storage capacity leads to a higher initial cost and a reduction in the overall efficiency of the system.

Wireless power transfer (WPT) emerges as a promising solution for robotic platforms that require autonomous and frequent recharging without physical connectors. In the broader field of robotics, WPT has already been successfully implemented in logistics robots, drones, and mobile service robots, offering benefits such as reduced maintenance and increased availability [6,7].

WPT enables flexible, intelligent, and efficient recharging. For example, wireless charging stations can be strategically deployed in the field to recharge robots without manual intervention [8]. Today, WPT occupies a central place in research and development, with rapidly expanding applications in sectors such as automotive, robotics, healthcare, maritime, railways, agriculture, and the Internet of Things (IoT). WPT can be used in applications for detecting moving objects or living beings, such as potential applications for monitoring the dispersal of agricultural seeds [9,10], as well as in aeronautics and space [11,12,13].

However, agricultural environments present specific challenges to the implementation of WPT. These include soil moisture, temperature variations, electromagnetic interference, unexpected misalignments during docking, and exposure to garden soil, wet soil, and water. Designing a reliable WPT system for agricultural robotics, therefore, requires thorough consideration of these environmental and electromagnetic conditions.

The main advantage of WPT lies in its ease of use, eliminating cable handling while reducing the need for onboard storage capacity. Nevertheless, several challenges remain, including the following: efficiency losses due to magnetic coupling, worsened by harsh environmental conditions such as temperature, dust, mud, or misalignment; the need to adapt WPT systems to maximize efficiency while meeting health and safety standards; and constraints related to electromagnetic characteristics (coupling coefficient, apparent self-inductance, etc.) that may vary depending on operational conditions.

This paper presents an analysis of wireless power transfer technologies adapted to agricultural environments while exploring the specific challenges associated with these applications. The main contributions and innovations of this work can be summarized as follows:

• Proposition of a methodology for design and implementation of a resonant inductive power transfer (RIPT) system specifically adapted for semi-autonomous agricultural robots, and evaluation under harsh agricultural environmental conditions such as garden soil, wet soil, fresh water, and direct sunlight exposure;
• Proposition of a hybrid simulation workflow combining electromagnetic modeling with Ansys Maxwell (2023 R2), environmental modeling, system analysis with Ansys Twin Builder (2023 R2), and power electronics modeling with MATLAB/Simulink (R2021a);
• Experimental evaluation of WPT performance in realistic agricultural scenarios, including garden soil, fresh water, and wet soil, analyzing their influence on the coupling coefficient and the power transfer efficiency;
• Assessment of electromagnetic exposure levels according to ICNIRP recommendations and proposal of design strategies to ensure safe operation in the field.

The study includes a brief state-of-the-art review of wireless charging technologies, the proposal of a design methodology, the co-simulation of the system’s electronic and electromagnetic parts using Ansys Maxwell and MATLAB-Simulink, and experimental results evaluating the impact of environmental conditions on the performance of WPT systems. The remainder of this paper is organized as follows: the literature review is presented in Section 2, the proposed methodology in Section 3, the development of the WPT prototype as well as co-simulation and experimental results in Section 4, analysis, discussion and concluding remarks are presented in Section 5 and Section 6.

2. Short Review of Wireless Power Transfer Technologies

A WPT system is defined as a set of technologies that enable the transfer of electrical energy without physical contact between the transmitter and the receiver. The transmitting unit, typically stationary and powered by an energy source, is responsible for generating and transmitting energy in a form suitable for wireless transfer. The receiving unit, which can be stationary or integrated into a mobile application, captures the transmitted energy to either use it directly or store it, depending on the application’s needs. Depending on the physical principle and configuration used, the WPT technologies cover different types that can be adapted for different contexts. We describe in this section some of the leading WPT technologies: inductive power transfer (IPT), capacitive power transfer (CPT), resonant magnetic induction power transfer (RIPT), radiofrequency power transfer (RFPT), and microwave power transfer (MWPT).

2.1. Inductive Power Transfer (IPT)

Inductive power transfer, or inductive coupling, traces its origins back to the 19th century, with Nikola Tesla laying the groundwork for the concept in 1891 [14,15]. This technology works based on the principle of magnetic induction: a transmitting coil generates a variable magnetic field, which is captured by a receiving coil placed nearby. It is similar to a transformer but without a ferromagnetic core, allowing energy to be transferred without direct physical contact between the two coils. Magnetically coupling two coils, with inductances $L_1$ and $L_2$, respectively, introduces what is known as mutual inductance (M). Mutual inductance is characterized by a positive value called the coupling coefficient ($k_{12}$), which represents the amount of magnetic flux transferred from the transmitter to the receiver coil and is defined by Equation (1).

$$k_{12}={\displaystyle \frac{M}{\sqrt{L_1{L}_2}}}.$$

(1)

According to Kirchoff’s voltage law, the voltages at the first terminal $V_1$ and at the second terminal $V_2$ on the inductive circuits can be defined as follows:

$$V_1=j\omega L_1{I}_1+j\omega M{I}_2$$

(2)

$$V_2=j\omega M{I}_1+j\omega L_2{I}_2$$

(3)

where $\omega$ is the angular frequency, and $I_1$ and $I_2$ are the currents flowing through the first and second inductors.

These equations represent a classic model of a magnetically coupled circuit, as seen in a transformer or inductive coupling system.

Inductive power transfer offers several advantages. It is simple to implement with relatively basic circuits and is safe, as there is no direct contact with electrical conductors, reducing the risk of electric shock. Additionally, it is quite robust, resistant to water and dust, which makes it suitable for challenging environments such as agricultural settings [14]. However, it also has some limitations. The transfer is effective only over short distances, typically a few centimeters. Furthermore, for efficient energy transfer, the coils must be well-aligned; otherwise, the energy transmission will not be optimal. Energy losses due to Joule heating and magnetic dissipation further reduce efficiency. Finally, this technology is not well-suited for very high-power transmissions or long distances [16].

Despite these limitations, it is widely used in various fields. For example, in consumer electronics, it enables wireless charging for smartphones, smartwatches, and earbuds. In the electric vehicle sector [17], it supports wireless charging for electric cars and buses. In medicine, it is used to recharge implants and portable devices, avoiding invasive connections. It is also applied in robotics and drones for industrial applications, as well as in home automation, where it powers wireless sensors and connected devices in smart homes.

Some related works show that inductive power transfer can be proposed as a promising alternative for underground wireless sensor network applications, as magnetic fields are not significantly affected by soil and water properties [18]. In summary, while inductive coupling is a reliable technology for transferring energy without physical contact, it remains limited by its range and energy efficiency. However, its robustness under harsh environments, including water and dust, broadens its application potential.

2.2. Capacitive Power Transfer (CPT)

Capacitive power transfer (CPT) relies on the use of capacitors to transfer electrical energy without physical contact by exploiting an oscillating electric field between two metallic electrodes. Unlike inductive power transfer, which is based on a magnetic field, CPT uses an alternating electric field to transmit energy [19,20]. In a CPT system, two conductive plates (transmitter and receiver) form a capacitor separated by a dielectric material such as air or polypropylene, which enables energy transmission [21]. The capacitance C between two parallel plates is given by:

$$C={\epsilon }_0{\epsilon }_r{\displaystyle \frac{A}{d}},$$

(4)

where ${\epsilon }_0$ is the permittivity of free space ($8.854\times {10}^{-12}$ F/m), ${\epsilon }_r$ is the relative permittivity of the dielectric (air: 1.00059 at 1 atm), A is the surface area of the plates (cm²), and d is the vertical distance between the plates (cm).

