# Innovative Design of Drone Landing Gear Used as a Receiving Coil in Wireless Charging Application

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. WPT Design

#### 2.1. System Configuration

#### 2.2. WPT Equivalent Circuit

_{in}

_{1}and capacitor C

_{in1}) to smooth the current spikes generated by the commutations of the inverter. The inverter permits the conversion from DC to high frequency AC signal. Generally, for medium–high power applications at the considered frequency of 300 kHz, the class-D topology inverter is used to reduce conduction and commutation losses. This inverter topology is made by four switches (in this case, the MOSFETs U1–U4) that permits to generate a full square wave with an easy control of the signal frequency.

_{1}. The two coils are characterized by self-inductances L

_{1}and L

_{2}, mutual inductance M, and self-resistances R

_{1}and R

_{2}modeling the power losses [9]. The coupling factor k is given by:

_{1}, L

_{2}, and M) can be extracted by numerical simulations or calculated by analytical methods for simple configurations. The lumped parameters can be also measured using an RLC meter or a vector network analyzer (VNA). After the assessment of the lumped circuit parameters, the compensation capacitors C

_{1}and C

_{2}can be obtained at resonance frequency for the selected compensation topology [7].

_{2}, then the high frequency AC signal is converted in a DC voltage by a full bridge diode rectifier (D1–D4). Finally, the output voltage is filtered and connected to load. Generally, the load is composed by many electronic components (electronic equipment, battery charger, etc.), but for the sake of simplicity, the whole load can be modeled at resonance with a simple resistor to evaluate the system performances.

_{s}with an internal resistance R

_{s}, and the load is modeled by an equivalent resistance R

_{L}[9]. The transferred power P

_{2}= R

_{L}|I

_{2}|

^{2}is the real power transferred to the load resistance R

_{L}, while the efficiency η = P

_{2}/P

_{1}is calculated as the ratio between the output real power P

_{2}at port 2-2’ and the input real power P

_{1}at port 1-1’ [14]. It should be noted that in the calculation formula of the efficiency η, the losses of the inverter and of the rectifier are not considered.

#### 2.3. Landing Gear Design as a Secondary Coil

_{Al}= 37 MS/m, the skin depth is δ = 0.15 mm. It is important that the geometry of the landing gear is suitably selected to form a closed loop and to guarantee electrical continuity. Moreover, the shape of the landing gear as a secondary coil must improve the coupling factor k with the primary coil. The proposed shape is shown in Figure 4, where it is worth noting that the landing gear is made by a continuous aluminum pipe terminated in the secondary circuit with attached load (not depicted in the picture). In this work a medium size commercial drone is considered (DJI F550, SZ DJI Technology Co. Ltd. , Shenzhen, China) that is characterized by a maximum takeoff weight of 2.5 kg. To ensure a good mechanical robustness, the aluminum pipe is chosen having the external diameter of the pipe equal to d

_{p}= 8 mm and a thickness equal to t

_{k}= 1 mm, which is a value much larger than the skin depth δ = 0.15 mm, leading to limited additional AC losses. The dimensions of the landing gear are: l

_{s1}= 30 cm, l

_{s2}= 20 cm, w

_{s1}= 25 cm, w

_{s2}= 15 cm, and h

_{s}= 10 cm. The weight of the realized landing gear, which can operate as a secondary coil, is m

_{c}= 91 g, while the original landing gear without any electrical function has a weight of 78 g. The additional weight is therefore only 13 g.

#### 2.4. Design of the Primary Coil

_{ij}produced by the ith current I

_{i}and linked with the jth coil when assuming a single turn for both primary and secondary coils (N

_{1}= N

_{2}= 1) is given by:

_{i}is the magnetic vector potential produced by the current I

_{i}, ${\ell}_{j}$ is the contour of the jth circuit, and i = {1, 2}, j = {1, 2}. Assuming the thin wire approximation, A

_{i}is given by:

_{i}flows and the observation point where

**A**

_{i}is calculated.

_{i}discrete current segments

**Δ**$\ell $

_{m}in the 3D space. Then the magnetic vector potential

**A**

_{i}is given by [36]:

_{m}is the distance from the observation point and the center of the mth segment. The flux can be numerically calculated in the jth coil discretized by n

_{j}segments as:

_{ij}can be obtained from the flux φ

_{ij}as:

_{1}and N

_{2}number of turns, respectively, the self-inductances L

_{1}and L

_{2}and the mutual inductance M are obtained by the Equation (7) as:

_{2}= 1, and Equations (8)–(10) become:

_{12}is proportional to N

_{1}. The equations described above are implemented in a MATLAB code and they are used for the calculation and optimization of the coil parameters, as described in the following.

_{d}, a ground pad of circular shape must have a diameter d

_{b}equal to:

_{b}of the square must be greater than or equal to the diameter d

_{b}, i.e., s

_{b}≥ d

_{b}. In conclusion, the maximum dimensions of the ground pad for the two considered shapes are:

- 1)
- Circle of diameter d
_{b}; - 2)
- Square of side s
_{b}.

