Wireless charging is the key technology to realize real autonomy of mobile robots. As the core part of wireless power transfer system, coupling mechanism including coupling coils and compensation topology is analyzed and optimized through simulations, to achieve stable and practical wireless charging suitable for ordinary robots. Multi-layer coil structure, especially double-layer coil is explored and selected to greatly enhance coupling performance, while shape of ferrite shielding goes through distributed optimization to guarantee coil fault tolerance and cost effectiveness. On the basis of optimized coils, primary compensation topology is analyzed to adopt composite LCL compensation, to stabilize operations of the primary side under variations of mutual inductance. Experimental results show the optimized system does make sense for wireless charging application for robots based on magnetic resonance coupling, to realize long-term autonomy of robots.

Robot technology has a wide range of applications, such as indoor and outdoor ground cleaning, security, substation patrol and so on. With the increasing utilization of mobile robots, the demand of functional requirements on mobile robots is getting higher and higher, including long-term duty, large-range operation and extended period of autonomy. Real long-term autonomy can only be achieved when the robot is able to realize self-support within the environment, thus to realize continuous loop task.1 Therefore, how to make the robot charge automatically, conveniently, and efficiently without human intervention is one of the key technologies to realize the long-term autonomy of robots.

Traditional self-charging for mobile robots is mainly based on contact charging technology.2–4 It requires high positioning accuracy. Wireless power transfer (WPT) was first presented by Nikola Tesla at the end of the 19th century.5 An autonomous inspection robot inducing the voltage from the transmission line as a power source was proposed in earlier stage,6 and a 50 Hz wireless charging method for moving robots with selective excitation system was designed in Ref. 7, which also tried to improve the total efficiency by attaching ferrite cores to the coils. These designs were essentially based on power frequency transformers, which was unable to transfer high power with separated cores on primary and secondary side by working at a low frequency. Research has been mainly focused on high frequency inductive WPT since the 1990s, to which research team of the university of Auckland has contributed a lot, including system modeling and coupling optimization.8,9 However, the inductive WPT demands a lot on the design of the magnetic circuit, resulting in low transmission distance and limited flexibility in its applications.

In recent years, with the in-depth study on magnetic-coupling resonant wireless power transfer (MCR-WPT), it has become a development trend to replace traditional charging technologies with MCR-WPT. MCR-WPT technology was proposed by research team of MIT in 2007,10 and the energy transfer mechanism between the coils was explained by the coupled mode theory.11 Due to its safety and convenience, MCR-WPT has been gradually applied in wireless charging for electric automobiles, transmission line equipment and biological implanted equipment.12,13 The energy transfer is not affected even with some kinds of obstacles in the transmission channel, guaranteeing charging stability and reliability of the system.14 Autonomous wireless self-charging of robots can be truly achieved via MCR-WPT.15 

Several further efforts have been dedicated into wireless charging applications in robots in recent years. Reference 16 combined battery swapping with wireless charging for battery, not directly charging for robots. Reference 17 also proposed a novel wireless charging system for robots battery with battery replacement, which worked at utility frequency of 60 Hz. To reduce the influence of coil size difference and misalignment on the wireless charging performance for robots, a relay coil was added in the plane of transmitting coil, with the axis of them overlapping each other to expand the magnetic field range, and a maximum 7 W power to load with overall efficiency between 20%∼30% at a frequency of 516.5 kHz was achieved based on MCR-WPT.15 However, coupling mechanism, the key part of a MCR-WPT system, has not been further optimized. Some works gave charging design of multi-coil array structure for mobile robots to achieve uniform magnetic field distribution and extend charging area. Reference 18 gave a design of PCB inductive charging platform with a particular multi-coil layout for swarm robots, and realized 3.4 W average charging power with a high operating frequency of 1.44 MHz, when four robots parked on it simultaneously, with their pick-up coils close to the platform. Based on MCR-WPT, Ref. 19 provided a constant power delivery to ambulatory microrobot by setting three relay coils in the same plane. And an average transfer efficiency of 20.8% with charging power requirements of 10 mW to 1 W at 13.56 MHz was achieved, when the microrobot moved along the coil array. But multi-coil structure causes high energy loss and magnetic field cancelation between coil and coil or layer and layer, which namely is not so cost-effective. Dynamic charging has also been presented in Refs. 20 and 21 for mobile robots, in which selective charging primary was excited. A charging platform with combined coil array was optimized to power multi small robots, each of which consumes hundreds of milliwatts of power with transmission distance below 10 mm.20 Reference 21 put forward a dynamic wireless charging system with segmented transmitting coils and decentralized energy pickup installed on the robot chassis before and after, for inspection robots in the substation. Dynamic charging requires a lot on charging control and system reliability if only certain coils need to work in real time, and location of the two pickup coils in Ref. 21 may affect the performance of robot mobility like obstacle negotiation.