The voltage across or the voltage stress $V_C$ appearing for each capacitor can be calculated as follows:

$$V_C={\displaystyle \frac{I_c}{\omega C}}$$

(5)

where $I_C$ is the current passing through the capacitor.

However, one of the main drawbacks identified for CPT systems is the presence of high voltages between the plates and the requirement for high operating frequencies (in the MHz range), which necessitate the implementation of safety measures [22]. The voltages and electric fields generated by CPT systems must comply with ICNIRP (International Commission on Non-Ionizing Radiation Protection) standards and recommendations [23], e.g., the exposure limits at frequencies between 100 kHz and 10 MHz are defined in

Table 1. Exposure limits at frequencies between 100 kHz and 10 MHz.

Field Type	General Public	Workers
Electric	83 V/m	300 V/m
Magnetic	0.73 A/m	2.7 A/m

, and the devices must be designed to limit exposure by maintaining adequate spacing.

This method offers several advantages, including reduced eddy current losses, lower cost, and better tolerance to misalignment compared to inductive power transfer (IPT) [24]. CPT is used in various industrial fields such as consumer electronics (mobile phones and laptops), transportation (electric vehicles (EVs), drone charging, and underwater charging), biomedical applications, such as powering medical implants, thanks to reduced electromagnetic interference, and electrical machines [24].

Capacitive power transfer is particularly advantageous for applications requiring lightweight design, low electromagnetic interference emissions, and reduced cost. However, this technology still faces challenges such as the need for high voltages and increased complexity in the design of compensation networks.

2.3. Resonant Magnetic Induction Power Transfer (RIPT)

The resonant inductive power transfer (RIPT) technique is similar to inductive power transfer but overcomes the limitation of short transmission distances. This method combines an inductor and a capacitor to create a magnetic resonance effect, hence the term “resonant circuit” [25]. Electrical energy is efficiently transferred from the primary coil to the secondary coil through the magnetic field generated by the resonance between the inductor and the capacitor [26].

Figure 1 illustrates the four main resonant circuit configurations used in wireless power transfer systems. These topologies are named based on how the resonant capacitors are connected either in series (S) and/or in parallel (P) with the inductor [27].

As described by Equation (1), the resulting coupling coefficient $k_{12}$ quantifies the portion of the magnetic flux transferred from the transmitting coil $L_1$ to the receiving coil $L_2$ [28,29]. The coupling coefficient ranges from 0% (no magnetic coupling) to 100% (perfect magnetic coupling, with optimal coil alignment). To reduce the size of the coils, a frequency of several tens of kilohertz is used [28,29]. This frequency, denoted by $f_r$, is given by Equation (6), where ${\omega }_0$ represents the angular resonance frequency (in rad/s)

$$f_r={\displaystyle \frac{{\omega }_0}{2\pi }}.$$

(6)

The choice of the resonant compensation circuit topology depends on the application and its environment, while also being economically viable.

Table 2. Comparison of the basic resonant circuit topologies.

Topology	Advantages	Disadvantages	Usage
Series–series (S-S)	Design simplicity, high efficiency	Sensitive to load variations,	45%
	for fixed loads.	requires additional regulation.
Series–Parallel (S-P)	Stability against variable loads,	Increased complexity,	30%
	suitable for mobile devices.	requires more precise control.
Parallel–Series (P-S)	Low losses for low power,	Inefficient for high loads,	15%
	ideal for implanted devices.	sensitive to misalignment.
Parallel–Parallel (P-P)	High stability, tolerance	Risk of overvoltage,	10%
	to misalignment.	complex design.

provides a clear and comparative overview of the different topologies based on several key criteria. It highlights the performance of each topology in terms of efficiency for various applications [26,30], voltage/current constraints [31], alignment impact [29,31], frequency independence [32], and overall efficiency [33,34,35]. From this comparison, it should be highlighted that series–series (S-S) is the most widely used topology (45%) due to its simplicity and efficiency for fixed loads, such as smartphone chargers and stationary batteries. Series–parallel (S-P) represents 30% of the market, primarily for applications where the load varies, such as IoT sensors and mobile devices. Parallel–series (P-S) is less common (15%), and it is mainly used in specific applications like implanted medical devices. Parallel–parallel (P-P) is the least used (10%) due to its complexity, but it is preferred for applications requiring high tolerance to misalignment, such as drones and electric vehicles.

Hybrid solutions have been developed to mitigate the sensitivity to the misalignment issue. These hybrid methods involve combining SS, PP, SP, and PS compensation circuits with another LC compensation network to form compensation circuits such as LCC-LCC, LCL-LCL, LCC-LCL, etc. [32,36,37,38,39].

Table 3. Comparison between basic resonant topologies and hybrid compensation topologies.

Criteria	Basic Resonant Topologies 1	Hybrid Compensation Topologies
Circuit structure	Simple: a single LC network in series or parallel.	Complex: a combination of multiple LC networks to enhance performance.
Energy efficiency	Good efficiency under precise alignment conditions, efficiency drops quickly under misalignment.	Higher efficiency over a wide misalignment range, improved robustness to position variations due to multi-path compensation.
Frequency stability	Sensitive to load and position changes.	More stable due to multiple compensation networks.
Design complexity	Low: simple to design and implement.	High: requires advanced design and parameter optimization.
Implementation cost	Low: uses standard components and a simple circuit.	High: involves more components and increased circuit complexity.
Typical applications	Wireless chargers for mobile devices, short-distance power transfer with minimal misalignment.	Electric vehicles (EVs), WPT systems in harsh environments (e.g., agricultural conditions), and applications requiring high misalignment tolerance.
Main advantages	Simplicity in design and implementation, lower cost, effective under optimal conditions.	Improved efficiency and stability, greater tolerance to misalignment, and adaptability to diverse conditions.
Main disadvantages	Sensitivity to misalignment, and efficiency loss under variable load conditions.	Increased design complexity, high cost, and it requires advanced control mechanisms.

¹ Basic resonant topologies are SS, SP, PS, PP, hybrid compensation topologies are LCC-LCC, LCL-LCL, LCC-LCL, etc.

compares basic resonant topologies and hybrid topologies of compensation circuits in wireless power transfer (WPT) systems. The goal of this hybridization is to create a compensation resonance to improve the efficiency of the power transmission system and ensure better tolerance to misalignment, improved efficiency and stability, and adaptability to diverse conditions. It remains that the main advantages of basic topologies are the simplicity in design and implementation, the low cost, and the efficiency under optimal conditions.

To maintain optimal efficiency without loss of performance, it is essential to study the characteristics of coupling systems, including the coupling coefficient (k), the quality factor (Q), and the misalignment tolerance.

Standards have been established to harmonize the use of this technology, ensure compatibility, and protect users. Among these, we can mention the SAE J2954 standard. It standardizes inductive charging so that a primary and a secondary coil manufactured by different companies are compatible. It specifies that the resonance frequency $f_r$ of power transfer systems for mobile applications must be limited to 100 kHz [28,29,40]. For maximum power transfer, the resonance frequencies of the primary and secondary coils must be matched. The standard also specifies that the coupling coefficient must be between 10% and 30% for wireless charging systems in mobile applications to maximize efficiency [29,41]. Additionally, it classifies inductive charging systems based on their nominal apparent power into different classes. It also defines a second classification based on the distance between the two coils (Z-classes) [28,29,40].

