Modeling and control of electroadhesion force in DC voltage
© The Author(s) 2017
Received: 9 April 2017
Accepted: 6 June 2017
Published: 14 June 2017
In this paper, a new model for electroadhesion between two surface-insulated plates under DC electric field is presented and control of dynamic responses of electroadhesion force is discussed. Under DC electric field, even if the voltage difference between the plates is constant, electroadhesion force increases or decreases over time depending on the insulating materials. The increase had been explained by Johnsen–Rahbek (JR) model, but the decrease had not been focused or modeled by physically meaningful way. In addition, the previous models did not explicitly consider the mechanical behaviors of the electrodes, although the mechanical behaviors considerably affect the response. In this work, we introduced a new model that combines both electrical and mechanical behaviors. The electrical part, which is based on JR model, explained the force decrease under DC field, in addition to the force increase that had been explained using JR model. The mechanical part was represented by a combination of a spring and a damper. Numerical simulations using the model successfully reproduced characteristics behaviors of electroadhesion force, which include force decay under constant voltages and relatively smaller initial force. Using the inverse model, we carried out experiments to control dynamic responses of electroadhesion force, which successfully controlled force responses against pulse voltages. Through the experiments, we also showed the importance of the neutralization of surface charges for obtaining reproducible responses.
Two surfaces having different electrical potentials stick to each other by electrostatic force, which is called electroadhesion. The electroadhesion has been utilized for various applications. The early application is electrostatic chucks for handling silicon wafers [1, 2] or glass substrates in IC or LCD production lines. Recently, the application areas of the electroadhesion have been expanding to robotics and haptics. In robotics field, researchers have proposed unique applications such as wall/ceiling-attachment for drones , soft grippers , and wall-climbing robots [5–9], as the electroadhesion can be realized with a simpler and lighter devices compared to other adhesion methods [5, 6, 10]. For those robotic applications, inter-digital electrodes have been preferred due to its adhesion capability to dielectric surfaces. The behavior of inter-digital electrodes in the context of electroadhesion has recently been studied extensively [8, 11, 12]. Electroadhesion has also been applied to surface haptic displays [13–18], in which electroadhesion modulates friction on a transparent electrode that covers an LCD surface, to create haptic effects. In those haptic applications, planar electrodes have been preferred, rather than inter-digital electrodes.
In these relatively new application fields, especially in the field of haptics, control of dynamic responses of electroadhesion force is required. To facilitate dynamic response control, an electric model that can describe the internal electric effect needs to be developed. In the conventional electrostatic chucks for wafer handling, electroadhesion force gradually increases under a DC voltage, which is called Johnsen–Rahbek (JR) effect. This JR effect is due to the conductivity of the surface insulators. The resulting electroadhesion force grows considerably large, much larger than typical electrostatic attraction force calculated using the text-book parallel plate model. Watanabe et al. developed an electric model to describe JR effect , which has been extensively utilized in analyzing the conventional electrostatic chucks [20, 21].
On the other hand, studies in the field of haptics reported that their electroadhesion force decreases under a constant DC voltage applications [13, 16, 22]. In those studies, less conductive materials are used as surface insulators, whereas electrostatic chucks intentionally add some conductivity to the insulating materials. To explain the decreases, those studies tried to develop different electric models. However, although those models successfully reproduced the force decrease, they do not explain the electroadhesion phenomena in a physically meaningful way. In addition, electroadhesion often involves mechanical responses of the electrodes. Therefore, electric model alone is not enough; an electro-mechanical combined model is required for dynamic response control.
Although fast and accurate control of electroadhesion force, especially under DC voltages, is imperative in the field of haptics and robotics, it has been a challenging issue, due to the lack of reasonable models. In this paper, we propose an electro-mechanical model for electroadhesion and demonstrate dynamic control of electroadhesion force using the inverse of the proposed model. The electric part of the proposed model is based on JR model. In this work, we have analyzed the JR model developed by Watanabe to show that it can also explain the force decreases observed in haptic studies. One of the reasons that the previous studies failed to model the electroadhesion would be unstable behaviors of electroadhesion device. This paper points out that the unstable behaviors originate in the initial electric charges on the surface of the electroadhesion device. Our experiments have shown that stable behaviors are obtained by removing the initial surface charges. Finally, we have demonstrated that dynamic response of the electroadhesion can be controlled based on the proposed electro-mechanical model.
The structure of this paper is as follows. “Related work” reviews issues on modeling and control of electroadhesion. “Electroadhesion model” introduces an electro-mechanical combined model. “Control of electroadhesion” demonstrates the force control based on the model. “Discussion” denotes limitations of the model and the experiments. “Conclusion” summarizes this paper.
Due to mechanical and electrical responses, the actual generated force changes dynamically. The mechanical response is caused by elastic deformation of asperity in surface roughness  and macroscopic deformation of the electrodes/insulators . In the previous study, the authors showed that the mechanical responses can be compensated by estimating the equivalent gap by using a built-in sensor that measures the capacitance of the paired plates .
The other model is JR model. Since its first report in , the increase of the force has been explained by charge accumulation at the borders of the microscopic air gap. When the dielectrics between the paired electrodes have conductivity, charges are accumulated and held by the gap, resulting to the force increase. This model is expressed as the equivalent circuit in Fig. 1b [19–21], which consists of an air-gap and conductive dielectric layers. The air gap is also assumed to have conductivity corresponding to the contact resistance. By calculating the adhesion force from the voltage across the air gap, the model can explain the force increase. However, our observations in our previous studies indicated that the responses of electroadhesion force cannot be perfectly explained with these electrical models alone; mechanical behavior needs to be taken into account.