As the core component of a MCR-WPT system, planar coupling coils are generally much popular in wireless charging for EVs or robots due to installation convenience, and has been further studied and optimized in research for EVs and other mobile devices charging applications to improve system performance. And single planner pads,22–24 and multiple coil array pads25–27 play different roles in static charging and dynamic charging respectively.

Since this research is for static wireless charging application in mobile robots with navigation system, single planar coil structure is preferable. There was also non equal turn spacing design for single coil structure to realize near uniform field,28 but it demands complex calculations, which is not convenient for practical processing and mass production. In addition, ferromagnet are often added to the coils to enhance coupling performance in WPT system, and ferrite cores with different shapes are commonly used.29,30 Basic properties of ferromagnet with influences of finite dimension and interfaces have been described in earlier works.31 

Moreover, with optimized coil design, resonance compensation topology is also the key to good system performance such as charging reliability and stability. In existing robots wireless charging designs, where the power level and load resistance are relatively low, a series or parallel resonance compensation topology is commonly adopted at the primary side. However, single series or parallel resonance scheme can not ensure stable and secure charging performance, with practical limitation of robots navigation considered.

This paper focuses on the characteristics of the mobile robot autonomous charging, and optimizes the coupling mechanism. Parameters such as coil structure and shape of ferrite shielding will be optimized, to increase the coupling coefficient and offset tolerance between transmitting and receiving coils, so as to improve the efficiency of the magnetic resonant coupling wireless charging system; and resonance compensation topology is studied to cope with coupling coefficient variation caused by coil offset, due to current robots’ positioning inaccuracy; providing a better wireless charging system for mobile robots in terms of simplicity and practicability.

The scheme of MCR-WPT is proposed on the basis of inductive wireless power transfer, and it solves the problems of short transmission distance and low transfer efficiency of the latter to some extent. The inductance of the transmitting coil is connected with a compensation circuit to form a resonant tank, and the receiving terminal is also composed of an inductance of the receiving coil and a compensation circuit; both transmitting and receiving terminals are operating at the same resonant frequency, to achieve high efficiency of wireless power transfer via strong magnetic resonance coupling. In the modeling analysis of MCR-WPT system, the coupled mode theory11 has certain advantages in describing the energy flow of the system,10 but specific parameters can’t be shown and acquired directly for further system parameter optimizations. The circuit theory modeling method is based on mutual inductance theory, through the accurate modeling of various components of the system to solve the actual parameter calculation,13,32 and is more convenient for system optimization design. Structure of a typical two-coil MCR-WPT system with SS (series and series) resonant compensation topology is shown in Fig. 1(a), and Fig. 1(b) is an equivalent circuit.

FIG. 1.

(a) Two-coil MCR-WPT system with SS compensation; (b) Equivalent circuit of MCR-WPT system.

FIG. 1.

(a) Two-coil MCR-WPT system with SS compensation; (b) Equivalent circuit of MCR-WPT system.