2.4. Radiofrequency (RF) Transfer and Microwave Power Transfer (MWPT)

Radiofrequency (RF) is an electromagnetic technology that emerged at the beginning of the 20th century with the development of wireless communications. Since its inception, it has undergone numerous advancements and found applications in various fields, including telecommunications, energy, and agriculture [42,43]. RF traces its origins to the work of pioneers such as Heinrich Hertz, who demonstrated the existence of electromagnetic waves, and Guglielmo Marconi [44,45], who achieved the first wireless transmission. Its development accelerated with the advent of radio, radar during World War II, and more recently with modern communication systems and wireless power transfer (WPT) [44,45]. Radiofrequency relies on the transmission of electromagnetic waves within a frequency spectrum ranging from 3 kHz to 300 GHz. For wireless power transfer, these waves are generated by an alternating electrical signal, typically in the MHz or GHz range, which is amplified to increase its power and then transmitted via a transmitting antenna. This antenna converts the electrical signal into electromagnetic waves, which propagate through space according to Equation (7). At the other end, a receiving antenna captures these waves and converts them back into an electrical signal. This energy can then be used to power a device.

$${\nabla }^2\mathbf{E}-\mu ϵ{\displaystyle \frac{{\partial }^2\mathbf{E}}{\partial t^2}}=0,$$

(7)

where $\mathbf{E}$ is the electric field, $\mu$ is the magnetic permeability of the medium, and $ϵ$ is the electric permittivity of the medium.

The transmission distance ranges from a few meters to several kilometers, depending on the frequency, signal power, and environmental conditions. However, the efficiency of the transfer decreases with distance due to energy losses in the form of heat or scattered radiation. The power received by a receiving antenna can be calculated using the Friis equation defined by (8).

$$P_r=P_t·G_t·G_r·{\left({\displaystyle \frac{\lambda }{4\pi d}}\right)}^2,$$

(8)

where $P_r$ is the received power, $P_t$ is the transmitted power, $G_t$ and $G_r$ are the gains of the transmitting and receiving antennas, $\lambda$ is the wavelength of the signal, and d is the distance between the antennas.

This equation shows that the power received decreases with the square of the distance, which explains the loss of energy over long distances. RF is widely used to power low-consumption devices, particularly in hard-to-access environments. For example, in remote agricultural areas, RF-powered IoT sensors measure critical parameters such as soil moisture, temperature, or air quality [46,47]. It is also used in the medical field to power deeply implanted devices, such as pacemakers, neurostimulators, or biomedical sensors [48]. In the consumer electronics sector, emerging technologies enable the wireless charging of small devices, such as wireless earbuds or smartwatches, through charging stations that emit RF signals [49]. Despite its advantages, RF technology has several major drawbacks. First, its energy efficiency is low: a significant portion of the energy is lost as heat or scattered (9) radiation, making the transfer less efficient than wired methods. This inefficiency increases with distance, limiting its use to low-power devices. For applications requiring high power, such as electric vehicles, RF is not yet viable. The thermal energy Q dissipated in a system can be calculated using Equation (9).

$$Q=I^2·R·t,$$

(9)

where I is the electric current, R is the resistance of the system, and t is the time.

Some drawbacks of RF waves concerning interference, safety, and health also appear, e.g., they may interfere with other electronic devices and have potential biological effects on human tissues, especially at high power or specific frequencies. Furthermore, RF systems are sensitive to physical obstacles, such as walls or metals, which can attenuate or block the waves. They can also interfere with other technologies using similar frequencies, such as Wi-Fi, Bluetooth, or mobile communications. Wireless power transfer via RF is particularly suitable for low-power devices and environments where cables are impractical. However, its limitations, particularly in terms of energy efficiency, safety, and sensitivity to obstacles, remain challenges to be addressed.

Similarly to RF, microwave power transmission (MWPT) has its origins in the pioneering work on electromagnetic waves in the 19th century. Heinrich Hertz in 1887 experimentally demonstrated the existence of electromagnetic waves, paving the way for their use in wireless power transmission. Nikola Tesla, at the end of the 19th century, explored the idea of transmitting electrical energy over long distances wirelessly, although his experiments did not lead to practical applications at the time. In the 1960s, William C. Brown revolutionized the field by demonstrating microwave power transmission to power a miniature helicopter. His work laid the foundation for modern microwave power transmission technology [44]. Since then, this technology has been studied for space applications, particularly in the context of space solar power (SSP) projects, where solar energy collected in orbit would be transmitted to Earth via microwaves [50,51].

Microwave power transmission relies on the conversion of electrical energy into electromagnetic waves in the microwave band (typical frequencies of 2.45 GHz or 5.8 GHz), followed by their transmission and reconversion into electrical energy [52]. A microwave generator, such as a magnetron or klystron, converts electrical energy into electromagnetic waves. These waves are then directed to a transmitting antenna in the form of a directed beam. The transmission distance depends on the emitted power, frequency, and antenna efficiency, as described by the Friis Equation (8). At the receiving end, an antenna equipped with rectennas (rectifying antennas) converts the microwaves into usable direct current.

Microwave power transmission and radio frequency (RF) power transmission are based on the same physical principle: the conversion of electrical energy into electromagnetic waves, their propagation through space, and their reconversion into electrical energy. Both technologies use antennas to emit and receive waves, and their efficiency depends on similar factors, such as frequency, emitted power, and transmission distance.

Table 4. Key differences between RF and microwave power transmission.

Criteria	Radio Frequency (RFPT)	Microwave (MWPT)
Frequencies	Frequencies from a few kHz to a few GHz.	Frequencies typically of 2.45 GHz or 5.8 GHz, which enable more directional transmission and better beam focusing, and are essential for long-distance applications, e.g., space solar power.
Applications	Short-range, low-power applications, e.g., wireless charging of small electronic devices and powering IoT sensors.	High-power, long-distance applications, e.g., energy transmission from space, and powering drones in flight.
Efficiency	More susceptible to interference and diffraction losses, limited efficiency over long distances.	Generally, more efficient for long-distance transmission, better beam focusing reduces losses.

provides a comparison of these technologies.

Microwave power transmission (MWPT) is a promising technology with enormous potential, particularly for applications such as space-based solar power, in-flight drone powering, or long-distance wireless charging. However, it must overcome several challenges to become a viable large-scale solution. On the technical side, a significant portion of energy is lost during the conversion, transmission, and reconversion stages. For instance, microwave generators (such as magnetrons or klystrons) have limited efficiency, and rectennas (rectifying antennas) only convert a fraction of the received energy into usable electricity. Additionally, long-distance transmission leads to losses due to beam divergence and atmospheric attenuation. Environmental conditions, such as rain, fog, or dust, can also attenuate or deflect the microwave beam, reducing transmission efficiency and requiring sophisticated compensation systems. Finally, on the societal front, the public often perceives this technology as risky due to concerns about the effects of microwaves on health and the environment. Although the power levels used are generally safe, skepticism persists, and clear communication, along with thorough studies, is necessary to reassure users and decision-makers.