In this work, we propose an electro-mechanical model for electroadhesion, with a special focus on force decreasing type. Although, the previous studies have tried to explain the force decrease by the leakage model, this work adopts JR model as it has better physical background.
Based on the assumption, this work models the electroadhesion mechanism as a bilayer dielectric with electric loss as shown in Fig 2b. The two insulators on actual setups are summarized into one insulating layer in this model for simplification. The model shares the same concept with the JR model developed by Watanabe . However, our model includes the mechanical aspect represented by the spring (spring constant: k) and the damper (damping constant: c), as shown in Fig 2b. To facilitate the combination with the mechanical aspect, our model focuses on electric field, E, whereas Watanabe’s JR model focuses on voltages.
Numerical simulation with mechanical response
In the actual systems, the air gap between the two plates fluctuates due to microscopic and/or macroscopic deformation of the electrodes. If the electroadhesion force changes rapidly, air damping by squeeze effect would also affect. In the proposed model, those gap variation is represented by the spring and the damper. The electroadhesion force compresses the air gap supported by the spring and the damper, and changes the air gap length, \(d_2\), in the model.
Control of electroadhesion
In preliminary measurements, we found that the responses of the electroadhesion force was not stable. This would be due to the initial surface charges, as explained in the model. To obtain reproducible results, the initial charges must be neutralized before the experiments.
In these results, protocol (d) showed larger friction force than other protocols. This would be probably because ethanol affected the surface treatment of the film. This suggests that the use of ethanol should be minimized to prevent surface damage.
Control of dynamic response
In plots (a) and (b), the force decay that appeared in PP model was successfully compensated by using the proposed model. As shown in plot (c), PP model showed residual force after cutting off the voltage. On the other hand, in the proposed model, the voltage was not totally cut but was kept at some small value, which resulted in zero residual force. In plot (d), responses against polarity-alternating pulses are shown. Although the proposed model showed far improved responses compared to the conventional PP model, the response against the negative pulse showed some deviation. This would be because the model parameters (\(\sigma _i\)) were identified for a positive voltage. For better force control, a better parameter identification method needs to be investigated.
The model proposed in this paper did not consider the relative motion of the electrodes, although the electrodes were moving during the experiments. In , it has been reported that the electrode motion affected the adhesion force. Since their electrodes were inter-digital electrodes, their results cannot immediately apply to our system. However, their results suggest that the adhesion force would change also in our system. In our system, if the electrodes relatively move, the charges at their interface, \(\sigma _f\), would virtually reduce, as the facing areas will be continuously changing. In other words, the charges accumulated on the stage surface will be left behind as the pad moves. The newly facing part does not have accumulated charge, which virtually decreases the interface charge, \(\sigma _f\).
In the experiments of this work, this effect was negligible, as the parameter identification and control experiments were all carried out at the same speed. However, to cope with various motion speeds, the model needs some modifications such that it can account for the virtual charge decrease due to the relative motions.
The voltages used in the experiments were limited to ±500 V, and most of the measurements were carried out at around 300–400 V. This voltage range is typical (or slightly higher) for haptic applications. For robotic applications, however, much higher voltages, such as several kilo volts, are often utilized. It has been experimentally shown that the electroadhesion force does not follow the square relationship in such a higher voltage range . Therefore, it should be verified in future work if the proposed model is valid in higher voltage ranges.
It has also been known that humidity affects the performance of electroadhesion [28, 29]. This would be because the humidity affects the conductivity of the air gap (and the surface insulator). In the proposed model, if we assume very high conductivity for the air gap, the resulting electroadhesion force vanishes instantly, which corresponds to the observation in . Such an aspect of the proposed model also needs to be further investigated in future work.
This paper proposed an electro-mechanical combined model for electroadhesion, which consists of an insulator and an air gap, and realized electroadhesion force control in DC voltage, which was found difficult in the previous studies. The electrical part of the model is based on the JR model, in which interface charges accumulate under a DC voltage. By considering the sign of the surface charges, the model can explain force decrease, which has been observed in haptic device applications. The mechanical part simulates fluctuation of the air gap, which affects the dynamic response, since the force magnitude and the time constant depend on the gap. The numerical simulations using the combined model successfully reproduced the characteristic behaviors of electroadhesion force. It was also shown that the initial response of the electroadhesion force can be reproduced only when mechanical part is actively involved. Using the inverse of the proposed model, as well as a built-in capacitive-type gap sensor, experiments to control dynamic force response were carried out. The experimental results verified that the proposed method can suppress errors due to characteristic behaviors of electroadhesion. This work also revealed the importance of surface-charge neutralization for reproducible responses of electroadhesion. These knowledges would contribute to better understanding and controlling of electroadhesion systems, especially for haptic and robotic applications.
TN contributed to the modeling, analysis, experiments, and drafting of the manuscript. AY took part in the modeling, interpretation of data, and revising of the manuscript. Both authors read and approved the final manuscript.
Both authors declare that they have no competing interests.
Availability of data and materials
The datasets supporting the conclusions of this article are included within the article.
This work was supported in part by Grant-in-Aid for JSPS Fellows (No. 269272) and Grand-in-Aid for Scientific Research (B) (No. 26280069) from JSPS, Japan.
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