Close modal

When the power source outputs alternating current at a frequency of f = ω/(2π). The equivalent circuit equation of the system under sinusoidal steady state can be obtained according to Kirchhoff's law:

U1=Z1I1+jωMI20=jωMI1+Z2I2.
(1)

where

Z1=RS+R1+jωL1+1/jωC1Z2=R2+RL+jωL2+1/jωC2.
(2)
k12=ML1L2.
(3)

Quality factor of the transmitting and receiving coils can be expressed as:33 

Q1=ωL1R1+RS,Q2=ωL2RL+R2.
(4)

When the system works at the resonant state, and ω=1/(L1C1)1/2= 1/(L2C2)1/2, Z1=R1+RS, Z2=R2+RL, the transfer efficiency of the system reaches the highest. Generally, the coil resistance of the receiving coil R2 is much smaller than the load resistance RL. In this case, the transfer efficiency of the system can be simplified as follow:

η=k122Q1Q21+k122Q1Q2,
PL=U122(R1+RS)k122Q1Q2(1+k122Q1Q2)2.
(5)

Clearly, the greater k122Q1Q2, the higher efficiency of the system. And the quality factor of coils and the coupling coefficient between the transmitter and receiver are decisive factors of the transfer efficiency and output power of the system.

MCR-WPT system applied to charging for robots is shown in Fig. 2. When the autonomous robot reaches the charging area, 220 V AC power is firstly transformed into high frequency AC current through a high-frequency inverter, and flows to the transmitter through a primary resonance compensation circuit. The high frequency AC sinusoidal current in the transmitting coil generates high frequency alternating magnetic field, which generates high frequency AC current in the receiver on the robot, followed by a rectifier and filter to supply power for the robot directly.

FIG. 2.

Block diagram of the MCR-WPT system for robots.

FIG. 2.

Block diagram of the MCR-WPT system for robots.

Close modal

Generally, charging of robots requires power level of tens to hundreds watts, and when the robot autonomously reaches the charging area via navigation, positioning inaccuracy will lead to horizontal offset between the transmitting coil on the ground and receiving coil located at the bottom of the robot. The robot chassis can’t be too low, otherwise the mobility and obstacle climbing capability might be limited, in other words, the wireless transfer distance h can not be too short in the MCR-WPT system for mobile robots. Correspondingly, the system embodies the following characteristics in the process of autonomous wireless charging for robots from the circuit principle:

  1. Loosely coupled. The parameter used to characterize two coils’ coupling degree is coupling coefficient, generally represented by k, determined by self-inductance of the primary and secondary coils and mutual inductance between them, and the mutual inductance is proportional to d-3 when the coupled two coils are perfectly aligned.33 Transfer distance in this study is no less than 5 cm, which means the MCR-WPT for mobile robots is a loosely coupled system with a small M, and correspondingly a small k.

  2. Variable mutual inductance. Due to the current limitation of navigation and positioning accuracy for autonomous robots, the relative position between the receiving coil and the energy transmitting coil may vary each time the robot returns to the charging area. For the MCR-WPT system of robots, variable k occurs, causing variation in the reflected impedance of the secondary side to the primary side, which will affect the operational stability of the primary side.

Integrated with the above two points, this paper focuses on the following two core issues in the designing of MCR-WPT system for mobile robots: 1) to increase k and Q as much as possible through optimizations of coil structure and shape of ferrite shielding under loosely-coupled condition; 2) to achieve the stability of the primary side under the variation of mutual inductance (or k), so as to improve performance of the system.

Then appropriate coupling coil and compensation topology will be studied and optimized in the following sections according to the above two obtained features.

The design of the coupling coils mainly includes shape and structure optimization of the coil and optimization of the magnetic shielding. This section explores ways to optimize coupling coils by replacing single-layer coil structure with double-layer structure and adding shape optimized ferrite shielding. And a resonant frequency of 58 kHz is chosen to decrease requirements on all parts of devices and system cost. For practical applications on robots, the width and length of the coil are chosen no larger than 200 mm.

The system designed in this study is mainly for low-power robots, so the shape and structure of the coil should not be too complicated. Common single coil shapes are circular and square. The square coil has a larger magnetic flux area than circular coil when the same diameter length is occupied, resulting in a stronger magnetic field strength, which has positive effect on the transfer power and transfer efficiency, and also improves the space utilization rate. However, in the case of spiral shape, since the square spiral has right angles, current changes abruptly at the right angle of the coil, and the resistance is large. Therefore, this paper combines the advantages of circular and square coil by replacing the right angle of the spiral square coils with rounded corner, thus rounded square coil is selected as the coil shape.