_{1}= 1) primary coil:

_{c}or s

_{c}for the test cases #1 and #2, respectively. In our simulation, the adopted values are: d

_{c}= 20, 30, 40, 50, 60 cm; s

_{c}= 20, 30, 40, 50, 60 cm. The secondary is always a single-turn 3D coil (N

_{2}= 1), whose dimensions are described in Section 2.3. The primary coil is assumed to be made of a copper Litz wire, while the secondary coil is made by a 3D-shaped aluminum pipe. The calculations are carried out considering a lateral misalignment between the projections of the two coils centers on the x−y plane at z = 0. The misalignment must be accurately considered, due to a possible imprecise landing of the drone. The results for a circular coil with variable diameter d

_{c}in terms of the coupling factor k versus lateral misalignment t

_{rx}along x-axis are reported in Figure 7 for three different values of landing gear height h

_{s}. From this figure, it is evident that the coupling factor k increases as h

_{s}decreases.

_{rx}in x-direction is shown in Figure 8 when considering a primary square coil. From the obtained results, it is evident that the coupling factor k is maximum for aligned coils when the coil size is comparable with the projection of the 3D secondary coil on the x–y plane. In the considered case, this condition is verified for d

_{c}= 30 cm, being w

_{s1}= 30 cm. The k value is much higher than that of other coil dimensions, but it rapidly decreases as the lateral misalignment. The k decrease appears also for other coils with different diameter d

_{c}, but this trend is not so rapid. This aspect is very relevant for stand-alone ground base stations, since any lack of charging due to a very imprecise landing requires human intervention. Thus, it is of paramount importance to assure an adequate charging of the drone battery, also in case of very poor landing. For this reason, it is highly suggested to select a large circular coil as the most adequate for the autonomous charging process of a drone, also in case of bad landing in a stand-alone ground base. Then, optimization in terms of system efficiency is proposed considering the circular coil configuration, which has been revealed to be better than the square shape, and assuming the SP compensation topology, which has been demonstrated to be the most performant topology [15]. The performance of the system is evaluated solving the equivalent circuit shown in Figure 3. The resonant frequency is assumed to be f = 300 kHz, which is the highest admissible frequency in the kilohertz range [37]. The load is modeled by a resistance R

_{L}= 5 Ω. The per unit length (p.u.l.) resistance of the Litz wire used for the primary coil is 10 mΩ/m, while the total resistance of the secondary coil is R

_{2}= 28 mΩ. In order to optimize the efficiency η, an analysis varying the number N

_{1}of the primary coil turns is carried out. The efficiency η versus the lateral misalignment t

_{rx}is shown in Figure 9 for several values of the circular primary coil diameter d

_{c}and for three values of the primary coil turns: N

_{1}= 1, 5, 10. The obtained results show that good values of η can also be found for small values of k when the lateral misalignment t

_{rx}is limited. When the misalignment exceeds the landing precision a, fixed here to 20 cm, only the largest circular coils can efficiently power the battery. Thus, the configuration with d

_{c}= 50 cm as the outer diameter is selected as the optimum value of the primary circular coil.

_{1}= 1–10 of the primary coil is shown in Figure 10 when assuming d

_{c}= 50 cm. The results highlight that an increase of N

_{1}significantly enhances the efficiency η. Thus, the configuration with N

_{1}= 10 is chosen as design parameter. The efficiency is calculated assuming both SP and SS compensation topologies, demonstrating that the selection of the SP topology is much more convenient than the SS one, because it permits to obtain higher performances with low turns on the receiving coil [14,15]. It should be noted that increasing the number of turns more than N

_{1}= 10 could lead to a slight improvement of the performance, but also to a significant increase of the coil weight and complexity.

_{L}, corresponding to different conditions of the battery during the charging process [38]. Thus, it is important to verify the efficiency of the system for several values of R

_{L}. The obtained results, shown in Figure 11, demonstrate the capacity of the system to maintain very good efficiency for a wide range of R

_{L}values.

_{s}demanded by the drone and by the payload. However, it has been demonstrated that the proposed WPT system can work well also assuming a different size of the landing gear (e.g., height h

_{t}of the landing leg). It implies that the proposed design procedure can also be used for different landing gears, but, obviously, the optimization can be carried out only for a single landing gear on a case-by-case basis.

## 3. Fabrication and Testing

_{c}= 50 cm was realized using a copper Litz wire made of 120 strands of AWG 32 wire. The self-inductances of the primary coil L

_{1}and of the landing gear/receiving coil L

_{2}were measured using an RLC meter. The mutual inductance M was measured by connecting the two coils in series and anti-series configurations as M = (X

_{p}− X

_{aph})/4ω, being ω the angular frequency, X

_{ph}and X

_{aph}the reactance in phase and antiphase configurations, respectively. All the measurements were performed at f = 300 kHz. The setup of the primary and secondary coil and the instrumentation are shown in Figure 12. The calculated and measured lumped parameters are reported in Table 1, where M was measured in the case of aligned coils. The coupling factor k between the two coils was obtained by (1) considering misalignment conditions, named, respectively, t

_{rx}and t

_{ry}in the x- and in the y- directions, respectively. The obtained results are shown in Figure 13. Then, a comparison in terms of efficiency η was performed. The circular primary coil obtained from the designing process described in Section 2.3 coil with N

_{1}= 10 turns and outer diameter d

_{c}= 50 cm was adopted. The measured primary coil resistance made of Litz wire at f = 300 kHz is R

_{1}= 830 mΩ and the self-inductance is L

_{1}= 85 μH. The primary coil was fed by a high frequency class-D amplifier and compensated using a series capacitor C

_{1}= 3.3 nF.