3. Study Case on Wireless Power Transfer for Semi-Autonomous Agricultural Robots

Based on the previously detailed study, we can establish that each wireless power transmission method has specific advantages and disadvantages, making them suitable for various applications. In agricultural environments, where robustness and tolerance to misalignment are essential criteria, technologies such as resonant inductive power transfer (RIPT) and capacitive power transfer (CPT) are particularly promising. However, technical challenges, particularly in terms of energy efficiency, safety, and adaptability to harsh environmental conditions, must still be overcome to enable large-scale adoption. Other methods, such as radio frequency (RF) and microwave power transmission (MWPT), also offer advantages in specific application areas. RF is particularly suitable for low-power, long-distance applications, such as powering IoT sensors in remote or hard-to-access areas. However, its energy efficiency is limited, making it less suitable for applications requiring high power. Microwave power transmission (MWPT), on the other hand, is ideal for high-power, long-distance applications, such as energy transmission from space or powering drones in flight. However, this technology is sensitive to environmental conditions (e.g., rain, fog) and requires strict precautions regarding electromagnetic safety.

We present, in this section, a case study on resonant inductive power transfer (RIPT) technology, an approach that can be effectively employed in agricultural settings to meet the specific needs of this sector. The analysis includes the main factors that can cause efficiency losses in wireless charging systems. More specifically, we consider the effects of the resonant circuit type [35,53], the type of materials [38,41], and the geometric shape of the coils [54,55]. Considering the target application in agricultural robots, and taking into account that none of the reviewed literature works specifically mention the environment of wireless charging systems, the focus of this research includes analyzing efficiency losses in agricultural settings. As part of this work, we define the specifications using series–series (SS) compensation because of design complexity and high efficiency when supplying fixed loads. We begin by establishing the mathematical formulation and the models of the system to highlight the key factors that may influence efficiency. Based on this theoretical work, the system is validated both through simulations and experimentally, under conditions representative of the agricultural environment.

3.1. Agricultural Robot and Wireless Charging System Specification

In the first step of a system design, it is important to define the target application of the wireless charging system. As illustrated in Figure 2, the intended system for agricultural applications includes, on the primary side, one or multiple fixed charging stations supplied by a solar PV system equipped with an MPPT battery charger and a primary battery as the primary source. On the secondary side, we have each mobile robot with an embedded power electronics circuit that includes a rectifier and a battery charger to feed the battery used for traction in the robot and to accomplish specific agricultural tasks.

Figure 3 illustrates a sample discharging and charging cycle. The discharge cycle corresponds to experimental tests performed while using the robot powered by the 8 Ah LiPo battery [56,57]. The charging cycle was obtained using an ECO-WORTHY 12 V smart battery charger (from ECO-WORTHY, Hong Kong). As illustrated in Figure 3c, the agricultural robot prototype measures 92 cm long, 74 cm wide, and 73 cm high. It has two drive wheels at the rear and two caster wheels at the front. For short-distance working cycles, the robot uses an 8 Ah LiPo (lithium polymer) battery with BMS. For longer journeys requiring more energy, a higher capacity battery (20 Ah) is used, significantly increasing the activity duration without interruption.

It is important to set the system specifications in order to determine all the characteristics of the system. The specifications that can be set at the very beginning of a wireless charging system project are the system input voltage, the resonant frequency, and the charging power. The characteristics of the targeted wireless charging system are listed in

Table 5. Characteristics of the targeted wireless charging system.

Description	Symbol	Value
Resonant circuit topology	-	Series–series
Powering primary source (1)	-	Solar PV with MPPT
Primary-side battery voltage (2)	$V_{DC-1}$	12–48 V
Secondary-side battery voltage (2)	$V_{DC-2}$	12–24 V
Maximum charging current of secondary battery	$I_{DC-2}$	4 A

⁽¹⁾ The primary power source permits charging the primary side battery, and it includes a battery charger with MPPT. ⁽²⁾ The primary side battery supplies the inverter. The secondary-side battery supplies the agricultural robot.

.

3.2. Modeling of Wireless Charging System with Resonant Circuit Using Serial-Serial Configuration

Figure 4a illustrates the general structure of a resonant inductive power transfer (RIPT) system with an SS compensation circuit. In this figure, the transmitting side (primary) consists of a high-frequency DC–AC inverter, a compensation capacitor ($C_1$), and a spiral coil ($L_1$), where ($R_1$) represents the internal resistance of the coil. The inverter on the primary side is powered by a direct current (DC) source (e.g., a battery) and generates a high-frequency alternating current (AC). The high-frequency output of the inverter is then applied to the resonant compensation circuit, which enables the generation and wireless transfer of energy to the receiving side (secondary) through electromagnetic coupling (induced current). The receiving side consists of a spiral coil ($L_2$), a compensation capacitor ($C_2$), and an AC–DC converter, where $R_2$ represents the internal resistance of the secondary coil. The secondary side receives the energy in the form of high-frequency alternating current (AC) through the coil. This energy is then converted into direct current (DC) using a rectifier, which allows the charging of a battery with the obtained DC power.

We would like to specify that the AC–DC converter of the receiving part is not taken into account in this work. The model of the system must serve to understand and anticipate the behavior of the system, so it is important to determine the type of model. There are four types of models that a system can have in general: deterministic or non-deterministic models, and parametric or non-parametric models [58]. Wireless power transmission systems can be represented by a non-deterministic model, since we have imperfect knowledge and unpredictable phenomena due to mutuality. WPT systems have complex mechanical, electrical, and electromagnetic sub-systems, and their design requires numerous compromises. Figure 4a shows the electrical circuit of a wireless transfer system with serial-serial (SS) compensation.

As illustrated in Figure 4b, this circuit is usually represented by a simple equivalent electrical model based on the first harmonic (fundamental) approximation ($h_1$). In this simplified model, the primary static converter is replaced by a voltage source $U_1$ defined by Equation (10) and all the load connected to the secondary compensation circuit by an equivalent load resistance $R_E$, which is defined by Equation (11) [41,59].

$$U_1={\displaystyle \frac{2\sqrt{2}}{\pi }}sin\left({\displaystyle \frac{\pi D}{2}}\right)V_{in}.$$

(10)

$$R_E={\displaystyle \frac{8}{{\pi }^2}}{R}_L.$$

(11)

Applying Kirchhoff’s law and Ohm’s law to Figure 4b, we obtain Equations (12) and (13)

$$U_1=\left[R_1+j\omega L_1+{\displaystyle \frac{1}{j\omega C_1}}\right]I_1-j\omega M{I}_2.$$

(12)

$$0=\left[R_2+R_E+j\omega L_2+{\displaystyle \frac{1}{j\omega C_2}}\right]I_2-j\omega M{I}_1.$$

(13)

In order to simplify the reasoning of the equations, we define the impedances $Z_1$ and $Z_2$ for the primary and secondary side as follows,

$$Z_1=R_1+j\omega L_1+{\displaystyle \frac{1}{j\omega C_1}}.$$

(14)

$$Z_2=R_2+j\omega L_2+{\displaystyle \frac{1}{j\omega C_2}}.$$

(15)