The spatial structure of the coil is usually planar spiral or cylindrical spiral. And the multi-layer single coil is equivalent to the combination of the planer and cylindrical spiral coils, of which the structure is shown in Fig. 3(a), and its self-inductance can be seen as connections of several inductors and strong positive mutual inductance between each layer, as shown in Eq. (6), namely self-inductance of multi-layer coil can be greatly increased, and the dislocation connection between the upper and lower layers can effectively improve the capacitance distribution and enhance the magnetic field intensity, as shown in Fig. 3(b). Since mutual inductance between two multi-layer coils can be regarded as mutual inductance between each layer of the transmitting and reciving coils, as presented in Eq. (7), this type of structure can greatly strengthen the coupling between the transmitting and receiving coils in the case of losing very small volume, and finally boost the effective transfer distance and transfer efficiency of the WPT system.

L=L1+M12+M13+...+M1n+L2+M21+M23+...+M2n...+Ln+Mn1+Mn2+...+Mn(n1)=L1+L2+...Ln+2(M12+...+M1n+M23+...+M2n+...+Mn(n1)).
(6)

Where, Li is the self-inductance of the ith layer of multi-layer coil , and Mij refers to mutual inductance between the ith and jth layers.

MTX=M11+M12+...+M1n+M21+M22+...+M2n...+Mn1+Mn2+...+Mnn.
(7)

Where, Mij refers to mutual inductance between the ith layer of the transmitting coil and jth layer of the receiving coil.

FIG. 3.

(a) Multi-layer coil structure; (b) Connection between each layer.

FIG. 3.

(a) Multi-layer coil structure; (b) Connection between each layer.

Close modal

Figures 4(a) and 4(b) is a single-layer coil named coil A and a double-layer coil referred to as coil B respectively; Figures 4(c) and 4(d) are the magnetic field intensity distributions of them in the front view, respectively, when the same excitations are given in FEM simulations.

FIG. 4.

(a) Single-layer coil model; (b) Double-layer coil model; (c) Magnetic field intensity distribution of the single-layer coil; (d) Magnetic field intensity distribution of the double-layer coil.

FIG. 4.

(a) Single-layer coil model; (b) Double-layer coil model; (c) Magnetic field intensity distribution of the single-layer coil; (d) Magnetic field intensity distribution of the double-layer coil.

Close modal

The coil is wound with Litz wire. The length, width and number of turns of those coils are equal, and they are 7-turn rounded square coils with 185 mm to the edge distance, 2.5 mm to the line diameter and 0.5 mm to the pitch of turns.

Compared with single-layer coil, the magnetic field intensity of double-layer coil is much boosted and the magnetic field distribution scale of double-layer coil is also further expanded, which means a larger effective transfer distance.

When the same current is given as excitation, compared with self-inductance and Q value of the single-layer coil structure, that of the double-layer coil has been greatly improved.

In order to better measure the coupling performance of the two coil structures, the coupling coefficient of the two coupling coils are compared with different offsets, as shown in Figs. 5(a), and 5(b).

FIG. 5.

Coupling coefficient k of single-layer and double-layer coils versus offset distance: (a) k versus horizontal offset; (b) k versus vertical offset.

FIG. 5.

Coupling coefficient k of single-layer and double-layer coils versus offset distance: (a) k versus horizontal offset; (b) k versus vertical offset.

Close modal

In these results, “horizontal offset” refers to relative displacement of the axial of two coupling coils towards one single direction at a vertical offset of 50 mm, such as tx or ty, and “vertical offset” describes the transfer distance between the coils without horizontal offset. It can be seen that coupling effectiveness of the double-layer structure stays better in different offset directions.

As mentioned earlier, MCR-WPT system is loosely-coupled, and ferrite shielding is often added to constrain flux to desired area to improve coupling effect and reduce leakage magnetic flux. On the basis of double-layer coil structure, the influence of different ferrite shielding structures on the system is studied.