_{2}= 221 nF and connected to the resistive load. For simplicity, the load was modeled with a power resistor R

_{L}= 5 Ω. The DC input voltage on the inverter was manually adjusted in order to get, in all cases, a fixed output power load resistor. The required power by the considered drone was of 64 W, considering a battery with four cells (total nominal voltage 14.4 V), a capacity of 4000 mA·h, and a charging time of 1 h [14]. Considering the losses on the rectifier and on the charging circuit, the required power was set to P

_{L}= 70 W. The real power P

_{1}= V

_{1}I

_{1}cosϕ

_{1}was calculated from the measured voltage V

_{1}, current I

_{1}, and phase difference ϕ

_{1}by means of an oscilloscope and a current probe clamp, while the output power P

_{L}= |V

_{2}|

^{2}/R

_{L}was derived by measuring the voltage drop V

_{2}on the load resistance R

_{L}. The measurement setup is shown in Figure 14 and the measured waveforms of V

_{1}, I

_{1}, and V

_{2}are shown in Figure 15. The efficiency η was measured and calculated for several misalignment conditions, i.e., different values of t

_{rx}and t

_{ry}on x- and y-axes, respectively. The obtained results reported in Figure 16 show good agreement between calculations and measurements. Furthermore, the results exhibit the capability of the proposed solution to maintain very good efficiency also in condition of strong misalignment. Finally, the aluminum landing gear was installed on the drone, as shown in Figure 17, and the charging process was tested, adopting a rectifier and a charging control system between the WPT systems and the drone battery, as described in [14].

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**WPT charging system with series-parallel (SP) compensation: complete electrical circuit (

**a**), and simplified equivalent circuit of two coupled coils (

**b**).

**Figure 5.**WPT system with primary single coil of circular shape (

**red**) and three-dimensional (3D) secondary coil (

**blue**).

**Figure 7.**Coupling factor k versus lateral misalignment t

_{rx}along x-axis for circular coil, for different landing gear height: hs = 0.1 m (

**a**), hs = 0.15 m (

**b**) and hs = 0.2 m (

**c**).

**Figure 8.**Coupling factor k vs. lateral misalignment t

_{rx}along x-axis for square coil, for different landing gear height: hs = 0.1 m (

**a**), hs = 0.15 m (

**b**) and hs = 0.2 m (

**c**).

**Figure 9.**Efficiency η vs lateral misalignment t

_{rx}along x-axis for different values of the primary coil turns: N

_{1}= 1 (

**a**), N

_{1}= 5 (

**b**), and N

_{1}= 10 (

**c**).

**Figure 10.**System efficiency varying the number of turns N

_{1}and the SP and SS compensation topologies.

**Figure 13.**Calculated and measured coupling factor k vs misalignment along x-axis (

**a**) and y-axis (

**b**).

**Figure 16.**Calculated and measured efficiency

`η`versus misalignments along x-axis (

**a**) and y-axis (

**b**).

**Table 1.**Calculated and measured circuit lumped parameters for the primary coil with N

_{1}= 1 and for the secondary coil/landing gear with N

_{2}= 1.

Calculated | Measured | ||||||||
---|---|---|---|---|---|---|---|---|---|

L_{1} (μH) | L_{2} (μH) | M (μH) | R_{1} (μΩ) | R_{2} (μΩ) | L_{1} (μH) | L_{2} (μH) | M (μH) | R_{1} (μΩ) | R_{2} (mΩ) |

2.20 | 1.33 | 0.28 | - | 28 | 2.25 | 1.27 | 0.29 | 65 | 33 |

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## Share and Cite

**MDPI and ACS Style**

Campi, T.; Cruciani, S.; Maradei, F.; Feliziani, M. Innovative Design of Drone Landing Gear Used as a Receiving Coil in Wireless Charging Application. *Energies* **2019**, *12*, 3483.
https://doi.org/10.3390/en12183483

**AMA Style**

Campi T, Cruciani S, Maradei F, Feliziani M. Innovative Design of Drone Landing Gear Used as a Receiving Coil in Wireless Charging Application. *Energies*. 2019; 12(18):3483.
https://doi.org/10.3390/en12183483

**Chicago/Turabian Style**

Campi, Tommaso, Silvano Cruciani, Francesca Maradei, and Mauro Feliziani. 2019. "Innovative Design of Drone Landing Gear Used as a Receiving Coil in Wireless Charging Application" *Energies* 12, no. 18: 3483.
https://doi.org/10.3390/en12183483