The primary side and secondary side currents, $I_1$ and $I_2$, can be defined, respectively, by Equations (16) and (17),

$$I_1={\displaystyle \frac{U_1\left[Z_2+R_E\right]}{Z_2\left[Z_2+R_E\right]+{\omega }^2{M}^2}}.$$

(16)

$$I_2={\displaystyle \frac{j\omega M{U}_1}{Z_2\left[Z_2+R_E\right]+{\omega }^2{M}^2}}.$$

(17)

The respective active powers $P_1$, $P_2$ are given by Equations (18) and (19).

$$P_1=\Re \left[U_1{I}_1\right]={\displaystyle \frac{U_1^2\left[Z_2+R_E\right]}{{\left[Z_2{Z}_1+R_E{Z}_1+{\omega }^2{M}^2\right]}^2}}.$$

(18)

$$P_E=\Re \left[R_E{I}_2^2\right]={\displaystyle \frac{U_1^2{\omega }^2{M}^2{R}_E}{{\left[Z_2{Z}_1+R_E{Z}_1+{\omega }^2{M}^2\right]}^2}}.$$

(19)

Equation (19) shows that the output power of the system can be controlled by varying one of the quantities $U_1$, $\omega$, or M. The efficiency $\eta$ is defined according to Equation (20).

$$\eta ={\displaystyle \frac{{\omega }^2{M}^2{R}_E}{\left(R_2+R_E\right)\left(R_1{R}_2+R_E{R}_1+{\omega }^2{M}^2\right)}}.$$

(20)

3.3. Efficiency Analysis in Agricultural Context

Mutual inductance is a key factor influencing the efficiency of a wireless power transfer (WPT) system, as shown by Equation (20). The mutual inductance M between two coils is determined by the integral of the magnetic flux generated by the first coil and captured by the second. This relationship is described by Neumann’s formula [60,61,62,63,64], which applies particularly to filamentary circuits, meaning when the wire diameter is very small compared to the coil radius. The mutual inductance $M_{12}$ between circuits $C_1$ and $C_2$, in henries, H, can be defined by Equation (21).

$$M_{12}={\displaystyle \frac{{\mu }_0}{4\pi }}{\oint }_{C_1}{\oint }_{C_2}{\displaystyle \frac{d{\mathbf{l}}_1·d{\mathbf{l}}_2}{|{\mathbf{r}}_1-{\mathbf{r}}_2|}}.$$

(21)

where ${\mu }_0=4\pi \times {10}^{-7}$ H/m is the permeability of free space, ${\oint }_{C_1}$ and ${\oint }_{C_1}$ are line integrals along the contours of circuits $C_1$ and $C_2$, $d{\mathbf{l}}_1$ and $d{\mathbf{l}}_2$ are infinitesimal length elements along circuits $C_1$ and $C_2$, ${\mathbf{r}}_1$ and ${\mathbf{r}}_2$ are position vectors of the elements $d{\mathbf{l}}_1$ and $d{\mathbf{l}}_2$, $|{\mathbf{r}}_1-{\mathbf{r}}_2|$ is the distance between the elements $d{\mathbf{l}}_1$ and $d{\mathbf{l}}_2$, and $d{\mathbf{l}}_1·d{\mathbf{l}}_2$ is the dot product between the length elements $d{\mathbf{l}}_1$ and $d{\mathbf{l}}_2$.

Although this formula is applicable to any coil geometry, it is often necessary to simplify the general integral based on the specific configuration of the coils. For instance, in the case of two circular coils aligned along the z-axis, the mutual inductance can be approximated by a simplified formula [65]. This approximation facilitates calculations while maintaining sufficient accuracy for many practical applications, and can be defined by Equation (22).

$$M={\mu }_0{\mu }_r{N}_1{N}_2{\displaystyle \frac{\pi R_p^2{R}_s^2}{2{\left(R_p^2+R_s^2+d^2\right)}^{3/2}}}.$$

(22)

where $R_p$ and $R_p$ are the radius of the first and second coil, d is the distance between the planes of the two coils, $N_1$ and $N_2$ are the number of turns of the coils, and ${\mu }_r$ is the relative permeability of the medium.

For square coils, the mutual inductance formula is given by Equation (23).

$$M={\mu }_0{\mu }_r{N}_1{N}_2{\displaystyle \frac{a^2{b}^2}{2{\left(a^2+b^2+d^2\right)}^{3/2}}}.$$

(23)

where a and b are the side lengths of the first and second square coils, and d is the distance between the two coils along the z-axis.

We can substitute the expression for mutual inductance M (22) into the efficiency Equation (20) to obtain an Equation (24) that expresses the efficiency $\eta$ in terms of all its constitutive parameters.

$$\eta ={\displaystyle \frac{{\omega }^2{\left({\mu }_0{\mu }_r{N}_1{N}_2\right)}^2{\pi }^2{R}_p^4{R}_s^4{R}_E}{4{\left(R_p^2+R_s^2+d^2\right)}^3\left(R_2+R_E\right)\left(R_1{R}_2+R_E{R}_1+{\omega }^2{\left({\mu }_0{\mu }_r{N}_1{N}_2\right)}^2\frac{{\pi }^2{R}_p^4{R}_s^4}{4{\left(R_p^2+R_s^2+d^2\right)}^3}\right)}}.$$

(24)

This equation will allow us to study the effect of the agricultural environment on the efficiency of a wireless power transfer (WPT) system. Indeed, several parameters of this equation can be influenced by environmental conditions specific to agriculture. A list of such parameters is presented in

Table 6. Parameters affecting the efficiency of wireless power transfer.

Symbol	Parameter	Description
${\mu }_r$	Relative magnetic permeability	Particles present in the soil, such as mud, clay, or organic matter, as well as plants, can alter the magnetic permeability of the medium, which directly affects the mutual inductance M.
d	Distance between the two coils along the z-axis	The presence of objects, such as plants, agricultural equipment, or terrain irregularities, can influence the effective distance between the coils, thereby altering the magnetic coupling.
$R_1$, $R_2$	Ohmic losses	Humidity, temperature, and soil composition can increase ohmic losses in the coils, thereby reducing the system’s efficiency.
$\omega$	Angular frequency	The agricultural environment can introduce dielectric losses, which affect the system’s optimal operating frequency.

.

To answer the central question regarding the effects of these parameters on the efficiency of the WPT, this manuscript provides an in-depth study based on numerical simulations using Ansys Maxwell (2023 R2) and MATLAB software and practical experiments using a prototype of the WPT system.

3.4. Wireless Power Transfer System Design

As mentioned before, a WPT system mainly consists of the following components: a high-frequency DC–AC power converter, a resonant circuit, and a high-frequency AC–DC power converter.

3.4.1. Consideration on Power Electronics Design

The design of DC–AC converters (inverters) primarily relies on power electronics switches. The selection of such electronic devices must be carried out carefully to meet the requirements of this particular application of a resonant circuit working at frequencies near a hundred kilohertz. It is crucial to select switches capable of handling the maximum voltages and currents of the system. The main characteristics to be considered are the blocking voltage ($V_{DS}$), the saturation current ($I_D$), and conduction and switching losses. This includes the condition that the switches must exhibit a low on-state resistance and short switching time to minimize power losses and improve system efficiency. Fast switching times reduce switching losses and minimize electromagnetic interference (EMI). Advanced technologies, such as silicon carbide (SiC) or gallium nitride (GaN), offer superior performance in terms of switching speed and thermal management.