Double-layer coil with block ferrite shielding is named coil C; double-layer coil with cross hollow ferrite shielding is called coil D; double-layer coil with distributed hollow ferrite shielding is referred to as coil E. And coupling coils in Figs. 6(a) - 6(d) are coil B-B, coil C-C, coil D-D and coil E-E, respectively.

FIG. 6.

(a) Coupling coils as coil B-B; (b) Coil C-C; (c) Coil D-D; (d) Coil E-E; (e) Magnetic field intensity distribution of coil B-B; (f) Magnetic field intensity distribution of coil C-C; (g) Magnetic field intensity distribution of coil D-D; (h) Magnetic field intensity distribution of coil E-E.

FIG. 6.

(a) Coupling coils as coil B-B; (b) Coil C-C; (c) Coil D-D; (d) Coil E-E; (e) Magnetic field intensity distribution of coil B-B; (f) Magnetic field intensity distribution of coil C-C; (g) Magnetic field intensity distribution of coil D-D; (h) Magnetic field intensity distribution of coil E-E.

Close modal

For two axial transmission coils, the magnetic field distribution in the axial transmission plane could reflect the coupling effect of the coils better.

Figures 6(e) - 6(h) present magnetic field intensity distributions in the axial transmission plane of those four different coupling coils respectively with a transfer distance of 50 mm, when the same excitations are given in FEM simulations.

It can be seen that addition of ferrite shielding could enhance the magnetic field intensity within the transmission area to strengthen the magnetic coupling. In addition, ferrite shielding can significantly confine the magnetic field distribution and minimize the leakage of magnetic field. Block ferrite shielding displays the greatest performance in enhancing coupling magnetic field and reducing the leakage of magnetic flux, followed by cross ferrite structure, since these two types of ferrite shielding are both a whole solid piece and longer ferrite permits higher and continuous flux paths without air gap path, however, these two structures are comparatively much fragile due to the geometry of a whole large piece.

Self-inductance, AC internal resistance, no-load Q value and mutual inductance of the above four coupling coil models obtained in simulations are shown in Table I. Self-inductance of double-layer coil with ferrite shielding is increased, and that with block ferrite is the largest, and there’s little difference of AC resistance between them in simulations. In practical applications, AC resistance of coil with block ferrite may be larger due to excessive hysteresis loss.

TABLE I.

Simulation results of four kinds of coil models.

Coupling coil structureL (μH)R (mΩ)QM (μH)
Coil B 56.717 22.769 907.3 14.437 
Coil C 96.526 22.804 1541.8 30.967 
Coil D 86.413 22.791 1381.0 24.741 
Coil E 84.402 22.781 1349.5 23.342 
Coupling coil structureL (μH)R (mΩ)QM (μH)
Coil B 56.717 22.769 907.3 14.437 
Coil C 96.526 22.804 1541.8 30.967 
Coil D 86.413 22.791 1381.0 24.741 
Coil E 84.402 22.781 1349.5 23.342 

Due to the non-directional nature of the MCR-WPT, the relative position between the transmitting and receiving coils is so called fault-tolerant. "Fault tolerance of position" means a certain horizontal or vertical offset between the receiving and transmitting coils should have little influence on the transmission performance of the system, especially on efficiency. Since current positioning and navigation technology is not able to guarantee the receiving coil on the robot to align precisely with the transmitting coil on the ground, the fault tolerance of position is also an important index to measure the performance of the robot wireless charging system. Horizontal tolerance of the wireless charging system should be large enough to compensate for the lack of positioning accuracy, to reduce the requirement on positioning of the robot.

The fault tolerance of the above four kinds of double-layer coupling coil structures is studied via collaborative simulations, and coupling coefficient k, transfer efficiency, power coupled to the load versus horizontal and vertical offsets are shown in Figs. 7, 8 and 9 respectively. PL curves are plotted when a 30 V AC voltage source is added.

FIG. 7.

Coupling coefficient k of the above four different coupling coils versus offset distance: (a) k versus horizontal offset; (b) k versus vertical offset.

FIG. 7.

Coupling coefficient k of the above four different coupling coils versus offset distance: (a) k versus horizontal offset; (b) k versus vertical offset.

Close modal
FIG. 8.

Transfer efficiency of the above four different coupling coils versus offset distance: (a) transfer efficiency versus horizontal offset; (b) transfer efficiency versus vertical offset.

FIG. 8.

Transfer efficiency of the above four different coupling coils versus offset distance: (a) transfer efficiency versus horizontal offset; (b) transfer efficiency versus vertical offset.

Close modal
FIG. 9.

Power coupled to the load of the above four different coupling coils versus offset distance: (a) PL versus horizontal offset; (b) PL versus vertical offset.

FIG. 9.

Power coupled to the load of the above four different coupling coils versus offset distance: (a) PL versus horizontal offset; (b) PL versus vertical offset.

Close modal

As shown, coupling coil with block ferrite shielding presents the best fault tolerance performance with the highest coupling coefficient k and transfer efficiency versus coil offsets. And coupling performance of coils with cross hollow ferrite shielding and that with distributed hollow ferrite shielding show slight difference, while coupling coil without ferrite shielding has the worst fault tolerance performance. Transfer effeciency of coupling coils with block ferrite shielding also tends to be the best against offset varaitions, while that with distributed hollow ferrite shielding presents to be similar to that of coils with cross hollow ferrite shielding.

As for load power characteristics aginst offset distance shown in Figs. 9(a) and 9(b), those coupling coils with ferrite shielding exhibit a trend of almost the same, but the difference of offset positions when PL reaches a maximum, compared with the ferrite free structure. In addition, the load power versus horizontal offset characteristic curve of the coils with block ferrite is more narrow, as dispalyed in Fig. 9(a), which means this coil structure is more sensitive to the offset variation. It can be found that the extreme points of power do not occur at zero horizontal offset or minimum vertical offset. The reason for this might be that the system stays in a state of over coupling at those positions.

It can also be noted that, a null occurs in the coupling coefficient, transfer efficiency, and load power profiles at horizontal offset of about 140 mm, as shown in Fig. 7(a), Fig. 8(a) and Fig. 9(a). This is caused by flux cancellation at this point, where magnetic flux of equal magnitude but with opposite directions passes through the receiving coil.34 

Parameters such as weight and cost should also be taken into account when optimizing the design of ferrite shielding. Parameters of different ferrite arrangements are given in Table II. Ferrite utilizations against horizontal and vertical offsets of the above three coupling coils with ferrite shielding are shown in Figs. 10(a) and 10(b) respectively.

TABLE II.

Parameters of different ferrite arrangements.

Ferrite shielding structureBlock shapeCross hollow shapeDistributed hollow shape
Thickness/mm 
Volume/cm3 188.72 99.9 98 
Ferrite shielding structureBlock shapeCross hollow shapeDistributed hollow shape
Thickness/mm 
Volume/cm3 188.72 99.9 98 
FIG. 10.

Ferrite utilization of the above three different coupling coils versus offset distance: (a) utilization versus horizontal offset; (b) utilization versus vertical offset.

FIG. 10.

Ferrite utilization of the above three different coupling coils versus offset distance: (a) utilization versus horizontal offset; (b) utilization versus vertical offset.

Close modal

The utilization of block ferrite structure is much lower than that of any other two, and utilization of distributed ferrite is slightly greater than cross ferrite structure with horizontal offset varying from 0 mm to 140 mm, with vertical offset fixed at 50 mm. However, within the effective transfer distance (50 mm-140 mm), shown in Fig. 10(b), ferrite with cross structure is not being utilized efficiently compared to distributed ferrite structure, regardless of horizontal offset.

In practical applications, the distributed ferrite stripe is more convenient for production, purchase and installation, and it is less likely to fracture to affect its initial performance. Therefore, distributed ferrite layout is selected as the ferrite shielding structure, with various factors fully taken into consideration.

When the traditional series compensation topology is applied to the primary coil, the transmitter current will be so large that the loss of the whole system is pretty high, leading to low efficiency, and the switching device needs to withstand all the current in the transmitter, namely to bear high current stress; as for the parallel compensation case, though only a small exciting current is needed in the inverter to generate high current in the resonant coil, the inverter switch has to bear much higher resonant voltage stress than the input voltage, which also requires high performance on switches. Therefore, it is not advisable to simply adopt series compensation or parallel compensation for the primary coil.