For our application, we designed a high-frequency DC–AC converter (inverter), capable of handling input voltages ranging from 12 V to 24 V DC, with a maximum switching frequency of 120 kHz and a nominal current of more than 20 A. The components were carefully selected to ensure fast, reliable, and safe operation. The switching devices are IRLZ44NPBF MOSFETs ( from Infineon Technologies, Neubiberg, Germany), chosen for their low on-resistance, high current handling capability, and compatibility with logic-level signals. Each MOSFET is driven by a 1EDI20N12AF isolated gate driver ( from Infineon Technologies, Neubiberg, Germany), which provides high output current for fast switching and ensures galvanic isolation from the control logic. These drivers are powered by PQME1-S15-S15-S isolated DC–DC converters (from Bel Power Solutions, Northridge, CA, USA) that supply the required bipolar voltages. Control signals are transmitted through an ISO7760FDWR optocoupler (from Texas Instruments, Dallas, TX, USA), a six-channel device that offers reinforced isolation and high immunity to electromagnetic noise. The entire control stage receives power via a CC6-1212SR-E DC–DC isolated converter (from TDK-Lambda, Tokyo, Japan), which protects the control logic from power-side disturbances. This architecture provides robust galvanic separation, minimizes interference, and supports reliable high-frequency switching, making it particularly suitable for resonant conversion and wireless power transfer (WPT) applications. Figure 5 illustrates a 3D view of the design of a power electronics board intended for the control of a DC–AC converter, with full isolation between the control signals and the power stage. This design was performed using Altium Designer (version 2025.1.2).

The control principle of the full-bridge inverter is based on Phase-Shifted Pulse Width Modulation (PS-PWM). As illustrated in Figure 4a, the inverter consists of two legs; leg 1 is formed by switches Q1 and Q2, and leg 2 by switches Q3 and Q4. To generate the PS-PWM, the two switches of each leg are controlled in a complementary manner: when Q1 is ON, Q2 is OFF, and vice versa; the same applies to Q3 and Q4. The generation of the PWM signals is based on a square waveform with a fixed duty cycle, initially applied to leg 1. The signals for leg 2 are then generated by applying a temporal shift $\Delta$ to the rising edges, corresponding to a phase shift that can vary from 0 to 180 electrical degrees, i.e., up to half of the period T. This variation in $\Delta$ allows the transmitted power to be controlled without changing the switching frequency, while maintaining a constant 50% duty cycle D. To ensure safe switching, a dead time (dt) is introduced between the complementary signals of each leg, preventing both switches from conducting simultaneously. The output voltage of the inverter is obtained by logically subtracting the signals from the two legs. More precisely, the control signal from leg 1 (Q1/Q2) is subtracted from that of leg 2 (Q3/Q4), which generates an alternating output signal with variable width, depending on the phase shift $\Delta$. The main advantage of this technique lies in its ability to effectively regulate the transmitted power at a fixed frequency, reducing switching losses and improving system stability. This approach is particularly well suited for resonant converters and wireless power transfer (WPT) systems operating at high frequency. In this context, the controlled object is the inverter’s output voltage waveform, while the control target is the transmitted power delivered to the secondary coil. Even though the system operates at the resonant frequency to maximize energy transfer, the phase shift $\Delta$ provides a precise and continuous means to modulate the effective voltage applied across the resonant tank. For experimental purposes, we have implemented the control on a Nexys A7 board with an AMD Artix 7 FPGA (XC7A100T). A sample of the control signals and inverter output voltage, from experiments, is shown in Figure 6.

3.4.2. Considerations on Inductor Design

Inductor sizing is a key element of all electromagnetic systems as it has a significant effect on the system’s efficiency. To perform a proper sizing, it is necessary to take into account several parameters of the coil geometry, including the inner diameter, conductor width or wire diameter, spacing between turns, and the number of turns. We designed the inductors in a simple and explicit manner, based on the load quality factor ($Q_L$), which is a measure of the efficiency of a resonant circuit in conserving energy and is defined by Equation (25).

$$Q_L={\displaystyle \frac{{\pi }^2{\omega }_0{L}_{2min}}{8R_L}}.$$

(25)

Here, $R_L$ is the load resistance, which can be obtained by knowing the power and battery voltage ($V_{Batt}$) according to Equation (26).

$$R_L={\displaystyle \frac{V_{Batt}^2}{P_{Batt}}}.$$

(26)

Using this load quality factor ($Q_L$), we can determine the minimum value of the secondary inductance ($L_{2min}$) required to deliver the desired power using Equation (27).

$$L_{2min}={\displaystyle \frac{8Q_L{R}_L}{{\pi }^2{\omega }_0}}.$$

(27)

It is important to note that the load current is equal to the current flowing through the secondary inductance. In the literature, the load quality factor ($Q_L$) of systems typically ranges between 2 and 4. Considering a power of 48 W, and setting $Q_L$ to 2.5, the minimum value of the secondary inductance ($L_{2min}$) is 9.5617 $\mathsf{\mu }$H. To provide a safety margin, the secondary inductance can be at least twice $L_{2min}$, i.e., more than 20 $\mathsf{\mu }$H.

The key question addressed here is as follows: How many turns are required to reach a given target inductance? To answer this, we follow a methodology based on geometric and electromagnetic considerations. The goal is to determine the optimal number of turns needed to reach a desired inductance value $L_{\mathrm{target}}$, taking into account the physical dimensions of the coil. The method relies on the use of the Wheeler formula [66], which is suitable for circular planar coils and is defined by (28).

$$L={\displaystyle \frac{31.33·{\mu }_0·n^2·a^2}{8a+11c}}.$$

(28)

with,

$$a={\displaystyle \frac{d_{\mathrm{in}}+n·d_{\mathrm{wire}}}{2}}.$$

(29)

and

$$c=n·d_{\mathrm{wire}}.$$

(30)

where the number of turns n and the inner diameter of the coil $d_{in}$ are variable parameters. The diameter of the wire $d_{\mathrm{wire}}$ can be established considering the current. In this case, we consider that we are using Litz wire AWG 38/160 with diameter $d_{wire}=1.65$ mm. To illustrate this analysis, Figure 7 shows the plot of inductance versus the number of turns and the inner diameter; the intersection of this plot with a specific value of inductance provides the characteristics of possible coils to be built.

Based on these results, and considering an inner diameter of $8.5$ cm, the number of turns required to obtain an inductance value of 23 $\mathsf{\mu }$H is approximately 12 turns. Knowing all the necessary design parameters, we used Ansys Maxwell software to validate this estimation by simulation, and we built the coil to confirm the design. As shown in Figure 8 and

Table 7. Inductance versus the distance between the primary and secondary coils using Ansys Maxwell.

Distance Between Coils (cm)	${\mathit{L}}_1$ [$\mathsf{\mu }$H]	${\mathit{L}}_2$ [$\mathsf{\mu }$H]	M [$\mathsf{\mu }$H]
2	23.6492	23.7145	11.9563
4	23.6485	23.7763	6.8334
6	23.6494	23.7967	4.1659
8	23.6487	23.8306	2.6576
10	23.6494	23.8597	1.7576
12	23.6493	23.9369	1.1972
14	23.6494	23.9473	0.8358
16	23.6496	23.9697	0.5955

, the design methodology permits the target value of inductance to be obtained, and simulation and measurements confirmed that the inductance achieved matched.