Consequently, an inductor is added between the inverter and the parallel resonant circuit on the primary side, forming a type of LCL compensation topology as shown in Fig. 11(a), so inverter switches only need to bear the magnitude of the input voltage (like series resonance), and part of the current of the resonant coil (like parallel resonance), that’s to say, the voltage stress and current stress of the inverter switch are reduced at the same time. The LCL compensation topology is approximately equivalent to stimulate a parallel resonant cavity with a current source inverter. And Fig. 11(b) is the equivalent LCL-S (series compensation in the secondary side) compensation topology after the secondary side reflected to the primary side.

FIG. 11.

LCL-S compensation topology of MCR-WPT system: (a) LCL-S compensation topology; (b) equivalent circuit after the secondary side reflected to the primary side.

FIG. 11.

LCL-S compensation topology of MCR-WPT system: (a) LCL-S compensation topology; (b) equivalent circuit after the secondary side reflected to the primary side.

Close modal

In general, the matching inductor Lf is equal to the resonant inductor L1 on the primary side. Under the resonant state of both sides, there is:

ω=1L1C1=1L2C2=1LfC1.
(8)

SS (series compensation in both primary and secondary side) resonance compensation is commonly used for independence of primary compensating capacitor with the secondary parameters. Therefore, current characristics with various coupling coefficient k of both LCL-S and SS compensation are compared in the same WPT model designed above using circuit simulations.

When 30 V AC voltage source is given, the amplitude of the transmitting coil current It and the inverter output current ILf with LCL-S resonance compensation versus the coupling coefficient are shown in Fig. 12(a). And the current in transmitting coil It with SS compensation (where It is also the current output by inverter) is presented in Fig. 12(b). It with LCL-S compensation keeps at around 0.97 A, when k (or mutual inductance) changes or even the secondary side disappears, ensuring stablility of the primary side with coil misalignment. And the output current of the inverter decreases with the decrease of coupling coefficient. However, current in transmitter with SS compensation scheme varies abruptly with various k, and stays so large if the secondary is far away, namely if k is quite small, which throws too much current stress on switches, and the primary might be short circuited with secondary disapeared.

FIG. 12.

(a) Amplitude of the transmitter coil current and the inverter output current versus k with LCL-S compensation; (b) Amplitude of the transmitter coil current versus k with SS compensation.

FIG. 12.

(a) Amplitude of the transmitter coil current and the inverter output current versus k with LCL-S compensation; (b) Amplitude of the transmitter coil current versus k with SS compensation.

Close modal

Therefore, the LCL type compensation topology in the primary side is preferable for MCR-WPT of mobile robots’ self-charging system.

To better verify the misalignment characristic of the optimized design, a prototype of the wireless charging system for mobile robots has been built, including the inverter power supply, the optimized coupling mechanism, rectifier and filter circuit at the receiver side and the load. And the overall efficiency versus variations of transfer distance and horizontal displacement were tested respectively, to ensure the reliability and stability of the charging system. The optimized double-layer coil is shown in Figs. 13(a) and (b), which display layout of the coil and ferrite shielding respectively. And Fig. 14 gives an overview of the experimental platform.

FIG. 13.

Experimental double-layer coil with distributed ferrite shielding: (a) coil side; (b) ferrite side.

FIG. 13.

Experimental double-layer coil with distributed ferrite shielding: (a) coil side; (b) ferrite side.

Close modal
FIG. 14.

Block diagram of the MCR-WPT system for robots.

FIG. 14.

Block diagram of the MCR-WPT system for robots.

Close modal

Both the primary and secondary coil were chosen to be double-layer coil with distributed hollow ferrite shielding as optimized before. Comparisons of coupling coefficient between simulation results and measurement results with horizontal and vertical offsets are shown in Figs. 15(a) and 15(b) respectively. Measurement results are in good agreement with simulations, with experimental measurent errors considered.