Table 7 presents the simulation results of primary $L_1$, secondary $L_2$ and mutual M inductance using Ansys Maxwell software. We analyzed how the inductance varies with the distance between the coils.

The values of $L_1$ and $L_2$ remain very stable (approximately 23.65 $\mathsf{\mu }$H and 23.7–23.71 $\mathsf{\mu }$H, respectively) at a distance of 2 cm. However, it is observed that $L_2$ becomes more sensitive as the distance increases from 2 cm to 16 cm. This indicates that the self-inductance of the coils is significantly influenced not only by their geometric and internal characteristics, but also by the distance, even though many studies in the literature assume $L_1$ = $L_2$ and neglect this variation. The mutual inductance M drops sharply from 11.96 $\mathsf{\mu }$H to 0.59 $\mathsf{\mu }$H, representing a reduction of more than 95% between 2 cm and 16 cm. This behavior is expected, since mutual inductance strongly depends on the magnetic coupling, which decreases rapidly with distance. This decline reflects a weakening of the magnetic link between the two coils, leading to a reduced power transfer efficiency.

Based on the inductance value and the target resonant frequency, we can calculate the value of the capacitor $C_x$ according to Equation (31).

$$C_x={\displaystyle \frac{1}{L_x{\omega }_0^2}}.$$

(31)

The value of the capacitor was determined as 149.32 nF for a resonant frequency of 85 kHz. It is important to note that the secondary inductance $L_2$ is equal to the primary inductance $L_1$, and similarly, the capacitors $C_1$ and $C_2$ are equivalent.

3.4.3. Verifying the Coupling Coefficient

The coupling coefficient $k_{12}$ between the primary and secondary coils can be defined by Equation (1), and provides information about the amount of magnetic flux transferred from the transmitter to the receiver. This definition can be used when using the Ansys (2023 R2) based on the design parameters. To verify experimentally this coupling coefficient, it is possible to employ a simple method that includes the following steps. The inverter is driven with a duty cycle above 90%. The primary coil $L_1$ is connected to the inverter output without a resonance capacitor. The secondary coil $L_2$ remains open-circuited, and a voltage sensor is placed at its terminals. Thus, we employ the coils as a transformer. The ratio of the output voltage $V_{L2}$ to the primary voltage $V_{L1}$ allows for the estimation of the coupling coefficient $k_{12}$ using Equation (32).

$$k_{12}={\displaystyle \frac{V_{L2}}{V_{L1}}}.$$

(32)

It is possible to use an AC signal generator instead of the inverter. This provides better stability in both frequency and amplitude. The results of the coupling coefficient using the three approaches are presented in Figure 9. It appears evident a gradual decrease in the coupling coefficient as the distance between coils increases (from 2 to 16 cm), confirming that the distance plays a critical role in magnetic coupling efficiency. At short distances (2 cm), the experimental values $k_{\exp 1}$ and $k_{\exp 2}$ are higher than the simulated value $k_{\mathrm{sim}}$. This discrepancy can be attributed to unmodeled parasitic effects in Ansys, such as nearby metallic structures. From 4 to 10 cm, a strong agreement between experimental and simulated results is observed (error < 5%), indicating the reliability of the Ansys Maxwell model within this range. Beyond 12 cm, the simulated coupling coefficient tends to be slightly underestimated compared to the experimental values. This may indicate solver or meshing limitations under weak coupling conditions.

Beyond this distance, larger discrepancies appear between simulated and experimental results. These deviations can be attributed to several factors: (i) modeling limitations, as magnetic coupling becomes very weak at long distances; (ii) unmodeled parasitic effects in practice, surrounding materials (e.g., metallic structures, wiring) may slightly influence the magnetic field under weak coupling conditions, which are not captured in the simulation; (iii) fabrication and alignment tolerances—small differences in positioning, orientation, or actual geometry of the coils may significantly affect the coupling at longer distances. These observations highlight the need to improve future models by incorporating environmental influences, performing geometric sensitivity analyses, and refining boundary conditions within simulations.

4. Experimental Results

In this section, we present co-simulation and experimental results of the proposed WPT system. We start with the description of the co-simulation environment and experimental setup, and continue with the presentation of results.

4.1. Co-Simulation Environment and Experimental Setup

We employ three complementary software parts to perform co-simulation evaluation: Ansys Maxwell, Vitis Model Composer (2022.1), and MATLAB/Simulink. Ansys Maxwell software was used for the accurate electromagnetic modelling of the system’s inductive part, and to take into account the effects of agricultural environmental constraints, such as the presence of water, sand, and other particles, as well as the effect of temperature. The resulting 2D model is imported into Ansys Twin Builder, where simulations in a purely electrical circuit are carried out. To ensure consistency with the real system, Vitis Model Composer was used to integrate the original VHDL control programs developed for the experimental inverter and to generate the PWM control signals. The complete system digital controller and physical model are then integrated into Twin Builder, enabling realistic validation under near-experimental conditions. Finally, the simulation of these components runs on a MATLAB/Simulink environment, facilitating post-processing analysis. Figure 10a presents a block diagram illustrating this co-simulation architecture, and Figure 10b provides a real view of the implemented experimental setup. The main characteristics of the implemented electromagnetic circuit are detailed in

Table 8. Parameters of the electromagnetic circuit.

Description	Symbol	Value
Number of turns of primary and secondary coils	$N_1$, $N_2$	12 turns
Primary, secondary inductance	$L_1$, $L_2$	23.788 $\mathsf{\mu }$H, 23.58 $\mathsf{\mu }$H
Primary, secondary capacitance	$C_1$, $C_2$	157.4 nF, 155.4 nF
Primary, secondary internal resistance	$R_1$, $R_2$	0.11 mΩ
Nominal resonance frequency	$f_r$	85 kHz

.

4.2. Results Under Standard Conditions

The wireless power transfer (WPT) system was analyzed under standard conditions, meaning in the absence of specific agricultural medium particles (e.g., water, sand, etc.), with only the distance between coils and the phase shift being varied. The goal of this analysis is twofold: to validate the system’s operational model and to identify its optimal performance range. Figure 11 presents the analysis of active power at the primary side for different distances between the coils and different phase shifts. These results were obtained using Ansys and MATLAB/Simulink co-simulation.

The co-simulation and experimental results, presented in Figure 12, reveal clear trends as a function of distance. As shown in Figure 12a,b, active power increases up to a distance of 6 cm, where it reaches a peak, and then decreases beyond that point. A comparison between the three environments (MATLAB, Ansys, and experimental results) shows a strong agreement between MATLAB and Ansys across the entire distance range. The experimental curve follows a similar trend but exhibits significant losses beyond 10 cm, likely due to real-world physical limitations (e.g., wire resistance, core losses, skin and proximity effects, etc.). Figure 12c presents the results of power transfer efficiency. From these results, we can observe that the efficiency drops drastically with increasing distance, from more than 90% at short range (2–4 cm) to less than 10% at 16 cm. This highlights that simulations using Ansys match almost perfectly experimental results.

This confirms the critical role of the coupling coefficient k, which should ideally remain in the range of 0.1 to 0.3 to ensure efficient transfer. The efficiency drop underscores the need for optimization strategies such as coil alignment, compensation circuit design, or adaptive control techniques to improve energy transfer.

In summary, this experimental study confirms the expected theoretical behaviour of resonant inductive WPT systems and highlights the strong sensitivity of efficiency to magnetic coupling and distance, which is essential for reliable deployment in real-world environments.

4.3. Results in the Presence of Surrounding Materials on Magnetic Coupling

In the context of inductive resonant wireless power transfer (WPT), the electromagnetic properties of surrounding materials, particularly the relative magnetic permeability (${\mu }_r$) and the electrical conductivity ($\sigma$), can influence the magnetic field distribution and, consequently, the coupling between coils. The relative permeability ${\mu }_r$ expresses a material’s ability to conduct magnetic flux compared to vacuum. It directly affects the shape and intensity of the magnetic field generated by the transmitter coil. In this study, typical agricultural materials such as air (named standard conditions), garden soil, wet soil, or freshwater exhibit values of ${\mu }_r$ close to unity, as shown in

Table 9. Typical values of relative permeability used in Ansys Maxwell.

Material	Relative Permeability ${\mathit{\mu }}_{\mathit{r}}$	Conductivity $\mathit{\sigma }$ [S/m]
Air	1.0000	0
Garden soil	1.0000–1.0005	${10}^{-6}$–${10}^{-4}$
Wet soil	1.0000–1.0008	${10}^{-3}$–0.1
Freshwater	0.99999	0
Seawater	0.99995	4

. These environments can therefore be considered weakly perturbing to the magnetic field and are modeled as non-magnetic in Ansys Maxwell. The electrical conductivity $\sigma$ determines a material’s ability to conduct induced currents when exposed to a time-varying magnetic field. In conductive media, eddy currents can be induced, locally attenuating the field and potentially reducing coupling efficiency. Table 9 shows typical conductivity values used in this study.

However, in our experimental setup, the coils are electrically insulated using enamel coating (e.g., polyurethane or nylon). As a result, even when immersed in conductive environments, no eddy currents can circulate in the coils or their immediate surroundings. Therefore, the magnetic field remains virtually unchanged, which aligns with the experimental measurements. As illustrated in Figure 13, electromagnetic simulations performed with Ansys Maxwell confirm these observations.

When the coils are surrounded by air or dry sand, the magnetic field propagates symmetrically and uniformly, indicating optimal magnetic coupling. As presented in Figure 13b, when more conductive materials are introduced, slight local attenuation of the field occurs near the contact region. However, this effect remains marginal as long as the coils are properly insulated. Figure 13c, shows the results of magnetic field exposure at a vertical distance of 20 cm above the coupling plane. The simulated magnetic field reaches approximately 78.4 µT, which remains below the occupational exposure limit set by ICNIRP at 85 kHz (100 µT), but exceeds the general public limit of 27 µT.

Nevertheless, to enhance safety in open-field applications, we plan to integrate magnetic shielding solutions in future developments, particularly when the system is embedded in the mobile robot. This will help reduce exposure for nearby animals and agricultural workers. To verify the possible effects of the surrounding material on the WPT efficiency, experimental tests were carried out varying the conditions, i.e., covering the primary coil with garden soil, wet soil, or freshwater. Each time, the height of the cover was 2 cm, which means the primary coil was completely immersed when using freshwater. For each condition of the primary coil, the distance between coils was varied from 2 cm to 16 cm. Figure 14 presents the results of the measured active power at the primary (Figure 14a) and secondary (Figure 14b) sides and the efficiency of the WPT (Figure 14c). These results show that applying a garden soil cover to the primary coil has a negligible impact on the WPT efficiency when dry, but in the presence of wet soil, the efficiency and the transferred power decrease. They also highlight that the presence of freshwater improves the efficiency while maintaining the transferred power, as in standard air conditions.

Figure 15 illustrates the experimental voltage and current waveforms measured at the input and output of the system under different environmental conditions: air (standard; Figure 15a), garden soil (Figure 15b), freshwater (Figure 15c), and wet soil (Figure 15d). All measurements were performed with a fixed distance of 4 cm between the coils and a phase shift of 108 degrees applied to the control signal. Figure 15 shows, for each case, on the one hand, the waveforms at the inverter output (square wave shape), and on the other hand, the quasi-sinusoidal waveforms observed at the secondary side after resonance. It can be observed that environmental conditions affect the current waveform, particularly in humid environments (wet soil or water).

5. Discussion

The numerical simulations and the experimental analysis of wireless power transfer (WPT) in agricultural environments highlight the influence of the surrounding medium on the system performance. The results show that the transmitted power at the secondary side reaches a peak of approximately 41 W at a 6 cm distance in air and freshwater, while it drops drastically to around 15 W in the case of wet soil. This reduction is also observed at the input power level, indicating a significant decrease in efficiency. However, simulations reveal that the magnetic coupling coefficient remains nearly identical across the different media, including wet soil. This suggests that the degradation in efficiency is not due to weakened inductive coupling, but rather to additional losses induced by the medium. Indeed, wet soil exhibits notable electrical conductivity (up to 0.1 S/m), due to the simultaneous presence of mineral particles and an ion-rich mix. This condition, present in agricultural applications, promotes the generation of eddy currents and ohmic losses within the magnetic field emitted by the coils, which absorbs part of the transferred energy. In contrast, freshwater, which is weakly conductive, does not cause significant losses, thereby maintaining high efficiency despite having a similar permittivity to wet soil. These observations confirm that dissipative media such as wet soil significantly reduce energy transfer efficiency not by weakening the magnetic coupling, but by introducing dissipation mechanisms. For agricultural applications, this underlines the need to implement proper isolation strategies or magnetic field optimization techniques to maintain high performance.

6. Conclusions

In this article, we presented a methodology for the design and implementation of a wireless charging system for smart agricultural robots (Smart Agribots). After a brief review of the main wireless power transfer technologies, including inductive (IPT), capacitive (CPT), magnetic resonance (RIPT), radio frequency (RF), and microwave (MWPT), our work focused on a series–series (SS) magnetic resonance approach. Through a case study, we defined the specifications of a charging system integrated into an agricultural robot, modeled the power transfer circuit, and examined its efficiency. Key technical highlights include the optimization of planar spiral coil geometry for medium-range operation, the evaluation of coupling coefficient variations under environmental influence, and the analysis of electromagnetic exposure levels in compliance with ICNIRP guidelines.

Experimental results showed a maximum power transfer (41 W at 6 cm) for air and freshwater as the surrounding medium, with a peak efficiency of approximately 84.3%, confirming the system’s potential for semi-autonomous agricultural robotics. However, highly dissipative conditions, such as wet soil, reduced the transferred power to about 15 W, highlighting the need for adaptive control.

The originality of this study lies in the experimental evaluation of WPT performance under real agricultural environmental conditions (garden soil, freshwater, wet soil, and ambient temperature), combined with a hybrid modeling approach integrating both electromagnetic simulation and power electronics co-simulation, and supported by rigorous component selection for harsh outdoor conditions.

Future work will aim to integrate intelligent alignment detection (optical or magnetic guidance), automatic impedance matching and frequency tuning, mechanical integration into the robot chassis, and environmental robustness testing (thermal cycling, prolonged humidity exposure). A magnetic shielding solution is also planned to reduce electromagnetic exposure and protect nearby animals.