FIG. 15.

Comparisons of coupling coefficient between simulation results and measurement results with offsets: (a) comparison versus horizontal offset; (b) comparison versus vertical offset.

FIG. 15.

Comparisons of coupling coefficient between simulation results and measurement results with offsets: (a) comparison versus horizontal offset; (b) comparison versus vertical offset.

Close modal

A proper transfer distance of 10 cm was chosen to verify the optimized system effciency with horizontal and vertical offsets. The experimental parameters are shown in Table III.

TABLE III.

Experimental parameters of the magnetic resonant wireless charging system for robots.

ParametersValuePositive errorNegative error
f (kHz) 58 3.0E-3 -3.0E-3 
P1 (W) 50 1.005 -1.005 
LP(μH) 84.14 0.21 -0.21 
LS(μH) 84.39 0.21 -0.21 
Coil width(mm) 180 0.336 -0.336 
Coil length(mm) 180 0.336 -0.336 
Turns 
Transfer distance(mm) 100 0.32 -0.32 
RL(Ω) 10 0.05 -0.05 
ParametersValuePositive errorNegative error
f (kHz) 58 3.0E-3 -3.0E-3 
P1 (W) 50 1.005 -1.005 
LP(μH) 84.14 0.21 -0.21 
LS(μH) 84.39 0.21 -0.21 
Coil width(mm) 180 0.336 -0.336 
Coil length(mm) 180 0.336 -0.336 
Turns 
Transfer distance(mm) 100 0.32 -0.32 
RL(Ω) 10 0.05 -0.05 

As shown in Fig. 16, the overall efficiency presents to be stable with a horizontal offset ranging from -5 cm to 5 cm, achieving a fine efficiency above 50%, though much lower than simulation results, since there exists considerably high loss in real inverter. As for vertical offset, the efficiency decreases slowly with vertical offset varying from -5 cm to 5 cm, thus any vertical transfer distance between 5cm and 15cm can be chosen according to practical requirements. And Fig. 17 shows the wireless charging robot installed with the optimized MCR-WPT system.

FIG. 16.

Overall efficiency versus horizontal and vertical offset distance respectively.

FIG. 16.

Overall efficiency versus horizontal and vertical offset distance respectively.

Close modal
FIG. 17.

Wireless charging robot after installed with the optimized MCR-WPT system.

FIG. 17.

Wireless charging robot after installed with the optimized MCR-WPT system.

Close modal

Chassis height of the robot is 6.5 cm, and the transmitting coil is buried underground within the charging area. Wireless charging power for the robot battery is about 24 W, namely the PL is 24 W, and the overall efficiency is tested to be 56%, better than charging performance achieved in Ref. 15 with a maximum 7 W power to load with overall efficiency between 20%∼30% at a frequency of 516.5 kHz.

This paper gives a design of wireless charging system for self-charging robots based on magnetic resonance coupling with optimized coil structures and better compensation topology. Specifically, double-layer coil structure has been selected to replace normal single-layer one, and ferrite shielding has gone through the optimization process from block structure to cross hollow one and to the final distributed hollow structure in terms of energy saving, lightness and cost effectiveness. And simulation results illustrated that coil with block ferrite embodied the best offset tolerance but the worst ferrite utilization. Performance and utilization of coil with cross hollow ferrite showed little difference with that of distributed hollow ferrite. Considering practical production, installation, and long-term performance reliability, double-layer coil with distributed ferrite shielding was selected as system coupling coil. Current characteristics of LCL-S and SS compensation topology has been compared and analyzed, and LCL-S was adopted to stabilize the operation of the primary side with varying mutual inductance. The result of prototype experiment showed that the overall efficiency of the designed charging system was higher above 50% within an allowable offset range, with transfer distance 100 mm and transfer power 50 W at a resonant frequency of 58 kHz, which does make sense for the application of magnetic resonance coupling system in power supply for autonomous mobile robots.

This work was supported in part by the National Natural Science Foundation of China under Project of 51707138 and 51507114, and in part by the National Key Research and Development Plan under Project of 2017YFB1201002.

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